masterproef_master_banking_and_finance_nicolas_dierick_pieterjan_tilleman

UNIVERSITY GHENT

FACULTY OF ECONOMICS AND BUSINESS ADMINISTRATION

ACADEMIC YEAR 2014 – 2015

THE RISK OF CTAs: HIGHER PROFITABILITY IN TIMES OF

CRISIS?

Masterdissertation submitted in fulfilment of the requirements for the degree of Master of Science in Banking and Finance

Nicolas Dierick Pieterjan Tilleman

Under supervision of

Prof. Dr. Michael Frömmel, University Ghent

Dr. Alexander Mende, RPM Risk and Portfolio Management AB

Abstract

This study investigates the ability of commodity trading advisors (CTAs), commonly

associated with managed futures, to provide investors with important diversification

benefits in times of crisis. By developing a systematic identification methodology and

employing a unique dataset, we show that managed futures do acquire positive gains in

most sector crises, stemming from two sources. Firstly, the asset class is diversified across

multiple futures markets. As a result, positive yields in other markets are able to

counterbalance the lacking performance in the crisis sector. Secondly, the downward

adjustment of managed futures exposure to their focus market allows them to put a halt

to the fall in their sector performance.

The authors would like to acknowledge that this work could not have been possible without

the contribution of others. We would like to express our sincere gratitude to Prof. Michael

Frömmel of Ghent University and Dr. Alexander Mende of RPM Risk and Portfolio

Management AB, for their guidance throughout this graduation project. We would also like

to thank RPM Risk and Portfolio Management AB for providing the resources to complete

our graduation project.

Any expressed opinions are not to be interpreted as anybody’s but the authors. All

remaining errors lie with the authors only.

I

Table of Contents

1 Introduction .................................................................................................................................................. 1

2 Literature Review ....................................................................................................................................... 5

3 Methodology .............................................................................................................................................. 17

3.1 Crisis Identification ........................................................................................................................................ 17 3.2 CTA Crisis Alpha .............................................................................................................................................. 20

4 Data ................................................................................................................................................................ 27

4.1 Crisis Identification ........................................................................................................................................ 27 4.2 CTA Crisis Alpha .............................................................................................................................................. 27

5 Empirical Results ..................................................................................................................................... 29

5.1 Crisis Identification ........................................................................................................................................ 29 5.2 CTA Crisis Alpha .............................................................................................................................................. 31 5.2.1 Aggregate CTA Performance Analysis ........................................................................................... 31 5.2.2 Sector Specific CTA Performance Analysis ................................................................................. 34 5.2.3 Managed Futures Dynamics in a Crisis Regime ........................................................................ 36

6 Robustness Tests ..................................................................................................................................... 41

7 Conclusion .................................................................................................................................................. 45

8 References: ................................................................................................................................................. 47

9 Appendix ..................................................................................................................................................... 53

9.1 Tables ................................................................................................................................................................... 53 9.2 Figures ................................................................................................................................................................. 81 9.3 MATLAB Code Crisis Identification Methodology ............................................................................ 90

II

List of Abbreviations

Aggr Aggregate AMH Adaptive Market Hypothesis BMA Bear Market Algorithm BTOP Barclays Top performing Index CMA Crisis Market Algorithm Comm. Agr Commodities Agriculture Comm. Energy Commodities Energy Comm. Metals Commodities Metals CTA Commodity Trading Advisor D Crisis Dummy Variable EMH Efficient Market Hypothesis EMS European Monetary System ERM Exchange Rate Mechanism FI Fixed Income GARCH Generalized AutoRegressive Conditional Heteroscedasticity HM Henriksson and Merton model IF Intensity Factor IF-‐adj Volatility adjusted Intensity Factor LPM Linear Probability Model LTCM Long Term Capital Management MDI Market Divergence Index MS Markov Switching NCTA Newedge CTA (Commodity Trading Advisor) OLS Ordinary Least Squares PTFS Primitive Trend-‐Following Strategy RPM Risk and Portfolio Management AB SBC Schwarz Bayesian Criterion TF Trend-‐Following TM Treynor and Mazuy model TW USD Trade-‐Weighted US Dollar VIX CBOE (Chicago Board Options Exchange) Volatility Index

III

List of Tables

Table 1: Data Crisis Identification Methodology ..................................................................... 53

Table 2: Summary Statistics ..................................................................................................... 53

Table 3: Employed Parameters ................................................................................................ 54

Table 4: Summary Statistics ..................................................................................................... 54

Table 5: Matching Contextual and CMA Stock Market Crises ................................................. 55

Table 6: Overlapping Crises ..................................................................................................... 56

Table 7: Granger Causality Test P-‐Values ................................................................................ 56

Table 8: Aggregate CTA Regime Dependent Returns .............................................................. 57

Table 9: Regime Dependent Correlations ................................................................................ 57

Table 10: Aggregate CTA HM Model ....................................................................................... 58

Table 11: Sector Regime Dependent Performance ................................................................. 59

Table 12: Equity and Fixed Income Sector HM Model ............................................................. 60

Table 13: Soft and Energy Commodities Sector HM Model .................................................... 61

Table 14: Commodity Metals and Currencies Sector HM Model ............................................ 62

Table 15: HM Model Aggregate Robustness to Alternative CTA Index ................................... 63

Table 16: HM Model Aggregate Robustness to Daniel and Moskowitz (2013) Bear Market

Identification ................................................................................................................... 64

Table 17: HM Model Aggregate Robustness to BMA Indicator ............................................... 65

Table 18: HM Model Aggregate Robustness to Chen and Liang (2007) Indicator ................... 66

Table 19: HM Model Aggregate Robustness to the Exclusion of the Credit Crunch ............... 67

IV

Table 20: HM Model Sectorial Robustness of Equity and Fixed Income Sectors to Daniel and

Moskowitz (2013) Bear Market Identification ................................................................. 68

Table 21: HM Model Sectorial Robustness of Soft Commodities and Commodities Energy

Sectors to Daniel and Moskowitz (2013) Bear Market Identification .............................. 69

Table 22: HM Model Sectorial Robustness of Commodities Metals and Composite Currencies

Sectors to Daniel and Moskowitz (2013) Bear Market Identification .............................. 70

Table 23: HM Model Sectorial Robustness of Equity and Fixed Income Sectors to BMA

Indicator .......................................................................................................................... 71


Sectors to BMA Indicator ................................................................................................. 72


Sectors to BMA Indicator ................................................................................................. 73

Table 26: HM Model Sectorial Robustness of Equity and Fixed Income Sectors to Chen and

Liang (2007) Indicator ...................................................................................................... 74


Sectors to Chen and Liang (2007) Indicator ..................................................................... 75


Sectors to Chen and Liang (2007) Indicator ..................................................................... 76

Table 29: HM Model Sectorial Robustness of Equity and Fixed Income Sectors to the

Exclusion of the Credit Crunch ........................................................................................ 77


Sectors to the Exclusion of the Credit Crunch ................................................................. 78


Sectors to the Exclusion of the Credit Crunch ................................................................. 79

V

List of Figures

Figure 1: Average Monthly Return of CTAs in Five Equity Market Regimes ............................ 81

Figure 2: Equity Market Crisis and Bear Market Identification ................................................ 81

Figure 3: Fixed Income Market Crisis and Bear Market Identification .................................... 81

Figure 4: Commodities Agriculture Market Crisis and Bear Market Identification .................. 82

Figure 5: Commodities Energy Market Crisis and Bear Market Identification ........................ 82

Figure 6: Commodities Metals Market Crisis and Bear Market Identification ........................ 82

Figure 7: Trade-‐Weighted USD Market Crisis and Bear Market Identification ........................ 83

Figure 8: Overlapping Crisis Periods ........................................................................................ 83

Figure 9: CTA’s Time-‐Varying Equity Market Risk Factor Exposures ....................................... 83

Figure 10: Managed Futures Dynamics in an Equity Market Crisis ......................................... 84

Figure 11: Managed Futures Dynamics in a Fixed Income Market Crisis ................................ 85

Figure 12: Managed Futures Dynamics in a Commodity Agriculture Market Crisis ................ 86

Figure 13: Managed Futures Dynamics in a Commodity Energy Market Crisis ....................... 87

Figure 14: Managed Futures Dynamics in a Commodity Metals Market Crisis ....................... 88

Figure 15: Managed Futures Dynamics in a Trade-‐Weighted USD Market Crisis .................... 89

1

1 Introduction

Most investment strategies are susceptible to suffering devastating losses during an equity

market crisis. Given this, for almost any investor, the key to finding true diversification is in

finding an investment that is able to deliver performance during these turbulent periods.

(Greyserman and Kaminski, 2014 p 72)

Quite recently, managed futures have gained renewed attention, due to their outstanding

performance during the past global financial crisis. Managed futures have therefore been

highlighted as an investment vehicle providing important hedging capabilities in downturn

markets. Certain authors, such as Kaminski (2011a) and Tee (2012), have stressed

Commodity Trading Advisors’ (CTAs) ability to provide investors with “crisis alpha”. In

particular, the capability to deliver significant returns during the great plummet in financial

markets of 2008, and the downfall of a number of large hedge funds, was argued to be one

of the main reasons why CTAs have undergone massive inflows in 2010 (Tee, 2012).

The potential of CTAs during downturn markets is not new in the academic literature. Fung

and Hsieh (1997) showed that their returns exhibit a non-‐linear relationship with global

equity markets. Figure 1 reproduces this graph with updated data and several managed

futures indices. More specifically, we divide monthly MSCI World returns in five quintiles, and

calculate the average monthly CTA return in each market regime between late 2000 and the

beginning of 2015. This regime-‐dependent performance pattern clearly illustrates the

dynamic nature of managed futures. A static capital asset-‐pricing model would provide a

poor approximation, because this initial anecdotal evidence stipulates positive equity market

betas in up trends, and negative ones during a severe downturn.

The stability of CTAs during times of general market distress remains an empirical question

that requires additional attention. This study addresses this by investigating the performance

of managed futures during past financial crises. Our research does not restrict itself to the

former global financial crisis of 2007-‐2008, but also incorporates previous ones such as the

Dot Com crash at the beginning of the millennium. In order to explore this, we first develop a

systematic methodology to detect crisis periods inspired by the dating algorithm of Lunde

and Timmerman (2004). Subsequently, we analyze CTAs’ performance in the identified time

2

periods and their potential higher profitability, by drawing upon the market timing literature.

We conclude our empirical investigation by exploring the sector dynamics of managed

futures in their respective crisis regimes.

We add to the existing literature on managed futures in two ways. Firstly, our systematic

crisis identification methodology, and its incorporation within the confines of market timing

models, allows to more accurately address the potential higher profitability of CTAs in crisis

regimes. Through this procedure we emphasize the important characteristic of managed

futures as trend-‐followers, exploiting profitable directional movements in financial markets

during strained market regimes dominated by lower liquidity and behavioral biases.

Secondly, we employ a unique dataset provided by RPM Risk and Portfolio Management AB,

a private market player specializing in portfolio management for directional alternative

Investments. This dataset contains aggregate and trend-‐following indices on the real

performance of CTAs from the times of investments. For this reason, it remains

uncontaminated by well-‐known reporting biases that plague many of the alternative asset

class databases. In addition, the dataset contains information on how managed futures

position in different sectors, such that we gain insight into the behavior of this asset class,

when confronted with this particular market regime.

Our results provide evidence that the managed futures industry in aggregate is able to

deliver positive returns, when most sectors are in crisis. These gains are the result of two

sources. CTAs are players active in multiple sectors: equity, fixed income, commodities and

foreign exchange rates. It goes without saying that this diversified orientation allows them to

acquire profits in other sectors, despite another being in a crisis. However, their capability to

go both long and short permits them to also adjust their sector positioning downwards. For

this reason, a second source of positive returns originates from their capability to prevent

consistent losses in the plummeting sector. In prolonged crises short positions may even lead

to sector gains overcoming their initial losses resulting from a long bias at the onset of a

crisis.

The remainder of this paper is structured as follows. Section two summarizes the literature

on managed futures and discusses the systematic methodologies that may be applied to date

crises. Section three sets out our empirical methodology to systematically identify crisis

3

regimes, and its incorporation in market timing models. Section four describes our unique

dataset provided by RPM Risk and Portfolio Management AB, and its difference from the

standard databases employed within the alternative investment literature. Section five

presents our empirical results, followed by a series of robustness checks in section six. The

final section of this study concludes.

5

2 Literature Review

Managed futures are generally classified as a component of the alternative asset class

universe. Kaminski (2011a) defined managed futures in a very appealing manner:

Managed Futures, commonly associated with Commodity Trading Advisors (CTAs), is a

subclass of alternative investment strategies which take positions and trade primarily in

futures markets. Using futures contracts and sometimes options on futures contracts, they

follow directional strategies in a wide range of asset classes including fixed income,

currencies, equity indices, soft commodities, energy and metals.

(Kaminski, 2011a p 2)

They are often considered a part of the hedge fund industry. This is the consequence of a

number of shared characteristics such as the low level of government regulation, the

investment class’ fee structure, and the use of leverage and complex financial instruments

(Liang, 2004 and Kazemi and Li, 2009). In spite of this, a number of fundamental disparities

form the basis for the differential risk-‐return profile, between pure hedge funds and CTAs.

Liang (2004) emphasized that CTAs are mostly trend-‐following strategies, active within

commodity and financial futures markets. In contrast, hedge funds are active in a broader

variety of financial markets and use different financial instruments. They are thus exposed to

different types of risk factors. Hedge funds are often regarded as being subject to illiquidity

and credit risk. This is however less applicable to CTAs that trade in highly liquid and credit

protected futures markets (Kaminski and Mende, 2011). For instance, Liang (2004) found that

hedge funds underperformed during market regimes when liquidity was eroded. Kazemi and

Li (2009) showed that CTA performance has more difficulty being explained by standard

factor models, in contrast to hedge fund’s returns. The trend-‐following nature of managed

futures results in their return structure being better approximated by the primitive trend-‐

following strategy (PTFS) factors of Fung and Hsieh (2001). Moreover, CTAs exhibit low

correlations with hedge funds or funds-‐of-‐funds (Liang, 2004). The literature review will

therefore solely focus on managed futures as a separate component of the alternative

investment industry.

6

CTAs have also come to be classified in the academic literature as trend-‐followers (Fung and

Hsieh, 2001). This may be attributed to their directional orientation. Surveys have indicated

that most of the industry does identify as trend-‐followers (Waksman, 2000). The use of

trend-‐following techniques may have a systematic or a discretionary nature. The former

refers to managed futures using technical models, oriented towards exploiting price trends,

while the latter involves an additional degree of discretionary judgment in the investment

process (Kazemi and Li, 2009).

The literature on the investment characteristics of managed futures has seen quite some

evolution over the past 35 years. The first studies on managed futures date back to the 80s.

In his seminal paper, Lintner (1983) highlighted the potential benefits that could be acquired

from adding managed futures to a standard portfolio of stocks and bonds. This alternative

asset class represented some attractive features, such as their low correlations with

traditional asset classes. However, later studies on public commodity funds casted doubt

upon how appealing managed futures may truly be, for they appeared unable to earn returns

above the risk-‐free rate (Elton, Gruber and Rentzler, 1987/1990 and Irwin, Krukemyer and

Zulauf, 1993).

Tee (2012) warned that some of the earlier studies could possibly suffer from limited data

availability at the time. Subsequent studies employing a larger dataset verified a number of

the earlier studies’ findings. Edward and Liew (1999) reaffirmed CTAs’ lower performance

and their interesting correlation structure. There may however be some variation in

managed futures’ documented return profile. For example, CTAs performed worse between

1989 and 1996 (Edward and Liew, 1999). Gregoriou, Hübner and Kooli (2010) noted that the

performance was much higher when a broader time period was considered (i.e. 1980 to

2005). Tee (2012) proposed that such variation might stem from a lack of profitable trends

within CTAs’ focus market during particular time periods. Some variation may also be the

result of a difference in applied trading systems. Brorsen and Towsend (1998) found -‐

although with smaller performance -‐ that CTAs using short-‐term trading systems, had returns

about one-‐fourth less than CTAs using medium-‐ or long-‐term systems, and supported the use

of longer time series when selecting funds.

7

The potential lower returns of managed futures respective to traditional asset classes may

not necessarily seem unreasonable. Schneeweis and Spurgin (1998) argued that CTAs are

mostly active within futures markets that, from a theoretical perspective, should be a zero-‐

sum game, earning the riskless rate of return. Nevertheless, managed futures still offer a

positive risk-‐adjusted performance that may be a compensation for bearing certain risk

factor exposures (Schneeweis and Spurgin, 1998). One appealing proposition relates to the

potential higher profitability of momentum strategies within lower transaction cost and

higher leveraged futures markets. In particular, the concept of time series momentum may

be quite in line with the trend-‐following behavior of the CTA industry. A survey conducted by

Wakman (2000) showed that 95% of all trend-‐following managed futures did employ

momentum related signals in the investment process. Moskowitz, Ooi and Pedersen (2012)

found evidence of time series momentum in different futures markets (i.e. equity index,

currency, commodity and bond futures). Hurst, Ooi and Pedersen (2013) showed that these

time series momentum strategies with different look-‐back horizons (1, 3 and 12 months)

have explanatory power for CTA returns.

Nevertheless, most authors have always agreed upon the potential diversification benefits

that managed futures may bring to the fold. The lack of correlation with traditional

investments, such as bonds and equities, allows managed futures to improve the risk-‐return

profile of a standard portfolio. In comparison to other alternative asset classes, some have

even stressed that commodity funds offer better downside risk protection than traditional

hedge funds (Lintner, 1983; Oberuc, 1992; Edwards and Liew, 1999; Kat, 2002; Jensen,

Johnson and Mercer, 2003; Edwards and Caglayan, 2001). Liang (2004) documented that

CTAs’ attrition rates are higher on average than hedge funds and funds-‐of-‐funds, but

decrease during downturn markets. The difference lies in the risks factors to which all are

exposed, as hedge funds shall be long biased towards equity markets, and shall fall to the

emergence of liquidity strains (Kaminski, 2011a; Liang, 2004). Fung and Hsieh (2001) and

Liang (2004) documented a non-‐linear relationship between managed futures’ and equity

market returns, which reflects a conditional return pattern similar to those of options. Criton

and Scaillet (2011) employed a static and a time-‐varying coefficient model, to investigate the

dynamic performance of CTAs for data between 1994 and 2007, and reported significant

differences between the two. Managed futures were able to deliver significant alphas during

8

the LTCM and Russian crisis, and the equity bubble crisis of 2001. The majority of CTAs under

their investigation have a relatively stable exposure to credit and emerging market risk

factors, as opposed to other hedge funds. Kaminski (2011a) and Kaminski and Mende (2011)

examined a number of equity crises and documented increasing performance during these

timespans. Finally, Hurst, Ooi and Pedersen (2013) argued that their time series momentum

strategies, which were able to explain managed futures’ returns, also performed the best in

strong up and down markets.

It should be emphasized that managed futures are not the same as tail risk insurance.

Kaminski (2011a) argued the Fung and Hsieh’s (2001) performance pattern to be similar to an

equity straddle option. CTAs acquire profits during severe downturns, but also in strong bull

markets. The difference between tail risk insurance and “crisis alpha” is thus that the latter

would solely provide a payoff in a crisis period, while managed futures are also able to

achieve stable returns in normal times such as market regime 4 of figure 1 (Kaminski, 2011b).

This is also consistent with the aforementioned findings from Hurst, Ooi and Pedersen

(2013).

This begs the question: why should managed futures be able to provide higher performance

during periods of overall market turmoil? Greyserman and Kaminski (2014) provided a

theoretical reasoning based upon the Adaptive Market Hypothesis (AMH) of Andrew Lo

(2004), to explain why (systematic) trend-‐following strategies via managed futures are able

to provide attractive returns during financial crises. The AMH tries to reconcile two views

within the domain of finance from an evolutionary perspective: the Efficient Market

Hypothesis (EMH) and concepts from Behavioral Finance. Within this context, the market is a

dynamic organism that is not always fully efficient. In an irregular environment, such as a

financial crisis, market efficiency may in fact break down and the impact of behavioral biases

on market participants may be considerably elevated. In such turbulent times, the presence

of herd behavior may start to dominate sufficiently for persistent trends to emerge,

providing trend-‐followers with the ideal opportunity to spread their wings. The systematic

trading strategy of many CTAs will leave them less affected by the aforementioned

behavioral biases. As active participants within futures markets, which retain a sufficient

degree of liquidity, they are able to adapt to the manifestation of exploitable profit

opportunities. From a similar perspective, Hurst, Ooi and Pedersen (2013) accredit the

9

profitability of time series momentum strategies to initial under-‐reaction and delayed over-‐

reaction in financial markets. These anomalies are the consequence of many well-‐known

behavioral biases, such as the disposition effect and herd behavior.

A related strand of literature has analyzed the performance of managed futures by

examining whether they exhibit market timing ability. Market timing refers to the ability of

portfolio managers to enter (leave) the market during upward (downward) trending markets.

Fung and Hsieh (2001) reasoned that market timing and trend following are quite alike. A

market timer would be able to provide a payoff resembling that of a primitive trend-‐

following strategy, where the latter’s payoff can be captured by a lookback straddle option.1

Tee (2012) also stressed that trend-‐followers and market timers are related. As a

consequence of this similarity, and the general consensus within the literature that managed

futures are trend-‐followers, this type of literature can provide interesting insights into the

ability of CTAs to deliver “crisis alpha”.

One may distinguish between two approaches to examine market timing ability: a portfolio-‐

based and a return-‐based method. The former focuses on the change in portfolio

composition, in order to determine a change in portfolio holdings before a particular market

regime. Despite the self-‐evident nature of the portfolio composition technique, the academic

literature on market timing has been dominated by the return-‐based methodology, where

the Treynor-‐Mazuy (1966) and Henriksson-‐Merton (1981) models reign supreme, as portfolio

composition data is often unavailable (Frömmel, 2013). These market timing models may be

considered an extension of standard factor models, which try to explain the variation in

excess portfolio returns by attributing them to specific factor exposures.2 The TM version

postulates a linear relationship between a portfolio’s market beta and the expected market

return. The HM model is more restrictive, distinguishing between positive and negative

excess market return regimes, by means of a differential market beta coefficient. Both

1 Fung and Hsieh (2001, p 316) define a lookback straddle option as follows: “The owner of a lookback call option has the right to buy the underlying asset at the lowest price over the life of the option. Similarly, a lookback put option allows the owner to sell at the highest price. The combination of these two options is the lookback straddle, which delivers the ex-‐post maximum payout of any trend-‐following strategy.” 2 Note that Fung and Hsieh (2001) have documented the low explanatory power of most standard factors models when applied to CTA excess returns. Instead, the authors advocate the usage of primitive trend-‐following strategy (PTFS) risk factors, which are constructed from the payoff of a portfolio of lookback straddle options.

10

designs have furthermore formed the basis for extensions that allow for volatility timing

(Busse, 1999) and market timing in multiple markets (Aragon, 2007).

With data between 1994 and 2002, Chen (2007) analyzed whether managed futures do have

market timing ability in their predefined focus markets (i.e. U.S. and non-‐U.S. bonds, foreign

exchange and commodity sectors). The results indicated that CTAs are able to time the non-‐

U.S. bond and currency markets. In other words, a significant increase in focus market

exposure was found during regimes of positive excess sector return. Chen and Liang (2007)

confirmed the market and volatility timing ability of self-‐declared market timing hedge funds

(including managed futures). The authors furthermore documented a stronger timing ability

during bear market regimes. Kazemi and Li (2009) examined the difference in market timing

ability for both systematic and discretionary CTAs to conclude that the latter seems less

suitable for the different timing models. They confirmed the former market and volatility

timing results of Chen and Liang (2007) for data between 1994 and 2004. Moreover, sector

specific managed futures only possessed timing ability in their focus market, similar to the

findings of Chen (2007), but diversified CTAs had multi-‐market timing ability. Finally, Elaut,

Frömmel and Mende (2014) altered the HM model definition of market timing by dividing the

CTAs’ focus markets between bull and bear regimes. This definition conforms to the general

consensus that managed futures represent trend-‐followers, as opposed to market timers

forecasting whether or not the return within a particular market shall be positive the

subsequent day, month or year. Subsequently, the authors analyzed managed futures’ ability

to time the different market states from 1994 to 2012 and found a statistically significant

increase in exposure to the different sectors throughout the bull market cycles.

The previous paragraph on managed futures’ market timing ability sheds some light on the

ability of CTAs to perform during crisis periods. Firstly, the academic evidence indicates a

dynamic adjustment of risk exposures to specific market regimes. This reflects consistency

with Greyserman and Kaminski’s (2014) notion that during periods of market turmoil,

managed futures may be able to adapt to the altered environment, as futures markets retain

their liquidity, and systematic trading rules prevent managers from being severely affected

by behavioral biases. Second, most of the previously discussed studies have focused on the

more traditional implementation of market timing models and the change in exposure during

upturn markets. Few of them have truly attempted to systematically identify crisis periods

11

and subsequently investigate the characteristics of CTAs during these specific market

regimes, despite the overall consensus on the diversification benefits they may bring to the

table.

Given the lack of most past literature to systematically identify crises, and as a way of

introducing the first component of this study’s applied methodology, it is worth discussing

the general literature on crisis identification. Most studies restrict themselves by focusing on

defining a bear market instead of crises. For instance, in the financial press a bear (bull)

market is commonly defined by a fall (rise) in the market greater than 20 or 25% (Pagan and

Sossounov, 2003). Liang (2004) and Chen and Liang (2007) determined a bear market regime

when the excess market return is positive. Daniel and Moskowitz (2013) employed an ex ante

bear market indicator that equals 1 if the cumulative return over the past 24 months is below

0.

Others have concentrated on identifying crises. Greyserman and Kaminski (2014) discussed a

number of possible approaches such as the use of the market divergence index (MDI). It is a

simple aggregate measure of “trendiness” in prices. It takes into account the signal to noise

ratio, or the level of volatility in the price series. Larger levels of divergence characterize

crises. This threshold is rather subjective in nature because changes in volatility and market

divergence are interrelated. As a substitute, the detection of crises can be done by using the

VIX index that plots extreme volatility changes. A second method may be to identify a crisis

month as any month with a move in the VIX greater than 20% at the end of the last month

(Greyserman and Kaminski, 2014). Alternatively, the authors suggested selecting sector

specific crises as those months when the index return is lower than a specific threshold,

which is based on a function of the rolling past average return and standard deviation for

consistency across the asset classes. In other words, a crisis month is detected when each

corresponding index is below its rolling five-‐year mean and two times its standard deviation.

Li and Liaw (2014) analyzed stock indices at one-‐minute intervals during the global financial

crisis between September 2008 and June 2009. They analyzed categorized stock indices in

three stages according to the change in stock prices: a plunging stage (stage 1) during which

the increments of the daily stock price are always large negative values, a fluctuating or

rebounding stage (stage 2) when the increments are near zero or positive, and a soaring

stage (stage 3) when the increments are mostly positive and large. Mishkin and White (2002)

12

investigated stock market crises based upon similarities with the commonly accepted Great

Depression and Black Monday stock market crash.

The aforementioned methods tend to be rather arbitrary with regards to the chosen

threshold values or do not apply a systematic methodology. However, the academic

literature has also proposed two systematic approaches. The parametric Markov-‐Switching

(MS) models divide the stock market in two different regimes. The bull market represents a

regime of high and stable returns, contrasting the volatile low-‐return bear market (Maheu

and McCurdy, 2000). Maheu, McCurdy and Song (2012) expanded the two-‐regime MS model

to a four regime one, which allows for richer and more heterogeneous intra-‐regime

dynamics. Frömmel (2010) extended this approach to detect volatility regimes via a GARCH

MS model, and Antonakakis and Scharler (2012) allowed for three different regimes of low,

medium and high volatility, where a crash tends to be preceded by the high volatility regime.

The nonparametric approaches include filter rules or dating algorithms that locate turning

points (i.e. peaks and troughs) within a time series. In the early 70s, Bry and Boschan (1971)

developed such a dating-‐algorithm that determined cyclical turning points. Their program

allowed making the distinction between expansions and contractions in individual economic

time series. The methodology encompassed the identification of initial turning points in

smoothed curves, which were subsequently matched with turning points in the actual data.

At each point in the program, the identified cycles are subjected to a variety of restrictions

such as the proper alteration between peaks and troughs, and a minimal duration of each

cycle. Pagan and Sossounov (2003) adapted the Bry-‐Boschan algorithm to identify similar

cycles within stock markets. In other words, their adaptation of the program allowed them to

date bear and bull equity regimes. Because the original algorithm employed smoothed

curves that might suppress important movements, the authors accounted for cycles within

the actual data only. Pagan and Sossounov (2003) also broadened the window to identify

local troughs and peaks within the data, increased the minimum duration of a full bear-‐bull

cycle to 16 months and decreased the minimum duration that one must find itself within a

specific market state to 4 months.

The adapted version of the Bry-‐Boschan program provides an interesting methodology to

identify bull and bear markets states within a time series. Nevertheless, it may be less suited

13

as a detection methodology for crises, due to their difference with a bear market state. For

example Sperandeo (1990, p 102) defined a bear market as: A long-‐term downtrend

characterized by lower intermediate lows interrupted by lower intermediate highs. In

contrast, Aboura (2015, p 2) argued that a stock market crash may be defined differently: … a

new definition of stock market crash that is risk-‐management oriented; … stock market crash

is defined as being sudden, significant and brief.3 As a consequence, the difference between a

crisis period and a bear market may lie with the time period over which the market falls, such

that a crisis need not necessarily reflect a longer-‐term downward trend in the sector. For

instance, the stock market crash on October 19 1987, more commonly known as Black

Monday, represented a severe plunge in the stock market during October. However, the

Pagan and Sossounov (2003) adapted version of the Bry-‐Boschan algorithm requires each

market phase to last at least 4 months from peak to trough. This implies that Black Monday

may not necessarily be detected. Other more short-‐lived crises, such as LTCM in ‘98 and the

more recent Flash Crash, may similarly remain undetected.

In contrast to the Pagan and Sossounev (2003) methodology, Lunde and Timmerman (2004)

developed a bull-‐bear market filter that does not impose the aforementioned restriction on

the phase length of a cycle. This approach encompasses the identification of a bull (bear)

market ex-‐post by analyzing whether the market has risen (fallen) sufficiently since the

former trough (peak) value. If the threshold value is exceeded, the program retroactively

identifies the regime as a bull (bear) state since the most recent trough (peak) value.

While the choice of the phase length represents the main problem for Pagan and Sossounov

(2003), the required choice of threshold values forms the main downfall of the Lunde and

Timmerman (2004) filter (Elaut, Frömmel and Mende, 2014). The authors proposed

parameters for the stock market that were motivated by readings in the financial press. More

specifically, they proposed that a transition from a bull to a bear market requires the equity

index to fall by at least 10 or 15% since its former local peak, and a subsequent rebound from

its trough by 15 or 20% would lead to a reversal back to a bull market. Lower parameter

values lead to the identification of more periods that may simply represent non-‐significant

3 However, the last definition understands brief as a one day timeframe, which is oriented towards a risk management view (i.e. after one day one may be able to hedge the position) (Aboura, 2015). Thus this ‘briefness’ definition may not be optimal within the present study.

14

short-‐term dynamics. Despite the proposals of Lunde and Timmerman (2004), there are no

clear-‐cut values for other asset classes such as fixed income or foreign exchange markets.

Elaut, Frömmel and Mende (2014) proposed to determine the threshold values by iteratively

identifying possible trends within the data, and saving their magnitudes.4 In spite of this

progress, the parameters remain oriented towards determining bear markets and not crises.

To conclude the literature review, it is necessary to stress that research on CTA performance

often has to deal with a number of important reporting biases present in most databases. As

previously discussed, managed futures are often characterized as a part of the hedge fund

industry. This asset class’ databases may not necessarily provide an accurate overview of the

entire industry (Fung and Hsieh, 2002). Firstly, selection bias results from the fact that

inclusion within hedge fund databases is voluntary, possibly leading to the non-‐inclusion of

funds that have delivered poor performance in the past (Bhardwaj, Gorton and Rouwenhorst,

2008). Survivorship bias arises when one only analyzes the performance of managed futures

that haven’t folded. Once more this may lead to an upward bias in CTAs’ performance. Fung

and Hsieh (2000) analyzed the performance characteristics of managed futures, and

estimated that the probability of a fund to drop out fluctuates around 19% per year. This

figure is very high compared to the 5% for mutual funds between 1989 and 1995. As a

consequence, the survivorship bias averaged 3,4% per year, as opposed to 0,5 to 1,5% for

mutual funds. Liang (2004) found a similar higher survivorship bias for CTAs and Bhardwaj,

Gorton and Rouwenhorst (2008) showed that the average surviving fund delivered 34%

higher returns than a group of surviving and dissolved CTAs. Finally, backfill bias leads to

positively skewed performance figures. It reflects the inclusion of past performance figures in

a database, once a fund decides to be included. A CTA may only voluntarily join a database

once it has obtained a sufficiently positive track record. Park (1995) estimated the incubation

period or backfill bias to be 27 months on average in the MAR CTA database, as opposed to

15 months in the TASS hedge fund database (Fung and Hsieh, 2000). For the Lipper-‐Tass

database, it was shown that the average real fund return (4,9%) considerably contrasted with

the average backfilled return (11,3%) (Bhardwaj, Gorton and Rouwenhorst, 2008).

In conclusion, the academic literature is in agreement on the diversification benefits that

managed futures may bring to the fold. However, a gap on the specific characteristics of CTAs 4 The methodology Elaut, Frömmel and Mende (2014) was inspired by the work of Wegscheider (1994).

15

during periods of financial crises remains. A systematic methodology should therefore be

developed, in order to detect crises and analyze their dynamics throughout these market

regimes. In performing such an analysis, one may draw upon the market timing literature to

assess whether managed futures adjust their market exposures to a particular market state.

However, all research should remain wary of reporting biases influencing empirical results,

and account for them in order to conduct proper inference.

17

3 Methodology

3.1 Crisis Identification

“On the face of it, defining a stock market crash or collapse is simple. When you see it, you

know it. However, attempting a more precise definition and measurement over the course of

a century is more difficult. The choice of stock market index, the size of the collapse and the

time frame of the decline are key factors.”

(Mishkin and White, 2002 p 5)

The methodology to detect crisis periods was inspired by the two key factors from Mishkin

(2002), and the filter rule proposed by Lunde and Timmerman (2004). More specifically, we

perform a two-‐step procedure. First we determine specific threshold values for the Lunde

and Timmerman (2004) algorithm through an iterative process, taking into account both the

fall in the market and its duration simultaneously. Next, we employ these determined

parameters within the algorithm, and use the detected market regimes for our analysis on

CTAs’ potential higher profitability in times of crisis.

As a starting point we discuss the Lunde and Timmerman (2004) filter rule to identify bear

and bull stock markets. The standard algorithm of Lunde and Timmerman (2004) is a filter

rule that identifies a regime as a bull market if the market has risen by a certain percentage

(i.e. 𝜆!) above its former trough value. Formally, an asset class transitions from a bull to a

bear state if:

𝑃! > 1+ 𝜆! ∗ 𝑃!!!!"#

With Pt the value of the index at time t, 𝜆! the threshold value by which the index must have

risen since its former trough value, 𝑃!!!!"#. If we now define the indicator 𝐼! as the market

state, which takes value 0 if the market is in a bull state and value 1 in a bear regime, then

the filter rule shall administer the value 0 between t-‐i and t retroactively, once the threshold

value has been exceeded (i.e. the market has already been in a bull regime since t-‐i).

Similarly, if

𝑃! < 1− 𝜆! ∗ 𝑃!!!!"#

18

with 𝜆! being the threshold value by which the index must fall since a former peak value, in

order to have retroactively transitioned from normal to crisis, then 𝐼! shall take value 1. In

other words, the market has transitioned from a bull to a bear market state since t-‐i. Note

that the peak and trough values, 𝑃!!!!"# and 𝑃!!!!"# are continuously updated to the extent

that:

𝑃! > 𝑃!!!!"# 𝑖𝑓 𝐼! = 0 𝑡ℎ𝑒𝑛 𝑃!!!!"# = 𝑃!

𝑃! < 𝑃!!!!"# 𝑖𝑓 𝐼! = 1 𝑡ℎ𝑒𝑛 𝑃!!!!"# = 𝑃!

In the original work of Lunde and Timmerman (2004) the 𝜆! ∈ [10% 15%] and 𝜆! ∈

[15% 20%]. However as these thresholds only applied to the stock market, Elaut, Frömmel

and Mende (2014) proposed additional parameter values for other asset classes: fixed

income, commodities and the USD exchange rate.

Nevertheless, these parameter values are suboptimal within the context of crisis market

identification, because they are determined to identify bear markets as opposed to crises. To

adjust for this deficiency, the Lunde and Timmerman (2004) methodology was applied, but

the parameter values were adjusted. More specifically, different combinations of 𝜆! and 𝜆!

were taken into account and employed within the standard Lunde and Timmerman (2004)

filter rule.5 Subsequently, each combination is employed to detect crises, and determine the

intensity factor, 𝐼𝐹!:

𝐼𝐹! =1𝑁 𝐼𝐹!,!

!

!!!

𝐼𝐹!,! =𝑅! 𝐼! , 𝐼!𝑇 − 𝑡

Where 𝐼𝐹! indicates the average intensity factor for loop i with specific chosen values of 𝜆!

and 𝜆!. N are the number of crisis periods identified for the chosen values of 𝜆! and 𝜆!. 𝐼𝐹!,!

is the intensity factor of a particular crisis n in loop i, where 𝑅! 𝐼! , 𝐼! is the fall in the market

during this time, and 𝑇 − 𝑡 is the timeframe over which the fall occurs expressed in year

fractions. Finally, we also determine the standard deviation of 𝐼𝐹!,!, 𝜎!.

5 𝜆! and 𝜆! are allowed to take on values between 0,01 and 0,40 with steps of 0,01. This leads to 1.600 different combinations of 𝜆! and 𝜆!.

19

These variables can be used to determine the optimal values of the parameters 𝜆! and 𝜆! to

identify crises as opposed to bear markets, because they are oriented towards maximizing

the fall in the market over a given timeframe. We thereby incorporate the Mishkin and

White’s (2002) key factors.

The 𝜆! and 𝜆! are eventually chosen such that they maximize the volatility adjusted intensity

factor:

𝐼𝐹 − 𝑎𝑑𝑗! =𝐼𝐹!𝜎!

The choice to maximize a volatility adjusted intensity factor, as opposed to the intensity

factor itself, was made to identify the parameter values that detect similarly intense crises

that aren’t dominated by a single and highly severe episode. The eventual parameter

selection remains open to a number of additional restrictions:

1. All values of 𝜆! and 𝜆! that only identify a single period are excluded, as this implies

that the 𝜎! is equal to 0 and the volatility adjusted intensity factor shall be infinite.

2. All values of 𝜆! and 𝜆! where the 𝐼𝐹! > 𝐼𝐹 are excluded to identify significant falls

within the market. If this restriction wouldn’t be applied, then the eventual values of

𝜆! and 𝜆! may result in the identification of non-‐severe market downfalls that are

simply similar in size. The resulting low 𝜎! would then be the main reason for their

selection.

3. Those combinations of 𝜆! and 𝜆! for which 𝜆! < 𝜆! are excluded. This restriction

implies that for a specific market to rebound out of a crisis state, it should not have to

recover as much as the original plummet required to enter a crisis phase.

Once the optimal parameters have been identified they are incorporated in the standard

Lunde and Timmerman (2004) algorithm in order to identify different periods, which can be

analyzed from a historical perspective. We compare these to a number of contextually

defined crises from RPM Risk and Portfolio Management AB, in order to assess the adequacy

of the identification procedure, and investigate the extent to which the different sector crises

tend to overlap.

20

We extend our descriptive analysis slightly further by assessing whether the market turmoil

in one sector has significant predictive power for a crisis in another. This provides us with

some evidence on the potential cross-‐sectorial crisis transferal. To analyze this, we run

Granger causality tests on the constructed indicators. Note that performing Granger causality

tests on this data implies the usage of a linear probability model (LPM), for the dependent

variable is a dummy that only takes on the value of one or zero. Fitted values for these

models may then be interpreted as the probability that a specific sector will be in a crisis

regime.

Most standard econometric textbooks warn for the problems that characterize the LPM (See

Gujarati and Porter, 2009). The error-‐terms will be non-‐normally distributed and

heteroscedastic. However, the greatest problem lies with the fitted probability values, which

may not adhere to the properties of standard probability bounds (i.e. they are not necessarily

confined to values between zero and one). For the purpose of this study, these problems are

less severe. The impact of heteroscedasticity may be circumvented by employing

heteroscedasticity robust standard errors (i.e. HAC robust standard errors). In the presence

of non-‐normally distributed error-‐terms, inference is still possible as OLS estimators are

normally distributed asymptotically. Finally, the nonfulfillment of standard probability

bounds does not pose a problem, since we are only exploring the potential presence of

Granger causality.

The Granger causality tests are performed on a weekly and monthly frequency. Lag length

selection criteria were employed, in order to determine the optimal lag length. In the event

of possible disagreement between information criteria, preference is given to the Schwarz

Bayesian Criterion (SBC). This imposes a harsher penalty for the incorporation of additional

regressors, but SBC has been shown to asymptotically choose the correct model (i.e. SBC is a

consistent model selection criterion).6

3.2 CTA Crisis Alpha

Following a proper crisis identification procedure, we now move on to an exploration of

CTAs’ performance in these crisis regimes. We start off our empirical results with an

6 This potential problem posed no real issue during the empirical investigation. Information criteria were always in consensus on the inclusion of only a single lag.

21

investigation of the regime dependent performance of the aggregate CTA industry. If

managed futures are able to perform during turbulent market regimes, they should acquire

positive returns. Subsequently, we calculate regime dependent correlations in order to see a

potential change in co-‐movement with the different focus markets.

A formal econometric investigation is performed through a two-‐fold analysis. Firstly, we

reexamine the non-‐linear relationship between managed futures’ returns and world equity

markets from Fung and Hsieh (2001). This would indicate that, while managed futures

market betas may be close to zero in general, they follow dynamic trading strategies, leading

to a time-‐variation in their exposure to the equity market risk factor. Kaminski (2011a)

similarly confirmed the former picture for CTAs between 2000 and 2010, and in the

introductory chapter of this paper we reconstructed this picture for a number of CTA indices.

To get a look into CTAs’ time-‐varying betas, we follow the methodology employed by Daniel

and Moskowitz (2013). In this paper, the authors estimated rolling regressions for an

extended single factor model (i.e. the market risk factor) with 126 days of data

(approximately 6 months in terms of trading days). The applied extension refers to the

inclusion of 10 daily lags of the excess market return. The eventual market beta of each CTA

index is then calculated as the sum of the eleven estimated coefficients, in order to account

for the delay in incorporation of market information. The thus estimated model is of the

following form:

𝑟!,! = 𝛼 + 𝛽!𝑟!,! + 𝛽!𝑟!,!!!+ . .+𝛽!"𝑟!,!!!" + 𝜀!,!

𝛽 = 𝛽! + 𝛽!+ . .+𝛽!"

Where 𝑟!,! is equal to the daily excess return of a CTA index at time t, 𝑟!,! reflects the excess

market return of the MSCI World at time t, 𝜀!,! is a random error term, and 𝛽 is the reported

estimated market beta coefficient from the rolling regressions.

If the empirical results would be in line with the notion of CTAs higher profitability in times of

crisis, then we should expect market betas to become negative during the equity market

crises. In addition, for the estimated coefficients to be consistent with the positive average

monthly returns from figure 1, we could expect market betas to be positive on average

22

during normal times. These expectations are fully in line with the original reasoning of Fung

and Hsieh (2001).

In a second step, we analyze the ability of CTAs to perform in the previously determined

crises, by drawing upon the market-‐timing literature. Two models are central within this

context: The models of TM (1966) and HM (1981). Both models stipulate that a portfolio

manager shall adjust his exposure to the market risk factor according to the expectation of

the market return (Kazemi and Li, 2009). However, the TM model differs from the HM model

by the extent to which the exposure changes with regards to this signal. In the TM model, a

portfolio manager’s market beta shall be a linear function of the expected market return,

which results in a convex relationship between the excess portfolio return, and the excess

market return. The model is thus of the form:

𝛽 = 𝛽! + 𝛾 𝐸 𝑟!,!

𝐸 𝑟!,! = 𝛼! + 𝛽 𝐸 𝑟!,! + 𝜀!

With 𝐸 𝑟!,! the expected excess portfolio return, and 𝐸 𝑟!,! the expected excess market

return. Via basic substitution this model may be rewritten:

𝐸 𝑟!,! = 𝛼! + 𝛽! 𝐸 𝑟!,! + 𝛾 𝐸 𝑟!,!! + 𝜀!

The parameter 𝛾 can be used to test whether the portfolio manager is able to adjust his

market risk factor exposure during up and down markets. A successful market timer will then

have a significantly positive value for 𝛾.

In contrast, the HM model doesn’t assume the portfolio manager to be a magnitude timer,

but a direction timer. The relationship between the manager’s excess return and the excess

market return is therefore similar to the payoff from a call option (Frömmel, 2013). The

model may be represented as:

𝑟!,! = 𝛼! + 𝛽! 𝑟!,! + 𝛾max 𝑟!,!; 0 + 𝜀!

The max 𝑟!,!; 0 term may be replaced by a dummy variable that takes on the value of 1, if

the excess market return is positive, and 0 otherwise. Again, a significantly positive estimate

23

of 𝛾 presents evidence of a successful market timer, who is able to increase his exposure to

the market risk factor in up markets.

From the previous discussion it should be clear that the TM model is suboptimal to analyze

the performance of managed futures in specifically identified market environments. In

contrast, the HM model may be adjusted by applying a different definition to the

aforementioned dummy variable. A similar approach was already applied by Elaut, Frömmel

and Mende (2014), who adjusted the dummy variable to be equal to 1 during a bull market.

Employing this adjusted version of the HM model is thereby a natural extension to our

former crisis identification procedure, and also accommodates the traditional view that CTAs

are trend-‐followers, as opposed to investment managers forecasting whether or not the

market return will be positive the following day.7

CTAs are generally active within multiple futures markets. Referring back to the definition of

managed futures by Kaminski (2011a), CTAs are active in sectors such as equities, fixed

income, currencies and commodities. For this reason, the single market framework of the

standard HM model may be considered too restrictive. To accommodate the multi-‐market

orientation of managed futures, we follow Kazemi and Li (2009) and employ a multi-‐market

timing version of the HM model:8

𝑟!,! = 𝛼! + 𝛽! 𝑟!,!

!

!!!

+ 𝛾!𝐷!,!𝑟!,!

!

!!!

+ 𝜀!

Note that as our previous detection procedure provides us with a 𝐷!,! dummy variable, equal

to 1 during crises and 0 otherwise, the expectations with regards to the 𝛽! and 𝛾!

coefficients change. The 𝛽! estimate will be an indication of the exposure to a specific sector

in normal times, while the 𝛾! coefficient shall be a differential partial slope coefficient,

stipulating how the normal times exposure changes during times of crises. If managed

futures are able to acquire higher profitability in times of crisis, it should be expected that 𝛾!

7 This is an essential point, because within this study we employ daily data on managed futures as opposed to the often-‐utilized monthly data. Thus simply employing the standard approach of the HM would assume that managed futures would be daily market timers forecasting whether or not the return will be positive the following day. 8 The initial work on a market-‐timing model in multiple markets is accredited to Aragon (2007).

24

is significantly smaller than 0. In the most ideal situation, 𝛽! + 𝛾! < 0 such that CTAs will

profit from the specific sector crisis.

This analysis can be extended further by allowing managed futures to also perform volatility

timing. Kazemi and Li (2009) argued that CTAs exhibit volatility timing ability. We thus also

estimate the HM model with a volatility timing extension, as suggested by Busse (1999), and

applied by Kazemi and Li (2009):

𝑟!,! = 𝛼! + 𝛽! 𝑟!,!

!

!!!

+ 𝛾!𝐷!,!𝑟!,!

!

!!!

+ 𝜆𝑟!,! 𝜎!,! − 𝜎! + 𝜀!

Here 𝜎!,! is a proxy for equity market volatility and 𝜎! represents the unconditional

expected volatility. If CTAs have volatility timing ability, then the 𝜆 would be significantly

negative. In other words, equity market exposure is reduced in highly volatile stock market

regimes. We only incorporate equity market volatility, which may be proxied by the VIX index

as in Chen and Liang (2007), because a multi-‐market volatility timing extension in futures

markets was shown to be less relevant in past research (Kazemi and Li, 2009).

If the empirical results are in line with higher profitability in times of crisis, this may be due to

two main sources. As the RPM USD Composite and trend-‐following index reflects the

aggregated performance of the included CTAs that are active in multiple sectors, the higher

profitability can be the result of the own sector performing during its crisis regime, or other

sectors acquiring profits that overcome the own sector’s losses. It is therefore necessary to

provide a sectorial decomposition of our former methodology.

In order to dive deeper into a sectorial analysis, we first decompose the regime-‐dependent

aggregate performance in its different subsector components. If the higher returns during

crisis regimes are the result of other sectors, their yields should be positive, while those of

the own sector should be negative. Next we apply the same HM models to the sector indices

in order to detect whether the specific sector does adjust its market exposure. Even if other

sectors perform well during another’s market crash, the individual sector may still adjust its

exposure to that sector in order to stop the bleeding. Finally, we explore how managed

futures adjust to a crisis environment, by looking into their sector dynamics within an event

window. We define each event window as 40 days preceding the onset of the sector crisis,

25

and 160 days after. Then we compile the evolution of the market index, the sector’s position

and cumulative return of the sector and aggregate CTA index, over the event window for

each sector’s crises. All information is then aggregated via an equally weighted average with

standard deviation bands.

27

4 Data


The data employed within the crisis identification methodology spans across four broad asset

classes: equities, fixed income, commodities and foreign exchange rate markets. We further

divide the commodity markets in three different sub-‐sectors: energy, metals and agriculture.

These reflect the main sectors in which managed futures are broadly active. Equity markets

are represented by the MSCI World, the Barclays U.S. Aggregate index was chosen for fixed

income markets, and for commodities we employ the different S&P GSCI Commodity indices.

These were termed to be the standard asset pricing benchmarks in the seminal paper of

Moskowitz, Ooi and Pedersen (2012). Finally, currencies markets are approximated by the

Trade-‐weighted USD (TW USD) exchange rate as in Elaut, Frömmel and Mende (2014).

All data samples are between 1975 and 2015, but may differ in total sample length, due to

data availability. A summary of the employed data and their sample lengths are presented in

table 1 of the appendix. Note that our equity market data of the MSCI world is monthly until

the 1st of January 2001. All values in between the beginning and end of the same month are

the same. While this may seem odd at first, it does not pose any real problems for the

developed algorithm. It simply implies that when a market regime transition occurs, this shall

have a minimal duration of a month for the first part of the data sample.


This study employs a unique dataset provided to us by RPM Risk and Portfolio Management

AB, a private market player specializing in portfolio management for directional alternative

investments. The dataset is exceptional within the literature on managed futures, because it

contains real performance data from CTA managed accounts at RPM Risk and Portfolio

Management AB. As such, it remains uncontaminated by standard reporting biases that

plague alternative investment databases (e.g. selection, survival and backfill bias).

The daily dataset provided to us by RPM Risk and Portfolio Management AB includes asset-‐

weighted performance indices from manager accounts denominated in USD between the

16th of April 2001 and the 31st of March 2015. The broadest index, The RPM USD Composite

28

index, encompasses all managers that may follow a trend-‐following, short-‐term or

fundamental trading approach. Sector subindices are included that encompass the

performance of the same managers incorporated in the RPM USD Composite index within a

specific market, such as equities or fixed income. In addition, to provide a more clear-‐cut

picture of pure CTA strategies, the RPM USD Trend-‐Following Composite index, and its sector

subindices, cover the live asset-‐weighted performance of all RPM manager accounts where

the underlying managers are, or were, classified as trend-‐followers. Finally, the dataset also

includes aggregated position data for each sector, as defined by RPM Risk and Portfolio

Management AB.

As this is a unique dataset, it is worth providing some summary statistics. For comparison

reasons we have included a number of other standard indices as well.9 Table 2 presents an

overview of these summary statistics. Overall, average monthly returns are very similar in

magnitude, ranging from 0,38% to 0,48% for the aggregate indices and 0,59% to 0,71% for

the trend-‐following subindices. Interestingly, most CTAs achieved their highest monthly

returns in the midst of the Dot Com crisis and their worst after the September 11 stock

market crash. Finally, all indices seem to strongly co-‐move with one another, as all

correlations range from 82 to 97% and the average correlation between the indices is 90%.

Differences in dynamics may be attributed to methodological differences in index

construction (e.g. equally or asset-‐weighted index construction).

Besides the managed futures dataset, we also acquired data through DataStream and the

Federal Reserve Bank of St. Louis database. This includes the market indices described

previously and data on the three-‐month US T-‐bill rate and the VIX index.

9 The other CTA indices are the Newedge CTA Index and its trend-‐following subindex, the Barclays CTA index and the Barclays BTOP 50. The Newedge CTA index and trend-‐following subindex are an equally weighted index of a pool of CTAs selected from the largest managers open to new investment (Societe General Corporate & Investment Banking, n.d.). The Barclays CTA index is once more an equally weighted index representing the overall CTA industry (Barclay Hedge, n.d.) and the Barclays BTOP50 index is an equally weighted index that contains the largest investable CTAs in terms of assets under management.

29

5 Empirical Results


The results of the parameter identification procedure are presented in table 3 for the

different sectors. For comparison, alternative parameters, employed by Lunde and

Timmerman (2004) and Elaut, Frömmel and Mende (2014) from the standard bear market

algorithm (BMA), are also included.

Table 310 illustrates that the determined parameter values of 𝜆! and 𝜆! for the crisis market

algorithm (CMA) are not considerably different from those of the BMA. The contrast

between the two is nevertheless quite intuitive. 𝜆! tends to be larger for the CMA than for

the BMA, which implies that for a crisis to materialize, the market should plummet more

severely. Furthermore, the 𝜆! parameter is in general lower in the case of the CMA, such that

a market must rebound to a lesser extent for the regime to adjust back to normal. This would

intuitively lead to an identification procedure that will detect bursts of significant declines

lasting for shorter periods of time. This is consistent with our perceived difference between a

bear market and a crisis period.

We now apply the Lunde and Timmerman (2004) algorithm to identify the crisis periods with

the parameters from table 3. One additional restriction is however imposed at this stage, i.e.

when a crisis period is identified that is less than 60 days apart from the former one then this

is considered to be a single period. The results of this application are summarized in table 4

and figures 2 to 7 highlight the different identified crises for each sector. For comparison, we

have once more included results from the standard BMA as well.

An analysis of table 4 illustrates some differences in identified periods between the BMA and

the CMA. Overall, the CMA detects a similar amount of periods in comparison to the BMA

and the average duration is shorter for equity, agricultural, and metal commodity sectors.

Furthermore, the average fall in the market tends to be at least as severe as the BMA

(𝑅! 𝐼! , 𝐼! ), but the CMA forces these falls to occur over shorter periods of time, such that the

10 For equity markets an additional restriction was imposed, which specified that 𝜆! < 15% to ensure the identification of the LTCM crisis in the ‘98s.

30

𝐼𝐹 is mostly higher. Most importantly, the 𝐼𝐹!"# is always higher than that of the BMA,

with the exception for commodity metals.

The identified crises seem to be quite consistent with an internal list of contextually

identified crises from RPM Risk and Portfolio Management AB. A list of matching contextual

and CMA equity crises are highlighted in table 5. This contextual definition first identifies

months where the MSCI World was down more than 4%. Then a crisis was defined as a

fundamental period around an event that caused a crisis according to the former threshold

approach. Differences between both approaches may be due to several reasons, such as the

usage of monthly versus daily data, and the filter rule requires both up and downward

movements for crisis identification, as opposed to a single downward evolution of the market

in a given month. Note that two conceptual crises may fall under a single CMA period. This is

the case for Enron and the September 11 crash.

In general, the main undetected conceptual crises are those where the fall in the MSCI World

was simply too small to be considered a crisis by the CMA. An additional reason for the non-‐

detection lies with their non-‐direct relation to the equity market. For instance, a great

number of periods in the 90s are primarily times of currency market turmoil: the EMS/ERM

crisis, the currency crisis in Turkey and the Mexican Peso crisis.

Figure 8 illustrates whether the different sectors tend to find themselves within a crisis state

simultaneously. This clearly illustrates that at no point in time, all sectors are within a crisis at

the same time.11 There are nevertheless multiple periods during which most markets are in

turmoil that coincide with widely accepted crises. An overview of these periods is provided in

table 6. Some important examples include the great stock market crash of 1987, the Russian

crisis and LTCM in 1998, the Dot Com Bubble burst at the beginning of the millennium and

the global financial crisis in 2008. In addition, equities and commodities seem to be

consistently part of these cross-‐sector crises, while foreign exchange markets are mostly

absent, followed by fixed income.

To conclude the first part of this section, we perform Granger causality tests on our crisis

data in order to explore potential cross-‐sectorial crisis transferal. We perform the analysis for

weekly and monthly data of which the F-‐tests are incorporated in table 7. Unfortunately, 11 Note that due to data availability, we have included a line that indicates how many sectors are present.

31

these tests yield no strong conclusions. Only the probability of an agricultural commodity

market crisis is Granger caused by equity and foreign exchange rate markets at the 5% level

of significance, which is robust to the employed data frequency. Less consistent findings

include the metal sector being Granger caused by agricultural commodities at a monthly

frequency and the metal sector Granger causing equity crises at a weekly frequency. Both

results are furthermore only significant at the 10% level.


5.2.1 Aggregate CTA Performance Analysis

As sector specific crises have now been identified, we proceed to explore the CTA industry’s

performance during these market regimes. Table 8 contains the overall performance of

managed futures between the 16th of April 2001 and the 31st of October 2015 and their

conditional performance in crisis regimes. This table shows that CTAs have acquired higher

returns than the risk-‐free rate (approximately 1%) over the entire sample with an annualized

return of 3,40% and 5,62% for the RPM aggregate and trend-‐following subindex respectively.

These figures remain positive throughout all crisis regimes, with the exception of commodity

metal crises. Nevertheless they tend to be lower for all asset classes in comparison to their

unconditional performance. Only in TW USD crash states do CTAs offer substantially higher

performance figures than their unconditional counterpart.

Table 9 provides an overview of regime dependent correlations of the RPM USD Composite

and trend-‐following subindex with the different market indices. This table shows that the

aggregate managed futures industry exhibits lower correlations with a specific sector in times

of crisis. Most importantly, during periods of market distress the conditional correlations

between the aggregate and trend-‐following indices with the MSCI World and the TW USD

markets turn substantially negative. This may clarify their very high performance during

equity and currency crises illustrated in table 8. For instance, the equity market correlation

plummets from 0,00 to -‐0,28 and -‐0,02 to -‐0,32 and the TW USD correlation falls from -‐0,19

to -‐0,38 and -‐0,16 to -‐0,35 for the aggregate and trend-‐following subindex respectively. The

remaining sectors have both full sample and crisis regime correlations fluctuating around

zero, consistent with the common perception that many hedge funds have a market neutral

exposure to their target markets.

32

Moving on to the estimation results, we start off with the potential time-‐varying exposure to

the equity market, which coincides with a more formal analysis of the documented non-‐

linear relationship between managed futures and the equity market return from Fung and

Hsieh (2001). This is performed by means of the rolling regression methodology of Daniel and

Moskowitz (2013). Figure 9 plots the rolling betas, which indicate that the RPM CTA indices

exhibit an important time variation in its equity market exposure during periods of equity

market crisis. We document a significant reduction in managed futures’ exposure to the

market risk factor from positive to negative territory, consistent with the notion of managed

futures’ considerable diversification benefits in times of market distress. For instance during

the Dot Com Crisis all managed futures indices have market betas below zero, rising only

after the end of the detected period. In the more recent global financial crisis, CTAs

experienced a massive plummet in their market risk exposures between mid 2007 and

November 2008. An important finding from figure 9 reflects the mostly positive exposures to

the equity market at the start of each regime. Opening a crisis with a consistent positive

exposure will lead to an initial loss that must be overcome by potential profits once a

negative equity market exposure is achieved.

The dynamic variation in market exposures is in line with Greyserman and Kaminski’s (2014)

theoretical justification of why managed futures are able to perform during periods of

market turbulence. They exhibit clear ability to dynamically adjust their equity risk factor

exposure in an equity sector crisis. The trend-‐following subindex also displays more drastic

swings than the aggregate index, and may thus be the driving force underlying their more

tempered dynamics. They do require some time in order to properly adapt, such that they

may still deliver negative returns at the beginning of a crash or if a crash lasts for a short

duration. This was a common characteristic of commodity metals crises in particular.

Up until now results have focused on equity market exposures. This is now extended by

analyzing the ability of CTAs to dynamically adjust their exposure to all markets that may be

in turbulence. For this we draw upon the market timing literature and estimate a multi-‐

market HM model. Table 10 provides the results for the HM model and the volatility

extended version of Kazemi and Li (2009). Model characteristics, such as the degree of

variation in returns that can be explained by the variation in the explanatory variables seem

to be consistent with values obtained by previous research (e.g. Kazemi and Li, 2009 and

33

Elaut, Frömmel and Mende, 2014). The volatility extended model may be preferred above

the standard multi-‐market model, as the addition of the stock market excess return and

implied equity market volatility interaction term is highly significant. This is the case both

statistically and economically. Finally, the volatility extended model performs better in terms

of R2 and R2-‐adjusted.

All estimated models show that the CTA industry in aggregate seems to have market timing

ability in a number of sectors. Managed futures have small exposures to the different

sectors, which can be significantly different from zero. Only with respect to fixed income

markets we identify a positive exposure that may not be classified as small. Interestingly and

consistent with the former findings from figure 2, CTAs significantly reduce their exposures to

most sectors during the identified periods. The main exceptions include commodities

agriculture and metals, two sectors performing quite poorly during their respective crisis

regimes.

The reductions in exposure to the specific sectors are the largest for equity, fixed income and

currency markets. This finding is fully consistent with the conditional performance pattern

provided in table 8, where the highest regime dependent profits were found in foreign

exchange rate, equity and fixed income crises. The sum of the partial and differential partial

regression coefficients nevertheless only turns negative for equity and foreign exchange

sectors. Unsurprisingly, the volatility extended model leads to smaller equity sector

coefficients, but are significantly negative. Thus managed futures significantly decrease

(increase) their market beta during periods of high (low) equity market volatility, such as

equity market crises.

To conclude, our results show that managed futures are able to acquire positive yields when

most sectors are in crisis. This may stem from two potential sources. Firstly, CTAs are active

in multiple sectors, which may acquire positive yields, counteracting the losses of a sector in

turmoil. Secondly, following the onset of the crisis, CTAs may adjust their sectorial exposure

downwards, putting a halt to the distressed sector’s losses and complement the other

sectors’ profits.

34

5.2.2 Sector Specific CTA Performance Analysis

To examine the two potential sources of CTAs’ positive returns in the different market

regimes we perform a sectorial decomposition of the aggregate performance. These

represent the sector performance of the same managers in the RPM USD Composite index.

The figures from table 11 show negative equity sector returns in an equity crisis,

counteracted by substantial gains via the performance in the fixed income sector and smaller

positive yields in the soft commodities and trend-‐following metals sector. Fixed income

performance is similarly negative throughout a bond market crisis, but all other sectors

deliver positive yields. Only the composite currency sector produces high profits in a TW USD

crisis, complemented by gains in most other sectors as well. In other words, table 11 would

lead to a preliminary conclusion that CTAs’ positive returns in different crisis regimes are not

driven by their sector specific performance.

Despite managed futures’ negative sector performance in their respective crises, they may

still dynamically adjust their exposure to that sector in line with Greyserman and Kaminski’s

(2014) proposition that CTAs are highly adaptable, and able to adjust to more extreme

market environments. We delve deeper into the second potential source of CTAs’

performance during crisis regimes, by examining their time-‐varying exposure to the different

focus markets. For this reason, we reestimate the former HM models with the sector

subindices. The results for equity, fixed income, soft, energy and metal commodities, and

currency market sectors are provided in tables 12 to 14.

The most important difference between the sector specific results and those from the

aggregate performance analysis logically lies with the specific markets within which the

managed futures appear to have market timing ability. In other words, the coefficients that

are found to be consistently significant across model specifications are those of the targeted

market. In addition, there is quite a degree of divergence in the amount of sector specific

CTA return variation that can be explained by the explanatory variables. The R2 of the

regressions range between 3% for soft commodities and 28% in the case of equities and

bonds.

Model 1 and 2 from table 12 illustrate small, but significantly positive exposures to the equity

market risk factor in normal times. During the identified equity market crises, exposures are

35

significantly reduced to the extent that they become market neutral or have minor negative

market betas. The volatility timing extended model provides further evidence that the equity

sector performance experiences a significant reduction in its market risk exposure during

times of high equity market volatility. All these findings are also slightly larger in magnitude

for the pure trend-‐following subindices. The remaining coefficients within the model are

never consistently significant, highlighting the fact that these results are from the CTAs’

sector performance. The results would indicate that the aggregate industry’s gains in times of

an equity market crisis are not solely driven by their diversified nature.

An important remark should be raised at this point. The ability of the equity sector to

perform during a stock market crisis may depend to a certain extent on the duration of the

crisis state. For instance, in more prolonged equity market crises, such as the global financial

crisis, the RPM USD equity sector performance amounted to an annualized return of 6,57%.

Other regimes of market turmoil may be too short in duration for managed futures to adjust

their positions, such as the Flash Crash of 2010, when the equity sector performance

acquired a disappointing annualized return of -‐3,72%.

Fixed income’s estimation results exhibit significant positive exposures to the bond market in

normal times. However, this positive factor loading is substantially reduced during a bond

market crisis, in line with the aggregate industry’s results. The sum of both regressions

coefficients is nevertheless positive, implying that the sector is less able to put a halt to the

fall in sector returns when the bond market is in distress. Finally, the sector also has a

consistent negative market beta during a standard and equity market crisis regime.

Turning our attention to the commodity sector performance, Table 13 reveals an inability of

the HM model to account for any of the variation in the soft commodities sector returns.

Either these managed futures are market neutral in general or the model is inadequate for

this specific sector. Moreover, the variables that are significant within the model

specification are so on an inconsistent basis, casting doubt on their true importance, or are of

a magnitude that may be regarded as irrelevant from an economic standpoint.

A more reasonable picture is portrayed by CTAs’ estimation results in the energy sector.

While being rather small in magnitude, all estimated coefficients are both of the right sign

and are consistently significant. This signals the importance of the second source in managed

36

futures’ performance during an energy crisis. Once more the volatility component of the

model is statistically significant and adds to the explanatory power of the model.

The metal commodity sector does not experience a significant fall in its exposure to the focus

market in times of market turmoil. Thus, the sectors’ dynamic adjustment does not lead to a

second source of their higher profitability in times of crisis. This may be explained by

commodity metal crises being generally smaller in length, leading to insufficient time for

factor loadings to be adapted. This was also the only sector where the aggregate industry

was unable to acquire positive returns in a crisis regime. Despite the lack of regime

dependent exposure within their own focus market, this sector specific performance does

have a surprisingly consistent exposure to the foreign exchange and the energy commodity

sector to which it adjust its factor loadings downwards in the event of a crisis.

Finally, the foreign exchange sector results present strong evidence in favor of the own

sectors performance being a source of their high profitability in times of a TW USD crisis.

During a standard market regime, the foreign exchange sector retains market neutrality that

is adjusted towards a significantly negative factor loading in a crisis regime. This sector also

exhibits persistent factor loadings in the stock and commodity metals market and seems to

possess volatility timing ability.

To conclude, the sector’s performance analysis showed that CTAs’ activity in multiple

markets is a very important first source for their positive returns in each crisis regime.

Furthermore, the sector specific estimation results presented evidence of managed futures’

ability to dynamically adjust their exposure downwards to the focus market in most sectors.

The performance pattern described by table 11 is therefore not the sole result of higher

performance in the different subsectors that do not find themselves in crisis.

5.2.3 Managed Futures Dynamics in a Crisis Regime

To gain further insight into the ability of CTAs to adapt their specific sectors’ market exposure

during the respective crises, we analyze their cumulative performance in conjunction with

how they position in the market over a specified event window of 201 days. More

specifically, we define an event window of 40 days preceding the onset of a crisis regime and

160 days after. Then, we determine the average evolution of the market index, the sectors

37

position and cumulative return of the sector and aggregate CTA index over the event

window. The results of this procedure are contained in figures 10 to 15 of the appendix.

Figure 10 illustrates the managed futures dynamics in an equity market crisis. Overall, the

characteristics of a stock market crisis are very similar in nature over the first 120 days of the

event window. The market acquires substantial gains up to the onset of the crisis. These

returns are matched by similar gains in CTAs equity sector performance, as they on average

have long equity positions in the run up to the equity market peak. Nevertheless, the entire

accumulated return of the stock market is quickly evaporated over a duration of

approximately 90 days after which the equity market return stabilizes around a cumulative

return of -‐10%. During this timeframe CTAs modify their positioning downwards, which

become negative on average after roughly 40 days of crisis. This allows them to compensate

for the initial losses suffered at the very beginning of the crisis, when the market was

plummeting and CTAs still retained their overall long positions. Most notable is the strong

increase in average equity sector performance between the 70th and 90th day after the onset

of the crisis. These profits are matched by an increase in the RPM USD Composite (trend-‐

following) index. The position data explains the results from the HM model and would

indicate that CTAs’ equity sector performance may also be able to acquire gains during more

prolonged equity market crises. It also clarifies the negative equity sector performance in the

European sovereign debt crisis and the Flash Crash, which were shorter in duration and

therefore did not provide exploitable downward trends.

The same graphs for fixed income are encompassed in figure 11. At first a bonds market crisis

leads to a notable fall of the cumulative return that stabilizes after 125 days and slightly

rebounds after 145 days. In the same way as the equity sector, fixed income positioning

decreased the existing long holdings. In spite of this adjustment, positions remain positive

overall. This is in line with the results from the HM model that also showed a decreased

exposure to the focus market, but to an insufficient extent in order to acquire a market

neutral or negative stance. The bonds sector performance therefore does not seem to profit

from the crisis and only acquires gains during the small market rebound near the end of the

event window. The overall managed futures performance on the other hand remains positive

and upward trending. This may thus be attributed to the ability of other sectors to obtain

38

positive yields throughout fixed income crises (e.g. table 8 indicated positive equity sector

yields).

In the commodities agriculture sector, figure 12 shows the continuing fall of the market

throughout the event window matched by a drop in soft commodities’ positioning. Once

more, the position data does not take on persistent negative values, but fluctuate around 0%

between day 50 and 160. The cumulative sector returns suffer an initial hit at the start of the

crisis, but neither gain nor suffer in the later part of the market regime. The overall sector

performance shows a comparable pattern, with only a small positive cumulative return at the

very end of the event window.

In general, an energy crisis exhibits a similar pattern to an agricultural one. Figure 13 displays

a consistent fall in the average cumulative sector return. However, the standard deviation

bands are much wider in the second half of the event window, indicating more diverse

events. Positioning once more starts off with a long bias that is built off to a market neutral

exposure around the 50th day after the start of the crisis. As a consequence, cumulative

returns deteriorate at first, stabilizing around 0% for the remainder of the event window.

Positive aggregate managed futures performance may thus be attributed to the ability of

other sectors to perform at the same time. For instance, table 8 showed positive fixed

income sector performance in energy market crises. The results are furthermore consistent

with those from the HM model that depicted a market neutral orientation during crisis

regimes.

The final group of commodities, metals, exhibits a fall in the market, paralleled by a

downward adjustment of metal sector positions that stagnates around 0% after 40 days

(figure 14). As CTAs start of the turbulent times with long positions, they quickly lose much of

the accumulated profits during this descend. Over the remainder of the event window the

sector performance quickly recuperates and is able to deliver positive yields. These results

should be nuanced to some extent, as the average metal sector crisis between 2001 and

2015 lasts for only 90 days. As a result, our event window may also be capturing a part of the

39

rebound within the market and is less adequate to represent the managed futures dynamics

in a metals sector crisis.12

In contrast with all other sectors, the RPM USD composite currencies reflects a completely

different dynamic in a TW USD crisis (figure 15). Leading up to the price peak in the TW USD,

the RPM composite currencies positions are short. For this reason, their sector performance

does not see a substantial fall during the first 40 days after the onset of the crisis. Instead,

the composite currencies performance on average rises throughout a foreign exchange rate

crisis. Especially in the second part of the event window the sector performance gains seem

to be matched by profits in the aggregate managed futures industry. Past results already

showed that this sector has a substantial negative exposure to the TW USD index in turbulent

times (table 14), as well as notable positive sector returns (table 11). Therefore the aggregate

CTA industry yields during foreign exchange rate crises do not stem from other sectors’

profits, but mainly from their own sectors ability to perform.

In conclusion, the performance pattern summarized in table 11 seems to not only be the

result of other sectors performing well. In fact, most sectors show a considerable degree of

adaptability as they adjust their positioning downwards following the onset of the crisis. For

this reason, most sectors’ performance has to bear upon accumulated profits at the start of

the crisis, which were acquired in the lead up to the sector price peak, but do not see a

consistent plummet throughout the remainder of the event window. The foreign exchange

rate and equity sector may also show the ability to perform within its own market in times of

crisis. The former tends to already be positioned in order to gain from a TW USD crash, while

the latter may only do so if the crisis duration is sufficiently long for the adjusted short

positions to gain from the downward price trends. Finally, all presented evidence highlights

the nature of managed futures as a diversified asset class that follows trends. They are not

market timers or early movers with an ability to anticipate the change in market regime.

12 We would like to emphasize that the choice to not employ a smaller event window for commodity metal crises was taken in order to provide a more consistent analysis.

41

6 Robustness Tests

To increase the power of our results, we perform a number of robustness checks. Firstly, we

test the robustness of our results to the employed data by reestimating the former HM

models with an alternative managed futures index, the Newedge CTA index, and its trend-‐

following subindex. Secondly, we adjust our crisis market indicator with three possible

alternatives: the bear market indicator of Daniel and Moskowitz (2013), Elaut, Frömmel and

Mende (2014) and Chen and Liang (2007). The Daniel and Moskowitz (2013) measure

determines a market to be in a bear regime if the cumulative return over the past 24 months

has been negative. Elaut, Frömmel and Mende’s (2014) index is similar to our own, but

reflects alternative parameters. Chen and Liang (2007) determine the market state to be in a

bear regime if the index return is smaller than the risk-‐free rate, such that the robustness

check boils down to a more traditional version of the HM model. Finally, we perform a

subsample analysis by restricting the data to a subsample between 2001 and May 2008. This

excludes the credit crunch and the Lehman Brothers bankruptcy, which may dominate our

empirical results. The alternative crisis indicators and subsample analysis are also applied to

the Newedge data as an additional robustness check.

Table 15 reflects the overall robustness of the aggregate CTA performance analysis to an

alternative managed futures index. As in previous tables, the numbers between parentheses

are the p-‐values and the bold figures denote significance of the variable at the 5% level of

significance. In addition the underlined p-‐values reflect inconsistency with former estimation

results. Besides some minor differences, the only striking discrepancy with an alternative

industry benchmark pertains to the commodities energy sector. When employing the

Newedge CTA indices we attain non-‐significant adjustments to the S&P GSCI Commodities

Energy in times of energy market crisis. We also note a now significant positive exposure to

the commodity agriculture sector. Nevertheless, all estimated coefficients remain stable in

magnitude and sign.

Our results seem robust to the alternative measure of Daniel and Moskowitz (2013). All

coefficients tend to retain their significance, magnitude and sign. Some differences include

an insignificant and significant exposure reduction to commodities energy and metals in

times of crisis, respectively. It is furthermore worth noting that the R2 tends to be higher. This

42

may be the consequence of Daniel and Moskowitz’s (2013) measure lagging our own, as it

requires the cumulative return over the last 24 months to be negative. Thus it may more

adequately capture the already downwards-‐adjusted positioning in most sectors.

Model results are also robust to potential alternative parameters from the BMA. All

estimates are robust in terms of sign and magnitude and only minor inconsistent differences

occur with regards to significance. It is also worth noting that when employing the CMA the

R2 and R2-‐adjusted from table 10 and 15 are slightly larger in magnitude than those from

table 17. This may reflect a very small degree of superiority of the CMA over the BMA.

Numerous differences, both in terms of significance and coefficient sign, arise when the

indicator from Chen and Liang (2007) is employed. The degree of variation that is captured by

the variation in explanatory variables is also much lower for the aggregate indices. This may

be clarified by the notable difference in their measure. For instance, their classification leads

to numerous very short periods of time that are never in line with potentially exploitable

trends for managed futures. This may stress the importance of adapting the HM model in

order to capture the nature of the asset class at hand, consistent with Elaut, Frömmel and

Mende (2014).

Restricting the data sample up to May 2008 does lead to a number of differences with

regards to the aggregate CTA performance analysis. For the Newedge CTA data, there is no

longer a significant positive exposure to the stock market in normal times. There are no

significant results for fixed income and commodity energy exposure in normal times with the

RPM USD Composite, or either data source in times of crisis. And for the TW USD, results are

significantly negative and non-‐significant in normal times and crises, respectively. We should

therefore be wary in drawing conclusions, because the robustness tests indicate our

estimation results being dominated by the global financial crisis.

Tables 20 to 31 encompass all estimation results to test the stability of tables 11 to 13. The

Daniel and Moskowitz (2013) measure leads to an overall consistent conclusion, but some

estimations do exhibit a more outspoken positive exposure in normal times that is

significantly reduced within a crisis regime (tables 20 to 22). The delayed nature of the Daniel

and Moskowitz (2013) measure also improves upon the degree of variation captured by the

model for all commodity and foreign exchange sectors. This can be attributed to the

43

aforementioned fallen sector positioning, which is better captured by a lagging indicator than

the CMA measure. Sector estimation results for the BMA parameters are provided by tables

23 to 25, which once more illustrate overall consistency. Most outcomes are not robust to

the Chen and Liang (2007) measure (tables 26 to 28), but they do remain unchanged to a

data sample restriction (tables 29 to 31) contrasting the aggregate robustness checks.

45

7 Conclusion

This paper has researched whether managed futures are able to acquire higher profitability

in times of crisis. This was achieved by adapting the Lunde and Timmerman (2004) dating

algorithm to detect different crisis regimes, and incorporating this measure in the well-‐

established Henriksson-‐Merton model. We furthermore examined each sectors’ intra-‐regime

dynamics in detail by exploiting a unique dataset on managed futures positioning.

Our results revealed that managed futures had on average acquired positive returns in all but

commodity metal crises. This is the result of the alternative investment following directional

strategies in multiple asset classes, which leads to standard diversification benefits: the

lacking performance in the crisis sector was counterbalanced by the gains in others.

Secondly, CTAs on average exhibited a long bias leading up to the market’s price peak, which

was subsequently decreased owing to their trend-‐following nature. For this reason, managed

futures sector performance stabilized rather quickly, as they acquired a market neutral or

negative exposure to the crisis sector.

The equity, fixed income and composite currency sectors exhibited the strongest ability to

adjust market exposures downwards. In addition, the composite currencies sector’s

dynamics were different, as they didn’t retain the same initial long-‐bias. This led to

composite currencies being the only sector capable at acquiring positive returns in its

respective crisis regime. Most estimation results were also robust to alternative crisis

measures, but a sample restriction indicated a strong impact of the global financial crisis.

In sum, we have argued that the stable returns of CTAs in times of crisis originate from the

two aforementioned sources: diversification and trend-‐following. Therefore, their regime

dependent performance does not stem from an ability to anticipate crises and adjust their

positioning accordingly, but from the features that characterize the asset class itself.

47

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53

9 Appendix

9.1 Tables

Table 1: Data Crisis Identification Methodology

Sector Index Start Sample

Stocks MSCI World 01/05/75 Bonds Barclays U.S. Aggregate 30/01/76 Comm. Agr. S&P GSCI Commodities Agriculture 01/05/75 Comm. Energy S&P GSCI Commodities Energy 31/12/82 Comm. Metals S&P GSCI Commodities Metals 16/01/95 TW USD Trade-‐Weighted USD 01/05/75

Source: DataStream and Federal Reserve Bank of St. Louis

Table 2: Summary Statistics

RPM

Aggr.

Newedge

Aggr.

RPM

TF

Newedge

TF

Barclays

Aggr.

Barclays

BTOP50

Mean 0,42% 0,48% 0,71% 0,59% 0,38% 0,43% Standard Deviation 2,30% 2,46% 3,07% 4,16% 1,89% 2,36% Min -‐4,34% -‐7,95% -‐5,90% -‐14,61% -‐4,73% -‐7,22% Date 30/04/04 30/11/01 30/11/01 30/11/01 31/03/03 30/11/01 Max 6,58% 8,48% 7,99% 13,46% 6,25% 9,37% Date 31/10/00 31/12/00 29/02/08 31/12/00 30/06/02 31/12/00 Correlation Matrix

RPM Aggr. 1,00 0,87 0,92 0,85 0,82 0,84 Newedge Aggr. 0,87 1,00 0,88 0,97 0,92 0,97 RPM TF 0,92 0,88 1,00 0,88 0,86 0,86 Newedge TF 0,85 0,97 0,88 1,00 0,92 0,97 Barclays Aggr. 0,82 0,92 0,86 0,92 1,00 0,93 Barclays BTOP 0,84 0,97 0,86 0,97 0,93 1,00

Source: RPM Risk and Portfolio Management AB and own calculations

54

Table 3: Employed Parameters

𝝀𝟏 𝝀𝟐 Data Sample Start

Equity BMA 10,00% 20,00% 01/05/1975

CMA 13,00% 5,00%

Fixed Income BMA 4,63% 2,56% 30/01/1976 CMA 7,00% 3,00%

Comm. Agr. BMA 19,58% 13,85% 01/05/1975 CMA 22,00% 11,00%

Comm. Energy BMA 19,71% 23,90% 31/12/1982 CMA 21,00% 13,00%

Comm. Metals BMA 16,01% 10,61% 16/01/1995 CMA 12,00% 1,00%

TW USD BMA 4,59% 4,07% 01/05/1975 CMA 10,00% 4,00%

Source: DataStream, Lunde and Timmerman (2004), Elaut, Frömmel and Mende (2014) and own calculations.

Table 4: Summary Statistics

Crises 𝑹! 𝑰𝒕, 𝑰𝑻 𝑻− 𝒕 𝑰𝑭 𝑰𝑭𝒂𝒅𝒋

Equity BMA 14 -‐24,81% 211 -‐0,65 -‐1,86

CMA 12 -‐26,31% 183 -‐0,74 -‐2,09

Fixed Income BMA 18 -‐9,56% 328 -‐0,15 -‐1,73

CMA 10 -‐13,29% 532 -‐0,10 -‐2,84

Comm. Agr. BMA 16 -‐40,13% 373 -‐0,71 -‐1,42

CMA 16 -‐40,24% 345 -‐0,59 -‐2,07

Comm. Energy BMA 18 -‐48,86% 260 -‐1,09 -‐1,35

CMA 20 -‐48,06% 214 -‐1,18 -‐1,61

Comm. Metals BMA 12 -‐28,47% 267 -‐0,90 -‐1,12

CMA 18 -‐21,07% 145 -‐1,06 -‐0,77

TW USD BMA 27 -‐12,69% 235 -‐0,30 -‐1,73

CMA 13 -‐18,22% 378 -‐0,23 -‐2,09

Description: Crises = Number of identified crises or bear markets, 𝑅! 𝐼! , 𝐼! = The average fall in the market over the crisis (bear) market regime, 𝑇 − 𝑡 = The average duration of the identified period and 𝐼𝐹 = the average intensity factor Source: DataStream, Lunde and Timmerman (2004), Elaut, Frömmel and Mende (2014) and own calculations

55

Table 5: Matching Contextual and CMA Stock Market Crises

Contextual CMA

Name Begin End Dur. Fall Begin End Dur. Fall

Japanese asset price bubble Jan-‐90 Apr-‐90 90 -‐15,44% Dec-‐89 Apr-‐90 122 -‐16,78% 1st Gulf War Aug-‐90 Sep-‐90 31 -‐18,89% Jul-‐90 Sep-‐90 59 -‐20,93% New Industrial Policy of India / India Trying to liberalize

Jun-‐91

30 -‐6,16% Not Identified

EMS/ERM Crisis Jan-‐92 Mar-‐92 60 -‐8,04% Not Identified Military Coup in Nigeria Nov-‐93


Currency Crisis in Turkey Feb-‐94 Mar-‐94 28 -‐5,52% Not Identified Mexican Peso Crisis Nov-‐94


Asian Financial Crisis Aug-‐97 30 -‐6,68% Not Identified October 27th Mini Crash Oct-‐97


Russian Financial Crisis and LTCM

Aug-‐98

30 -‐13,32% Jun-‐98 Aug-‐98 62 -‐14,44%

Greenspan warns of stock market bubble

Jan-‐00


Dot Com Bubble Burst Apr-‐00 Mar-‐01 334 -‐24,87% Mar-‐00 Mar-‐01 356 -‐33,17% Enron Aug-‐01 30 -‐4,78%

May-‐01 Sep-‐01 123 -‐30,55% 09/11 Sep-‐01

30 -‐8,80%

Accounting Scandal Jun-‐02 Sep-‐02 92 -‐23,24% Mar-‐02 Mar-‐03 359 -‐31,54%

Anticipation of 2nd Gulf War Dec-‐02 Feb-‐03 62 -‐9,28%

Sub-‐prime Mortgage Crisis Nov-‐07 Mar-‐08 121 -‐13,73% Oct-‐07 Jan-‐08 83 -‐18,59% Credit Crunch and Lehman Bankruptcy Jun-‐08 Feb-‐09 245 -‐49,82% May-‐08 Mar-‐09 295 -‐74,44%

Obama's Bank Speech Jan-‐10 30 -‐4,11% Not Identified Flash Crash May-‐10 30 -‐9,48% Apr-‐10 Jun-‐10 53 -‐16,91% European Sovereign Debt Crisis Jul-‐11 Sep-‐11 62 -‐16,52% May-‐11 Aug-‐11 100 -‐19,94%

European Sovereign Debt Crisis Part II

May-‐12


Source: RPM Risk and Portfolio Management AB, DataStream and Own Calculations

56

Table 6: Overlapping Crises

Markets in Crisis Start End Stock Bond

Comm. Agr.

Comm. Energy

Comm. Metals FX

4 31/08/87 29/09/87 x x

x

x 4 03/01/90 27/04/90 x x x x 4 30/06/98 28/08/98 x

x x x

4 12/11/98 01/12/98 x x x x 4 31/03/00 07/04/00 x x

x x

4 26/10/04 03/11/04 x x x x 5 14/07/08 30/10/08 x x x x x

4 31/10/08 05/12/08 x x x x 4 26/07/11 09/08/11 x

x x x

Source: DataStream and own calculations

Table 7: Granger Causality Test P-‐Values

Frequency Equity FI Comm. Agr.

Comm. Energy

Comm. Metals TW USD

Equity Weekly

0,71 0,92 0,89 0,09 0,33

Monthly

0,76 0,82 0,66 0,15 0,38

Fixed Income Weekly 0,24

0,76 0,28 0,58 0,39 Monthly 0,28

0,39 0,32 0,20 0,18

Comm. Agr. Weekly 0,04 0,64

0,18 0,23 0,03 Monthly 0,04 0,53

0,48 0,55 0,02

Comm. Metals Weekly 0,19 0,60 0,12

0,58 0,60

Monthly 0,17 0,50 0,08

0,82 0,47

Comm. Energy Weekly 0,69 0,89 0,74 0,18

0,11 Monthly 0,50 0,89 0,79 0,44

0,06

TW USD Weekly 0,32 0,76 0,84 0,47 0,21 Monthly 0,24 0,82 0,89 0,51 0,22 Source: DataStream and own estimations. Figures in bold reflect significance at the 5% level.

57

Table 8: Aggregate CTA Regime Dependent Returns

Crisis Definition Aggregate Trend-‐Following

Unconditional 3,40% 5,62% Equity 1,68% 5,25% Fixed Income 3,30% 4,48% Comm. Agr. 1,31% 1,89% Comm. Energy 1,76% 3,35% Comm. Metals -‐7,76% -‐9,09% TW USD 7,60% 11,38% Source: RPM Risk and Portfolio Management AB and own calculations. Annualized returns are determined under the assumption of 260 trading days.

Table 9: Regime Dependent Correlations

RPM Aggregate RPM Trend-‐Following

Full Sample Crisis Full Sample Crisis

Equity 0,00 -‐0,28 -‐0,02 -‐0,32 Fixed Income 0,15 0,00 0,18 0,07 Comm. Agr. 0,08 0,05 0,07 0,06 Comm. Energy 0,09 0,01 0,10 0,00 Comm. Metals 0,19 0,09 0,17 0,10 TW USD -‐0,19 -‐0,38 -‐0,16 -‐0,35

Source: RPM Risk and Portfolio Management AB and own calculations

58

Table 10: Aggregate CTA HM Model

Aggregate Trend-‐Following Aggregate Trend-‐Following

Constant -‐0,00 0,00 -‐0,00 0,00 (0,06) (0,45) (0,05) (0,42)

Equity 0,06 0,09 0,08 0,12 (0,02) (0,01) (0,00) (0,00)

Equity * D -‐0,17 -‐0,27 -‐0,07 -‐0,14 (0,00) (0,00) (0,11) (0,02)

Fixed Income 0,39 0,63 0,41 0,66 (0,00) (0,00) (0,00) (0,00)

Fixed Income * D -‐0,25 -‐0,32 -‐0,24 -‐0,30 (0,02) (0,03) (0,03) (0,05)

Comm. Agr. 0,01 0,02 0,01 0,02 (0,29) (0,18) (0,26) (0,16)

Comm. Agr. * D -‐0,01 -‐0,01 0,00 -‐0,00 (0,73) (0,62) (0,92) (0,99)

Comm. Energy 0,03 0,05 0,03 0,05 (0,00) (0,00) (0,00) (0,00)

Comm. Energy * D -‐0,04 -‐0,06 -‐0,04 -‐0,05 (0,01) (0,01) (0,02) (0,04)

Comm. Metals 0,05 0,07 0,05 0,06 (0,00) (0,00) (0,00) (0,00)

Comm. Metals * D -‐0,01 0,00 0,00 0,01 (0,84) (0,94) (1,00) (0,78)

TW USD -‐0,01 0,03 -‐0,01 0,02 (0,88) (0,65) (0,74) (0,77)

TW USD * D -‐0,25 -‐0,31 -‐0,25 -‐0,32 (0,00) (0,00) (0,00) (0,00)

Equity * VIX -‐0,48 -‐0,66

(0,00) (0,00)

𝑅! 0,15 0,15 0,17 0,17 𝑅!"#! 0,15 0,15 0,16 0,17

Sources: DataStream, Federal Reserve Bank of St. Louis, RPM Risk and Portfolio Management AB and own estimations. Values in parenthesis are p-‐values and significant estimates at the 5% level of significance are highlighted in bold. All models employ Newey-‐West heteroskedasticity and autocorrelation consistent standard errors that are valid asymptotically.

59

Table 11: Sector Regime Dependent Performance

Crisis Definition Equity Fixed Income Soft Comm.

Aggr. TF Aggr. TF Aggr. TF Equity -‐2,39% -‐3,87% 7,05% 10,63% 0,65% 1,52% Fixed Income 2,48% 3,81% -‐0,49% -‐1,22% 0,37% 0,32% Comm. Agr. 0,21% 0,45% 2,51% 3,36% 0,05% 0,09% Comm. Energy 0,60% 1,46% 2,21% 2,50% -‐0,23% -‐0,16% Comm. Metals -‐3,55% -‐6,50% 3,66% 3,92% -‐1,03% -‐1,46% TW USD 0,79% 1,77% 1,80% 2,85% 0,16% 0,11%

Crisis Definition Comm. Energy Comm. Metals TW USD

Aggr. TF Aggr. TF Aggr. TF

Equity -‐7,99% -‐4,78% -‐0,01% 0,48% -‐1,49% -‐1,24% Fixed Income 0,80% 1,34% 0,91% 1,17% 1,00% 1,23% Comm. Agr. -‐1,01% -‐1,55% -‐0,13% -‐0,13% 0,55% 0,35% Comm. Energy -‐2,17% -‐3,52% 0,02% 0,25% 0,95% 1,61% Comm. Metals -‐0,66% -‐0,59% -‐2,91% -‐3,54% -‐2,90% -‐2,28% TW USD -‐0,88% -‐1,18% 0,99% 1,16% 4,85% 6,26% Source: RPM Risk and Portfolio Management AB and own calculations. Annualized returns are determined under the assumption of 260 trading days. Figures in bold reflect positive returns during the crisis regime.

60

Table 12: Equity and Fixed Income Sector HM Model

Equity Fixed Income

Aggr. TF Aggr. TF Aggr. TF Aggr. TF

Constant 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 (0,00) (0,03) (0,00) (0,02) (0,89) (0,09) (0,86) (0,08)

Equity 0,10 0,15 0,11 0,17 -‐0,04 -‐0,06 -‐0,05 -‐0,07 (0,00) (0,00) (0,00) (0,00) (0,00) (0,00) (0,00) (0,00)

Equity * D -‐0,12 -‐0,21 -‐0,06 -‐0,11 0,01 0,00 -‐0,02 -‐0,03 (0,00) (0,00) (0,01) (0,00) (0,47) (0,74) (0,06) (0,01)

Fixed Income -‐0,01 -‐0,02 0,00 0,00 0,26 0,49 0,25 0,48 (0,46) (0,41) (0,94) (0,89) (0,00) (0,00) (0,00) (0,00)

Fixed Income * D 0,01 0,04 0,02 0,05 -‐0,27 -‐0,20 -‐0,27 -‐0,20 (0,72) (0,37) (0,64) (0,31) (0,00) (0,01) (0,00) (0,01)

Comm. Agr. -‐0,00 -‐0,00 -‐0,00 -‐0,00 0,01 0,01 0,01 0,01 (0,32) (0,29) (0,35) (0,32) (0,00) (0,01) (0,00) (0,01)

Comm. Agr. * D -‐0,00 -‐0,01 0,00 -‐0,00 -‐0,01 -‐0,00 -‐0,01 -‐0,01 (0,58) (0,23) (0,74) (0,91) (0,22) (0,50) (0,07) (0,21)

Comm. Energy 0,01 0,00 0,01 0,00 -‐0,00 -‐0,00 -‐0,00 -‐0,00 (0,04) (0,25) (0,02) (0,19) (0,13) (0,34) (0,12) (0,33)

Comm. Energy * D -‐0,00 0,00 0,00 0,01 -‐0,00 0,00 -‐0,00 -‐0,00 (0,50) (1,00) (0,85) (0,26) (0,92) (0,71) (0,50) (0,86)

Comm. Metals 0,01 0,01 0,00 0,00 -‐0,00 -‐0,00 -‐0,00 -‐0,00 (0,10) (0,18) (0,37) (0,68) (0,55) (0,23) (0,89) (0,47)

Comm. Metals * D 0,01 0,02 0,01 0,03 -‐0,00 -‐0,00 -‐0,01 -‐0,01 (0,30) (0,07) (0,13) (0,02) (0,52) (0,53) (0,37) (0,37)

TW USD 0,02 0,05 0,02 0,04 -‐0,01 -‐0,02 -‐0,01 -‐0,02 (0,11) (0,01) (0,18) (0,03) (0,37) (0,10) (0,47) (0,14)

TW USD * D 0,01 -‐0,01 0,01 -‐0,01 -‐0,00 -‐0,02 -‐0,00 -‐0,02 (0,56) (0,84) (0,61) (0,70) (0,75) (0,40) (0,80) (0,44)

Equity * VIX

-‐0,29 -‐0,47

0,13 0,18

(0,00) (0,00)

(0,00) (0,00)

𝑅! 0,20 0,22 0,25 0,28 0,19 0,27 0,20 0,28 𝑅!"#! 0,19 0,22 0,25 0,28 0,18 0,27 0,20 0,28


61

Table 13: Soft and Energy Commodities Sector HM Model

Soft Commodities Energy Commodities


Constant 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 (0,00) (0,00) (0,00) (0,00) (0,00) (0,01) (0,00) (0,01)

Equity 0,00 0,00 0,00 0,00 -‐0,00 -‐0,00 0,00 0,00 (0,59) (0,64) (0,16) (0,18) (0,57) (0,45) (0,66) (0,74)

Equity * D -‐0,01 -‐0,02 -‐0,00 -‐0,00 -‐0,01 -‐0,01 0,01 0,02 (0,00) (0,00) (0,58) (0,63) (0,15) (0,30) (0,23) (0,10)

Fixed Income -‐0,01 -‐0,02 -‐0,01 -‐0,01 0,03 0,03 0,03 0,04 (0,22) (0,18) (0,37) (0,30) (0,09) (0,22) (0,04) (0,11)

Fixed Income * D -‐0,01 -‐0,01 -‐0,01 -‐0,01 -‐0,02 -‐0,02 -‐0,02 -‐0,02 (0,67) (0,73) (0,72) (0,78) (0,46) (0,60) (0,52) (0,67)

Comm. Agr. 0,01 0,01 0,01 0,01 -‐0,01 -‐0,01 -‐0,01 -‐0,01 (0,06) (0,02) (0,06) (0,02) (0,08) (0,03) (0,08) (0,03)

Comm. Agr. * D -‐0,00 -‐0,01 -‐0,00 -‐0,00 0,01 0,02 0,02 0,02 (0,77) (0,53) (0,89) (0,64) (0,03) (0,02) (0,01) (0,01)

Comm. Energy 0,00 0,00 0,00 0,00 0,03 0,04 0,03 0,04 (0,73) (0,43) (0,73) (0,43) (0,00) (0,00) (0,00) (0,00)

Comm. Energy * D -‐0,00 -‐0,01 -‐0,00 -‐0,01 -‐0,03 -‐0,04 -‐0,02 -‐0,04 (0,03) (0,01) (0,06) (0,02) (0,00) (0,00) (0,00) (0,00)

Comm. Metals 0,00 0,00 0,00 0,00 0,01 0,01 0,01 0,01 (0,15) (0,24) (0,26) (0,39) (0,03) (0,01) (0,06) (0,03)

Comm. Metals * D -‐0,00 -‐0,00 -‐0,00 -‐0,00 0,00 0,00 0,00 0,01 (0,35) (0,54) (0,43) (0,63) (0,83) (0,69) (0,71) (0,57)

TW USD 0,01 0,01 0,01 0,01 -‐0,01 -‐0,01 -‐0,01 -‐0,01 (0,03) (0,03) (0,04) (0,04) (0,45) (0,50) (0,35) (0,39)

TW USD * D -‐0,00 -‐0,00 -‐0,00 -‐0,00 0,02 0,03 0,02 0,03 (0,96) (0,92) (0,92) (0,88) (0,13) (0,08) (0,13) (0,08)

Equity * VIX

-‐0,05 -‐0,07

-‐0,11 -‐0,17

(0,00) (0,00)

(0,00) (0,00)

𝑅! 0,03 0,03 0,04 0,04 0,08 0,09 0,09 0,10 𝑅!"#! 0,03 0,03 0,03 0,04 0,08 0,09 0,09 0,10


62

Table 14: Commodity Metals and Currencies Sector HM Model

Metal Commodities Composite Currencies


Constant 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 (0,00) (0,00) (0,00) (0,00) (0,02) (0,11) (0,02) (0,10)

Equity -‐0,00 -‐0,00 0,00 0,00 0,02 0,03 0,03 0,04 (0,41) (0,75) (0,99) (0,69) (0,03) (0,01) (0,00) (0,00)

Equity * D -‐0,01 -‐0,01 0,00 0,00 -‐0,03 -‐0,05 0,00 -‐0,01 (0,04) (0,03) (0,48) (0,83) (0,01) (0,00) (0,82) (0,72)

Fixed Income 0,01 0,01 0,01 0,02 0,00 -‐0,04 0,01 -‐0,04 (0,27) (0,29) (0,14) (0,18) (0,98) (0,14) (0,71) (0,24)

Fixed Income * D -‐0,01 -‐0,02 -‐0,01 -‐0,02 0,10 0,06 0,11 0,06 (0,46) (0,24) (0,51) (0,27) (0,02) (0,31) (0,02) (0,28)

Comm. Agr. 0,00 0,00 0,00 0,00 -‐0,00 0,00 -‐0,00 0,00 (0,05) (0,08) (0,04) (0,08) (0,88) (0,62) (0,91) (0,59)

Comm. Agr. * D -‐0,00 -‐0,01 -‐0,00 -‐0,01 -‐0,00 -‐0,01 -‐0,00 -‐0,00 (0,20) (0,17) (0,34) (0,28) (0,50) (0,32) (0,84) (0,58)

Comm. Energy 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 (0,01) (0,01) (0,01) (0,01) (0,72) (0,43) (0,72) (0,42)

Comm. Energy * D -‐0,01 -‐0,01 -‐0,01 -‐0,01 -‐0,00 -‐0,00 -‐0,00 0,00 (0,00) (0,00) (0,00) (0,00) (0,40) (0,72) (0,71) (0,96)

Comm. Metals 0,02 0,03 0,02 0,03 0,02 0,02 0,02 0,02 (0,00) (0,00) (0,00) (0,00) (0,00) (0,00) (0,00) (0,00)

Comm. Metals * D -‐0,01 -‐0,02 -‐0,01 -‐0,02 0,00 0,01 0,01 0,01 (0,12) (0,14) (0,14) (0,16) (0,69) (0,62) (0,54) (0,49)

TW USD 0,02 0,04 0,01 0,03 -‐0,00 0,02 -‐0,00 0,02 (0,02) (0,00) (0,03) (0,00) (0,92) (0,45) (0,85) (0,50)

TW USD * D -‐0,05 -‐0,07 -‐0,05 -‐0,07 -‐0,22 -‐0,25 -‐0,22 -‐0,25 (0,00) (0,00) (0,00) (0,00) (0,00) (0,00) (0,00) (0,00)

Equity * VIX

-‐0,06 -‐0,07

-‐0,17 -‐0,20

(0,00) (0,01)

(0,00) (0,00)

𝑅! 0,13 0,10 0,14 0,11 0,10 0,08 0,11 0,08 𝑅!"#! 0,13 0,10 0,13 0,11 0,10 0,07 0,11 0,08


63

Table 15: HM Model Aggregate Robustness to Alternative CTA Index

Newedge CTA Index

Aggregate Trend-‐Following Aggregate Trend-‐Following

Constant -‐0,00 -‐0,00 -‐0,00 -‐0,00 (0,19) (0,16) (0,18) (0,14)

Equity 0,03 0,08 0,05 0,10 (0,22) (0,05) (0,02) (0,00)

Equity * D -‐0,15 -‐0,30 -‐0,06 -‐0,17 (0,00) (0,00) (0,09) (0,02)

Fixed Income 0,45 0,77 0,47 0,80 (0,00) (0,00) (0,00) (0,00)

Fixed Income * D -‐0,36 -‐0,51 -‐0,35 -‐0,50 (0,00) (0,02) (0,00) (0,02)

Comm. Agr. 0,02 0,03 0,02 0,03 (0,04) (0,05) (0,03) (0,05)

Comm. Agr. * D -‐0,01 -‐0,02 -‐0,00 -‐0,00 (0,48) (0,57) (0,83) (0,89)

Comm. Energy 0,03 0,06 0,03 0,06 (0,00) (0,00) (0,00) (0,00)

Comm. Energy * D -‐0,03 -‐0,04 -‐0,02 -‐0,03 (0,07) (0,11) (0,16) (0,22)

Comm. Metals 0,05 0,08 0,05 0,08 (0,00) (0,00) (0,00) (0,00)

Comm. Metals * D -‐0,01 -‐0,00 -‐0,01 0,00 (0,50) (0,91) (0,63) (0,94)

TW USD 0,04 0,04 0,04 0,03 (0,33) (0,54) (0,40) (0,63)

TW USD * D -‐0,31 -‐0,42 -‐0,31 -‐0,42 (0,00) (0,00) (0,00) (0,00)

Equity * VIX

-‐0,44 -‐0,65

(0,00) (0,00)

𝑅! 0,15 0,15 0,16 0,16 𝑅!"#! 0,14 0,15 0,16 0,16 Sources: DataStream, Federal Reserve Bank of St. Louis, RPM Risk and Portfolio Management AB and own estimations. Values in parenthesis are p-‐values and significant estimates at the 5% level of significance are highlighted in bold. All models employ Newey-‐West heteroskedasticity and autocorrelation consistent standard errors that are valid asymptotically. Underlined p-‐values reflect inconsistency with the results from table 10.

64

Table 16: HM Model Aggregate Robustness to Daniel and Moskowitz (2013) Bear Market Identification

Newedge CTA Index RPM CTA Index


Constant 0,00 0,00 -‐0,00 -‐0,00 -‐0,00 0,00 -‐0,00 0,00

(0,44) (0,67) (0,97) (0,76) (1,00) (0,23) (0,36) (0,79)

Equity 0,05 0,12 0,06 0,14 0,06 0,11 0,08 0,13

(0,05) (0,00) (0,01) (0,00) (0,02) (0,00) (0,00) (0,00)

Equity * D -‐0,15 -‐0,30 -‐0,06 -‐0,16 -‐0,17 -‐0,24 -‐0,03 -‐0,09

(0.00) (0.00) (0,10) (0,01) (0,00) (0.00) (0,48) (0,10)

Fixed Income 0,56 0,97 0,59 1,02 0,39 0,78 0,55 0,84

(0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00)

Fixed Income * D -‐0,64 -‐1,06 -‐0,68 -‐1,12 -‐0,25 -‐0,74 -‐0,63 -‐0,81

(0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00)

Comm. Agr. 0,02 0,04 0,02 0,04 0,01 0,02 0,02 0,03

(0,05) (0,03) (0,01) (0,01) (0,22) (0,09) (0,08) (0,02)

Comm. Agr. * D -‐0,01 -‐0,04 -‐0,02 -‐0,05 -‐0,01 -‐0,03 -‐0,02 -‐0,04

(0,46) (0,23) (0,19) (0,08) (0,47) (0,25) (0,19) (0,08)

Comm. Energy 0,03 0,06 0,04 0,07 0,03 0,03 0,03 0,04

(0,00) (0,00) (0,00) (0.00) (0,04) (0,01) (0,01) (0,00)

Comm. Energy * D -‐0,02 -‐0,03 -‐0,03 -‐0,04 -‐0,04 -‐0,02 -‐0,02 -‐0,03

(0,20) (0,18) (0,06) (0,06) (0,46) (0,43) (0,19) (0,15)

Comm. Metals 0,07 0,11 0,06 0,10 0,05 0,12 0,08 0,11

(0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00)

Comm. Metals * D -‐0,06 -‐0,09 -‐0,06 -‐0,08 -‐0,01 -‐0,13 -‐0,09 -‐0,12

(0,01) (0,02) (0,01) (0,03) (0,00) (0,00) (0,00) (0,00)

TW USD 0,06 0,01 0,04 -‐0,02 -‐0,01 0,03 0,05 -‐0,00

(0,30) (0,89) (0,48) (0,87) (0,10) (0,68) (0,25) (0,98)

TW USD * D -‐0,24 -‐0,25 -‐0,21 -‐0,21 -‐0,25 -‐0,23 -‐0,27 -‐0,19

(0,00) (0,04) (0,00) (0,08) (0.00) (0,01) (0.00) (0,03)

Equity * VIX -‐0,47 -‐0,74

-‐0,54 -‐0,76

(0,00) (0,00)

(0,00) (0.00)

𝑅! 0,16 0,15 0,18 0,19 0,18 0,17 0,20 0,20 𝑅!"#! 0,16 0,15 0,18 0,18 0,18 0,17 0,20 0,20 Sources: DataStream, Federal Reserve Bank of St. Louis, RPM Risk and Portfolio Management AB and own estimations. Values in parenthesis are p-‐values and significant estimates at the 5% level of significance are highlighted in bold. All models employ Newey-‐West heteroskedasticity and autocorrelation consistent standard errors that are valid asymptotically. Underlined p-‐values reflect inconsistency with the results from table 10.

65

Table 17: HM Model Aggregate Robustness to BMA Indicator



Constant -‐0,00 -‐0,00 -‐0,00 -‐0,00 -‐0,00 -‐0,00 -‐0,00 -‐0,00 (0,07) (0,08) (0,05) (0,06) (0,02) (0,28) (0,01) (0,21)

Equity 0,02 0,04 0,04 0,08 0,04 0,06 0,07 0,10 (0,37) (0,37) (0,04) (0,04) (0,08) (0,08) (0,00) (0,00)

Equity * D -‐0,13 -‐0,22 -‐0,04 -‐0,06 -‐0,14 -‐0,20 -‐0,04 -‐0,05 (0.00) (0.00) (0,22) (0,34) (0.00) (0.00) (0,35) (0,38)

Fixed Income 0,43 0,74 0,46 0,78 0,37 0,63 0,40 0,67 (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00)

Fixed Income * D -‐0,35 -‐0,50 -‐0,33 -‐0,46 -‐0,26 -‐0,38 -‐0,23 -‐0,34 (0,00) (0,02) (0,01) (0,04) (0,02) (0,01) (0,05) (0,03)

Comm. Agr. 0,03 0,04 0,03 0,05 0,02 0,03 0,02 0,03 (0,02) (0,02) (0,01) (0,01) (0,10) (0,05) (0,08) (0,04)

Comm. Agr. * D -‐0,02 -‐0,04 -‐0,02 -‐0,03 -‐0,02 -‐0,04 -‐0,01 -‐0,02 (0,15) (0,15) (0,34) (0,33) (0,24) (0,15) (0,48) (0,35)

Comm. Energy 0,04 0,07 0,04 0,07 0,03 0,05 0,03 0,05 (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00)

Comm. Energy * D -‐0,04 -‐0,07 -‐0,03 -‐0,05 -‐0,05 -‐0,07 -‐0,04 -‐0,06 (0,02) (0,02) (0,05) (0,05) (0,00) (0,00) (0,01) (0,01)

Comm. Metals 0,07 0,11 0,06 0,10 0,07 0,10 0,06 0,08 (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00)

Comm. Metals * D -‐0,04 -‐0,06 -‐0,04 -‐0,05 -‐0,05 -‐0,05 -‐0,04 -‐0,04 (0,06) (0,15) (0,08) (0,21) (0,05) (0,15) (0,07) (0,21)

TW USD 0,04 0,01 0,05 0,03 -‐0,02 -‐0,01 -‐0,01 0,01 (0,45) (0,93) (0,32) (0,74) (0,69) (0,86) (0,91) (0,91)

TW USD * D -‐0,24 -‐0,28 -‐0,27 -‐0,33 -‐0,18 -‐0,19 -‐0,21 -‐0,24 (0,00) (0,02) (0,00) (0,01) (0,01) (0,04) (0,00) (0,01)

Equity * VIX -‐0,49 -‐0,84

-‐0,54 -‐0,81

(0,00) (0,00)

(0,00) (0,00)

𝑅! 0,14 0,14 0,16 0,16 0,14 0,14 0,17 0,17 𝑅!"#! 0,14 0,13 0,16 0,15 0,14 0,13 0,16 0,17

Sources: DataStream, Federal Reserve Bank of St. Louis, RPM Risk and Portfolio Management AB and own estimations. Values in parenthesis are p-‐values and significant estimates at the 5% level of significance are highlighted in bold. All models employ Newey-‐West heteroskedasticity and autocorrelation consistent standard errors that are valid asymptotically. Underlined p-‐values reflect inconsistency with the results from table 10.

66

Table 18: HM Model Aggregate Robustness to Chen and Liang (2007) Indicator



Constant 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 (0,00) (0,00) (0,00) (0,00) (0,03) (0,01) (0,00) (0,00)

Equity -‐0,08 -‐0,12 -‐0,01 -‐0,00 -‐0,44 -‐0,07 0,03 0,03 (0,00) (0,00) (0,74) (0,93) (0,04) (0,01) (0,27) (0,31)

Equity * D 0,02 0,03 0,08 0,13 0,00 0,02 0,06 0,11 (0,56) (0,61) (0,03) (0,05) (0,94) (0,76) (0,12) (0,04)

Fixed Income 0,26 0,42 0,32 0,52 0,24 0,43 0,30 0,52 (0,00) (0,00) (0,00) (0,00) (0,00) (0,00) (0,00) (0,00)

Fixed Income * D 0,07 0,24 0,06 0,21 0,06 0,09 0,04 0,06 (0,57) (0,29) (0,65) (0,34) (0,62) (0,59) (0,72) (0,69)

Comm. Agr. 0,01 0,02 0,01 0,03 0,04 0,01 0,01 0,02 (0,50) (0,40) (0,28) (0,22) (0,75) (0,54) (0,47) (0,29)

Comm. Agr. * D 0,01 0,01 0,01 0,01 0,00 -‐0,00 0,01 0,00 (0,78) (0,89) (0,64) (0,75) (0,94) (0,93) (0,80) (0,93)

Comm. Energy 0,02 0,03 0,02 0,04 0,01 0,02 0,02 0,03 (0,11) (0,07) (0,05) (0,03) (0,25) (0,11) (0,12) (0,04)

Comm. Energy * D -‐0,00 0,01 0,00 0,01 -‐0,01 -‐0,01 -‐0,00 -‐0,00 (0,98) (0,81) (0,83) (0,63) (0,71) (0,66) (0,92) (0,88)

Comm. Metals 0,02 0,05 0,01 0,03 0,03 0,04 0,02 0,02 (0,06) (0,04) (0,30) (0,20) (0,01) (0,05) (0,07) (0,29)

Comm. Metals * D 0,06 0,10 0,06 0,10 0,05 0,09 0,05 0,09 (0,01) (0,01) (0,01) (0,01) (0,02) (0,00) (0,01) (0,00)

TW USD -‐0,10 -‐0,21 -‐0,09 -‐0,19 -‐0,17 -‐0,20 -‐0,16 -‐0,18 (0,07) (0,02) (0,11) (0,04) (0,00) (0,01) (0,00) (0,02)

TW USD * D -‐0,00 0,08 -‐0,02 0,07 0,08 0,11 0,07 0,09 (0,95) (0,52) (0,84) (0,62) (0,23) (0,28) (0,31) (0,36)

Equity * VIX -‐0,65 -‐1,10

-‐0,70 -‐1,04

(0,00) (0,00) (0,00) (0,00)

𝑅! 0,08 0,09 0,14 0,15 0,08 0,09 0,15 0,16 𝑅!"#! 0,08 0,09 0,13 0,14 0,08 0,08 0,14 0,15


67

Table 19: HM Model Aggregate Robustness to the Exclusion of the Credit Crunch



Constant -‐0,00 -‐0,00 -‐0,00 -‐0,00 -‐0,00 -‐0,00 -‐0,00 -‐0,00 (0,24) (0,16) (0,14) (0,08) (0,27) (0,91) (0,18) (0,70)

Equity 0,02 0,06 0,03 0,07 0,07 0,11 0,07 0,11 (0,45) (0,28) (0,35) (0,20) (0,03) (0,03) (0,02) (0,02)

Equity * D -‐0,20 -‐0,42 -‐0,13 -‐0,27 -‐0,18 -‐0,32 -‐0,13 -‐0,23 (0,00) (0,00) (0,02) (0,01) (0,00) (0,00) (0,01) (0,00)

Fixed Income 0,32 0,66 0,32 0,66 0,17 0,51 0,17 0,51 (0,01) (0,01) (0,01) (0,01) (0,09) (0,00) (0,09) (0,00)

Fixed Income * D -‐0,30 -‐0,50 -‐0,32 -‐0,53 -‐0,18 -‐0,30 -‐0,19 -‐0,32 (0,09) (0,14) (0,08) (0,12) (0,16) (0,15) (0,14) (0,13)

Comm. Agr. 0,02 0,04 0,02 0,04 0,02 0,03 0,02 0,03 (0,05) (0,04) (0,05) (0,04) (0,14) (0,05) (0,15) (0,06)

Comm. Agr. * D 0,01 0,02 0,02 0,03 0,00 0,01 0,01 0,02 (0,67) (0,67) (0,49) (0,47) (0,93) (0,76) (0,75) (0,58)

Comm. Energy 0,05 0,09 0,05 0,09 0,04 0,06 0,04 0,06 (0,00) (0,00) (0,00) (0,00) (0,00) (0,00) (0,00) (0,00)

Comm. Energy * D -‐0,01 -‐0,02 -‐0,02 -‐0,03 -‐0,02 -‐0,02 -‐0,02 -‐0,03 (0,56) (0,56) (0,41) (0,39) (0,20) (0,36) (0,12) (0,23)

Comm. Metals 0,07 0,12 0,07 0,11 0,07 0,10 0,06 0,09 (0,00) (0,00) (0,00) (0,00) (0,00) (0,00) (0,00) (0,00)

Comm. Metals * D 0,01 0,02 0,01 0,02 0,04 0,06 0,04 0,06 (0,72) (0,62) (0,75) (0,64) (0,08) (0,11) (0,09) (0,12)

TW USD -‐0,18 -‐0,29 -‐0,18 -‐0,28 -‐0,27 -‐0,28 -‐0,27 -‐0,28 (0,02) (0,03) (0,02) (0,04) (0,00) (0,00) (0,00) (0,01)

TW USD * D -‐0,19 -‐0,25 -‐0,18 -‐0,23 -‐0,09 -‐0,10 -‐0,08 -‐0,09 (0,07) (0,17) (0,08) (0,21) (0,27) (0,42) (0,32) (0,49)

Equity * VIX

-‐0,71 -‐1,48

-‐0,58 -‐1,01

(0,04) (0,01)

(0,02) (0,02)


68

Table 20: HM Model Sectorial Robustness of Equity and Fixed Income Sectors to Daniel and Moskowitz (2013) Bear Market Identification

Equity Fixed Income


Constant -‐0,00 -‐0,00 -‐0,00 -‐0,00 0,00 0,00 0,00 0,00 (0,28) (0,91) (0,01) (0,09) (0,42) (0,03) (0,23) (0,01)

Equity 0,11 0,18 0,12 0,20 -‐0,05 -‐0,07 -‐0,05 -‐0,08 (0,00) (0,00) (0,00) (0,00) (0,00) (0,00) (0,00) (0,00)

Equity * D -‐0,11 -‐0,22 -‐0,05 -‐0,13 0,01 0,02 -‐0,01 0,00 (0,00) (0,00) (0,03) (0,00) (0,21) (0,03) (0,54) (0,87)

Fixed Income 0,01 0,05 0,04 0,09 0,26 0,48 0,26 0,47 (0,51) (0,06) (0,04) (0,00) (0,00) (0,00) (0,00) (0,00)

Fixed Income * D -‐0,04 -‐0,11 -‐0,07 -‐0,15 -‐0,30 -‐0,19 -‐0,29 -‐0,18 (0,26) (0,02) (0,08) (0,00) (0,00) (0,01) (0,00) (0,02)

Comm. Agr. -‐0,01 -‐0,01 -‐0,00 -‐0,00 0,01 0,01 0,01 0,01 (0,10) (0,06) (0,46) (0,34) (0,00) (0,00) (0,01) (0,01)

Comm. Agr. * D 0,01 0,02 0,01 0,01 -‐0,01 -‐0,00 -‐0,00 -‐0,00 (0,03) (0,04) (0,26) (0,34) (0,27) (0,58) (0,44) (0,81)

Comm. Energy -‐0,00 -‐0,01 0,00 0,00 -‐0,01 -‐0,01 -‐0,01 -‐0,01 (0,72) (0,12) (0,20) (0,82) (0,02) (0,05) (0,00) (0,02)

Comm. Energy * D 0,01 0,02 0,01 0,01 0,00 0,01 0,00 0,01 (0,03) (0,00) (0,28) (0,02) (0,35) (0,09) (0,19) (0,04)

Comm. Metals 0,01 0,01 0,00 0,00 0,00 -‐0,00 0,00 -‐0,00 (0,11) (0,11) (0,44) (0,47) (0,90) (0,70) (0,66) (0,92)

Comm. Metals * D 0,01 0,02 0,01 0,02 -‐0,01 -‐0,01 -‐0,01 -‐0,01 (0,18) (0,11) (0,06) (0,03) (0,18) (0,21) (0,13) (0,16)

TW USD 0,02 0,01 0,00 -‐0,01 -‐0,03 -‐0,04 -‐0,03 -‐0,03 (0,30) (0,68) (0,81) (0,70) (0,03) (0,09) (0,05) (0,14)

TW USD * D 0,00 0,04 0,02 0,06 0,02 -‐0,00 0,02 -‐0,01 (0,99) (0,18) (0,35) (0,02) (0,18) (0,99) (0,29) (0,80)

Equity * VIX -‐0,33 -‐0,48

0,09 0,11

(0,00) (0,00)

(0,00) (0,00)


69

Table 21: HM Model Sectorial Robustness of Soft Commodities and Commodities Energy Sectors to Daniel and Moskowitz (2013) Bear Market Identification



Constant -‐0,00 -‐0,00 -‐0,00 -‐0,00 -‐0,00 -‐0,00 -‐0,00 -‐0,00 (0,00) (0,00) (0,00) (0,00) (0,00) (0,04) (0,00) (0,01)

Equity -‐0,00 -‐0,00 0,00 0,00 -‐0,00 -‐0,01 0,00 -‐0,00 (0,67) (0,77) (0,92) (0,79) (0,74) (0,43) (0,80) (0,89)

Equity * D -‐0,01 -‐0,01 0,01 0,01 -‐0,01 -‐0,00 0,02 0,03 (0,10) (0,06) (0,18) (0,23) (0,40) (0,83) (0,06) (0,01)

Fixed Income -‐0,02 -‐0,03 -‐0,02 -‐0,03 -‐0,01 -‐0,03 -‐0,00 -‐0,02 (0,01) (0,01) (0,03) (0,05) (0,46) (0,15) (0,93) (0,40)

Fixed Income * D 0,03 0,04 0,03 0,03 0,04 0,07 0,03 0,06 (0,01) (0,03) (0,04) (0,09) (0,12) (0,05) (0,25) (0,12)

Comm. Agr. 0,02 0,03 0,02 0,03 -‐0,00 -‐0,01 -‐0,00 -‐0,00 (0,00) (0,00) (0,00) (0,00) (0,41) (0,21) (0,66) (0,40)

Comm. Agr. * D -‐0,04 -‐0,06 -‐0,04 -‐0,07 0,01 0,01 0,00 0,01 (0,00) (0,00) (0,00) (0,00) (0,28) (0,17) (0,44) (0,30)

Comm. Energy -‐0,00 -‐0,00 -‐0,00 -‐0,00 0,03 0,05 0,03 0,05 (0,30) (0,27) (0,73) (0,64) (0,00) (0,00) (0,00) (0,00)

Comm. Energy * D -‐0,00 0,00 -‐0,00 -‐0,00 -‐0,04 -‐0,07 -‐0,05 -‐0,07 (0,83) (0,97) (0,51) (0,69) (0,00) (0,00) (0,00) (0,00)

Comm. Metals 0,01 0,01 0,01 0,01 0,01 0,02 0,01 0,02 (0,00) (0,00) (0,00) (0,00) (0,00) (0,00) (0,00) (0,00)

Comm. Metals * D -‐0,01 -‐0,02 -‐0,01 -‐0,02 -‐0,01 -‐0,02 -‐0,01 -‐0,02 (0,00) (0,00) (0,00) (0,00) (0,04) (0,04) (0,05) (0,05)

TW USD 0,01 0,01 0,01 0,01 0,01 0,02 0,01 0,01 (0,06) (0,19) (0,09) (0,30) (0,36) (0,38) (0,60) (0,64)

TW USD * D -‐0,01 -‐0,00 -‐0,00 0,00 -‐0,02 -‐0,02 -‐0,01 -‐0,01 (0,35) (0,70) (0,55) (1,00) (0,23) (0,31) (0,43) (0,57)

Equity * VIX -‐0,06 -‐0,09

-‐0,12 -‐0,18

(0,00) (0,00)

(0,00) (0,00)


70

Table 22: HM Model Sectorial Robustness of Commodities Metals and Composite Currencies Sectors to Daniel and Moskowitz (2013) Bear Market Identification



Constant -‐0,00 -‐0,00 -‐0,00 -‐0,00 -‐0,00 -‐0,00 -‐0,00 -‐0,00 (0,00) (0,01) (0,00) (0,00) (0,11) (0,44) (0,05) (0,29)

Equity -‐0,02 -‐0,02 -‐0,02 -‐0,02 0,04 0,06 0,04 0,06 (0,00) (0,00) (0,00) (0,00) (0,00) (0,00) (0,00) (0,00)

Equity * D 0,02 0,03 0,04 0,05 -‐0,05 -‐0,08 -‐0,03 -‐0,06 (0,00) (0,00) (0,00) (0,00) (0,00) (0,00) (0,01) (0,00)

Fixed Income 0,01 0,02 0,02 0,03 0,10 0,08 0,10 0,09 (0,11) (0,13) (0,01) (0,02) (0,00) (0,01) (0,00) (0,00)

Fixed Income * D -‐0,03 -‐0,05 -‐0,03 -‐0,06 -‐0,12 -‐0,23 -‐0,12 -‐0,24 (0,03) (0,01) (0,01) (0,00) (0,01) (0,00) (0,01) (0,00)

Comm. Agr. 0,00 0,00 0,00 0,00 -‐0,00 -‐0,00 -‐0,00 0,00 (0,36) (0,38) (0,13) (0,15) (0,41) (0,89) (0,54) (0,93)

Comm. Agr. * D 0,00 0,00 0,00 0,00 0,00 0,00 0,00 -‐0,00 (0,44) (0,61) (0,75) (0,94) (0,52) (0,97) (0,68) (0,85)

Comm. Energy -‐0,00 -‐0,00 -‐0,00 -‐0,00 0,00 0,01 0,00 0,01 (0,15) (0,03) (0,61) (0,18) (0,67) (0,23) (0,47) (0,14)

Comm. Energy * D 0,01 0,01 0,01 0,01 0,00 -‐0,00 -‐0,00 -‐0,00 (0,00) (0,00) (0,01) (0,00) (0,98) (0,73) (0,81) (0,55)

Comm. Metals 0,04 0,06 0,04 0,06 0,02 0,02 0,02 0,02 (0,00) (0,00) (0,00) (0,00) (0,00) (0,00) (0,00) (0,00)

Comm. Metals * D -‐0,06 -‐0,09 -‐0,06 -‐0,09 -‐0,01 -‐0,01 -‐0,01 -‐0,01 (0,00) (0,00) (0,00) (0,00) (0,12) (0,50) (0,14) (0,55)

TW USD 0,02 0,03 0,02 0,03 0,09 0,08 0,09 0,07 (0,00) (0,01) (0,02) (0,02) (0,00) (0,03) (0,00) (0,05)

TW USD * D -‐0,05 -‐0,05 -‐0,04 -‐0,05 -‐0,27 -‐0,23 -‐0,26 -‐0,22 (0,00) (0,00) (0,00) (0,00) (0,00) (0,00) (0,00) (0,00)

Equity * VIX -‐0,09 -‐0,12

-‐0,09 -‐0,11

(0,00) (0,00)

(0,01) (0,01)

𝑅! 0,25 0,22 0,27 0,23 0,14 0,09 0,14 0,09 𝑅!"#! 0,24 0,21 0,27 0,23 0,14 0,09 0,14 0,09


71

Table 23: HM Model Sectorial Robustness of Equity and Fixed Income Sectors to BMA Indicator

Equity Fixed Income


Constant -‐0,00 -‐0,00 -‐0,00 0,00 0,00 0,00 0,00 0,00

(0,00) (0,02) (0,00) (0,01) (0,92) (0,09) (0,85) (0,08)

Equity 0,12 0,16 0,13 0,18 -‐0,05 -‐0,06 -‐0,05 -‐0,07

(0,00) (0,00) (0,00) (0,00) (0,00) (0,00) (0,00) (0,00)

Equity * D -‐0,14 -‐0,21 -‐0,09 -‐0,12 0,01 0,00 -‐0,01 -‐0,03

(0,00) (0,00) (0,00) (0,00) (0,21) (0,86) (0,24) (0,01)

Fixed Income -‐0,02 -‐0,03 -‐0,00 0,00 0,22 0,47 0,22 0,46

(0,30) (0,25) (0,80) (0,85) (0,00) (0,00) (0,00) (0,00)

Fixed Income * D 0,00 0,02 0,01 0,05 -‐0,17 -‐0,14 -‐0,18 -‐0,15

(0,99) (0,57) (0,70) (0,30) (0,00) (0,06) (0,00) (0,05)

Comm. Agr. -‐0,00 -‐0,00 -‐0,00 0,00 0,01 0,01 0,01 0,01

(0,12) (0,27) (0,15) (0,33) (0,00) (0,01) (0,00) (0,01)

Comm. Agr. * D -‐0,00 -‐0,01 0,00 0,00 -‐0,01 -‐0,00 -‐0,01 -‐0,01

(0,94) (0,16) (0,44) (0,81) (0,21) (0,49) (0,09) (0,24)

Comm. Energy 0,00 0,00 0,00 0,00 0,00 -‐0,00 -‐0,00 0,00

(0,07) (0,32) (0,04) (0,28) (0,17) (0,48) (0,18) (0,50)

Comm. Energy * D 0,00 0,00 0,00 0,01 0,00 0,00 -‐0,00 0,00

(0,80) (0,81) (0,46) (0,12) (0,74) (0,90) (0,35) (0,62)

Comm. Metals 0,00 0,01 -‐0,00 0,00 0,00 -‐0,00 0,00 0,00

(0,26) (0,13) (1,00) (0,90) (0,96) (0,44) (0,56) (0,84)

Comm. Metals * D 0,02 0,03 0,02 0,03 -‐0,01 -‐0,01 -‐0,01 -‐0,01

(0,01) (0,01) (0,00) (0,00) (0,17) (0,26) (0,11) (0,17)

TW USD 0,02 0,04 0,03 0,05 0,00 -‐0,02 -‐0,00 -‐0,03

(0,15) (0,08) (0,06) (0,02) (0,99) (0,14) (0,81) (0,08)

TW USD * D -‐0,00 -‐0,01 -‐0,02 -‐0,03 -‐0,02 -‐0,01 -‐0,01 0,00

(0,94) (0,82) (0,34) (0,19) (0,20) (0,64) (0,40) (0,98)

Equity * VIX -‐0,26 -‐0,49

0,12 0,17

(0,00) (0,00) (0,00) (0,00)

𝑅! 0,23 0,21 0,28 0,29 0,17 0,27 0,18 0,28

𝑅!"#! 0,23 0,21 0,28 0,29 0,17 0,27 0,18 0,28


72

Table 24: HM Model Sectorial Robustness of Soft Commodities and Commodities Energy Sectors to BMA Indicator



Constant -‐0,00 -‐0,00 -‐0,00 -‐0,00 -‐0,00 -‐0,00 -‐0,00 -‐0,00

(0,00) (0,00) (0,00) (0,00) (0,00) (0,01) (0,00) (0,01)

Equity -‐0,00 -‐0,00 0,00 0,00 -‐0,01 -‐0,02 -‐0,01 -‐0,01

(0,82) (0,47) (0,46) (0,73) (0,04) (0,01) (0,33) (0,13)

Equity * D -‐0,01 -‐0,01 0,00 0,01 0,00 0,01 0,03 0,05

(0,04) (0,13) (0,57) (0,24) (0,62) (0,21) (0,00) (0,00)

Fixed Income -‐0,01 -‐0,01 -‐0,01 -‐0,01 0,03 0,03 0,04 0,04

(0,27) (0,20) (0,46) (0,37) (0,04) (0,10) (0,01) (0,03)

Fixed Income * D -‐0,01 -‐0,02 -‐0,01 -‐0,01 -‐0,03 -‐0,04 -‐0,02 -‐0,03

(0,44) (0,52) (0,54) (0,63) (0,23) (0,31) (0,34) (0,44)

Comm. Agr. 0,01 0,02 0,01 0,02 -‐0,00 -‐0,01 -‐0,00 -‐0,01

(0,01) (0,00) (0,01) (0,00) (0,28) (0,16) (0,29) (0,17)

Comm. Agr. * D -‐0,01 -‐0,01 -‐0,01 -‐0,01 0,01 0,01 0,01 0,02

(0,19) (0,12) (0,25) (0,16) (0,19) (0,13) (0,10) (0,06)

Comm. Energy 0,00 0,00 0,00 0,00 0,03 0,04 0,03 0,04

(0,72) (0,42) (0,73) (0,42) (0,00) (0,00) (0,00) (0,00)

Comm. Energy * D -‐0,00 -‐0,01 -‐0,00 -‐0,01 -‐0,03 -‐0,05 -‐0,03 -‐0,05

(0,04) (0,01) (0,09) (0,02) (0,00) (0,00) (0,00) (0,00)

Comm. Metals 0,00 0,01 0,00 0,00 0,01 0,01 0,01 0,01

(0,03) (0,04) (0,08) (0,12) (0,01) (0,00) (0,02) (0,01)

Comm. Metals * D -‐0,01 -‐0,01 -‐0,00 -‐0,01 -‐0,00 0,00 -‐0,00 0,00

(0,10) (0,14) (0,14) (0,19) (0,74) (0,97) (0,88) (0,82)

TW USD 0,01 0,02 0,01 0,02 -‐0,01 -‐0,02 -‐0,01 -‐0,01

(0,03) (0,04) (0,02) (0,02) (0,27) (0,22) (0,40) (0,34)

TW USD * D -‐0,00 -‐0,01 -‐0,01 -‐0,01 0,02 0,04 0,02 0,03

(0,61) (0,59) (0,35) (0,33) (0,12) (0,05) (0,24) (0,11)

Equity * VIX -‐0,05 -‐0,09

-‐0,12 -‐0,18

(0,00) (0,00) (0,00) (0,00)

𝑅! 0,03 0,04 0,04 0,05 0,09 0,10 0,10 0,12

𝑅!"#! 0,03 0,03 0,04 0,05 0,09 0,10 0,10 0,11


73

Table 25: HM Model Sectorial Robustness of Commodities Metals and Composite Currencies Sectors to BMA Indicator



Constant -‐0,00 -‐0,00 -‐0,00 -‐0,00 -‐0,00 -‐0,00 -‐0,00 -‐0,00

(0,00) (0,00) (0,00) (0,00) (0,00) (0,05) (0,00) (0,04)

Equity -‐0,00 -‐0,00 0,00 0,00 0,01 0,01 0,02 0,02

(0,46) (0,77) (1,00) (0,72) (0,35) (0,51) (0,03) (0,07)

Equity * D -‐0,01 -‐0,01 0,00 -‐0,00 -‐0,01 -‐0,01 0,03 0,04

(0,05) (0,04) (0,87) (0,87) (0,31) (0,59) (0,03) (0,02)

Fixed Income 0,01 0,01 0,01 0,02 0,03 -‐0,01 0,05 0,00

(0,17) (0,29) (0,08) (0,18) (0,21) (0,75) (0,09) (0,92)

Fixed Income * D -‐0,02 -‐0,03 -‐0,02 -‐0,02 0,00 -‐0,05 0,01 -‐0,03

(0,24) (0,22) (0,32) (0,28) (0,96) (0,39) (0,78) (0,55)

Comm. Agr. 0,01 0,01 0,01 0,01 0,00 0,01 0,00 0,01

(0,00) (0,01) (0,00) (0,01) (0,68) (0,39) (0,61) (0,33)

Comm. Agr. * D -‐0,01 -‐0,01 -‐0,01 -‐0,01 -‐0,01 -‐0,01 -‐0,01 -‐0,01

(0,02) (0,02) (0,04) (0,03) (0,13) (0,11) (0,30) (0,27)

Comm. Energy 0,00 0,00 0,00 0,00 0,00 0,01 0,00 0,01

(0,03) (0,02) (0,02) (0,02) (0,45) (0,22) (0,46) (0,21)

Comm. Energy * D -‐0,01 -‐0,01 -‐0,01 -‐0,01 -‐0,01 -‐0,01 -‐0,00 -‐0,00

(0,01) (0,00) (0,02) (0,00) (0,26) (0,37) (0,59) (0,76)

Comm. Metals 0,03 0,04 0,03 0,04 0,03 0,03 0,02 0,03

(0,00) (0,00) (0,00) (0,00) (0,00) (0,00) (0,00) (0,00)

Comm. Metals * D -‐0,03 -‐0,04 -‐0,03 -‐0,04 -‐0,02 -‐0,02 -‐0,02 -‐0,02

(0,00) (0,00) (0,00) (0,00) (0,02) (0,07) (0,03) (0,11)

TW USD 0,01 0,03 0,01 0,03 -‐0,01 0,02 -‐0,00 0,03

(0,30) (0,01) (0,22) (0,01) (0,85) (0,56) (0,99) (0,44)

TW USD * D -‐0,02 -‐0,04 -‐0,03 -‐0,05 -‐0,16 -‐0,19 -‐0,17 -‐0,21

(0,03) (0,01) (0,01) (0,00) (0,00) (0,00) (0,00) (0,00)

Equity * VIX -‐0,06 -‐0,07

-‐0,22 -‐0,29

(0,00) (0,00) (0,00) (0,00)

𝑅! 0,15 0,12 0,16 0,13 0,09 0,06 0,11 0,08

𝑅!!"! 0,15 0,12 0,15 0,12 0,09 0,06 0,10 0,08


74

Table 26: HM Model Sectorial Robustness of Equity and Fixed Income Sectors to Chen and Liang (2007) Indicator

Equity Fixed Income


Constant -‐0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00

(0,56) (0,78) (0,78) (0,13) (0,05) (0,00) (0,09) (0,00)

Equity 0,05 0,04 0,09 0,11 -‐0,05 -‐0,06 -‐0,06 -‐0,07

(0,00) (0,03) (0,00) (0,00) (0,00) (0,00) (0,00) (0,00)

Equity * D -‐0,02 0,01 0,01 0,07 0,00 -‐0,01 -‐0,00 -‐0,02

(0,14) (0,78) (0,44) (0,00) (0,66) (0,52) (0,66) (0,15)

Fixed Income -‐0,04 -‐0,06 -‐0,01 0,00 0,14 0,38 0,13 0,37

(0,09) (0,14) (0,72) (0,97) (0,00) (0,00) (0,00) (0,00)

Fixed Income * D 0,05 0,07 0,04 0,05 0,03 0,06 0,04 0,06

(0,27) (0,27) (0,37) (0,34) (0,45) (0,39) (0,41) (0,36)

Comm. Agr. -‐0,00 -‐0,00 0,00 0,00 0,01 0,00 0,00 0,00

(0,86) (0,96) (0,59) (0,42) (0,16) (0,41) (0,21) (0,51)

Comm. Agr. * D -‐0,01 -‐0,02 -‐0,01 0,01 0,00 0,01 0,00 0,01

(0,34) (0,19) (0,43) (0,23) (0,59) (0,20) (0,65) (0,23)

Comm. Energy 0,00 0,00 0,00 0,00 -‐0,00 -‐0,01 -‐0,00 -‐0,01

(0,51) (0,88) (0,09) (0,20) (0,13) (0,19) (0,09) (0,14)

Comm. Energy * D -‐0,00 -‐0,00 0,00 0,00 0,00 0,01 -‐0,00 0,01

(0,92) (0,87) (0,68) (0,68) (0,93) (0,48) (0,99) (0,54)

Comm. Metals 0,01 0,02 0,01 0,01 -‐0,00 -‐0,01 -‐0,00 -‐0,01

(0,00) (0,00) (0,13) (0,08) (0,34) (0,05) (0,53) (0,10)

Comm. Metals * D 0,00 0,00 0,00 0,00 0,00 0,01 0,00 0,01

(0,63) (0,80) (0,66) (0,88) (0,70) (0,23) (0,67) (0,22)

TW USD -‐0,00 0,02 0,01 0,03 -‐0,01 -‐0,03 -‐0,01 -‐0,04

(0,97) (0,45) (0,71) (0,22) (0,67) (0,12) (0,59) (0,10)

TW USD * D 0,02 0,00 0,01 -‐0,01 -‐0,01 0,01 -‐0,01 0,01

(0,36) (0,99) (0,53) (0,73) (0,73 0,87 0,77 0,82

Equity * VIX -‐0,40 -‐0,67

0,09 0,11

(0,00) (0,00) (0,00) (0,00)

𝑅! 0,07 0,06 0,23 0,26 0,16 0,27 0,16 0,27

𝑅!"#! 0,07 0,05 0,23 0,26 0,15 0,27 0,16 0,27


75

Table 27: HM Model Sectorial Robustness of Soft Commodities and Commodities Energy Sectors to Chen and Liang (2007) Indicator



Constant -‐0,00 -‐0,00 -‐0,00 -‐0,00 -‐0,00 -‐0,00 0,00 0,00

(0,09) (0,31) (0,12) (0,41) (0,79) (0,79) (0,96) (0,99)

Equity -‐0,00 -‐0,00 0,00 0,01 -‐0,01 -‐0,01 0,01 0,01

(0,41) (0,36) (0,15) (0,17) (0,17) (0,18) (0,28) (0,32)

Equity * D -‐0,01 -‐0,01 -‐0,00 -‐0,00 -‐0,01 -‐0,01 0,00 0,01

(0,14) (0,18) (0,76) (0,85) (0,39) (0,58) (0,77) (0,59)

Fixed Income 0,01 0,01 0,01 0,02 0,04 0,05 0,05 0,07

(0,52) (0,55) (0,27) (0,28) (0,08) (0,11) (0,02) (0,03)

Fixed Income * D -‐0,04 -‐0,06 -‐0,04 -‐0,07 -‐0,05 -‐0,07 -‐0,05 -‐0,08

(0,04) (0,04) (0,03) (0,03) (0,16) (0,13) (0,12) (0,10)

Comm. Agr. 0,00 0,00 0,00 0,00 -‐0,00 -‐0,00 -‐0,00 -‐0,00

(0,52) (0,47) (0,45) (0,40) (0,44) (0,47) (0,57) (0,61)

Comm. Agr. * D 0,01 0,01 0,01 0,01 0,00 0,00 0,01 0,01

(0,27) (0,21) (0,24) (0,18) (0,52) (0,70) (0,44) (0,62)

Comm. Energy -‐0,00 -‐0,00 -‐0,00 -‐0,00 0,02 0,03 0,02 0,03

(0,08) (0,18) (0,13) (0,28) (0,00) (0,00) (0,00) (0,00)

Comm. Energy * D 0,00 0,00 0,00 0,00 -‐0,00 -‐0,01 -‐0,00 -‐0,01

(0,47) (0,84) (0,36) (0,69) (0,77) (0,52) (0,86) (0,59)

Comm. Metals 0,00 0,00 0,00 0,00 -‐0,00 0,00 -‐0,00 0,00

(0,52) (0,43) (0,85) (0,73) (0,91) (0,66) (0,56) (0,99)

Comm. Metals * D 0,00 -‐0,00 0,00 -‐0,00 0,02 0,02 0,02 0,02

(0,79) (0,95) (0,82) (0,92) (0,01) (0,02) (0,01) (0,02)

TW USD 0,00 0,00 0,01 0,00 -‐0,01 -‐0,01 -‐0,01 -‐0,01

(0,50) (0,75) (0,40) (0,63) (0,51) (0,49) (0,62) (0,60)

TW USD * D 0,01 0,01 0,00 0,01 0,01 0,02 0,01 0,02

(0,58) (0,38) (0,63) (0,43) (0,54) (0,39) (0,60) (0,44)

Stocks * VIX -‐0,06 -‐0,09

-‐0,12 -‐0,16

(0,00) (0,00) (0,00) (0,00)

𝑅! 0,02 0,02 0,04 0,04 0,05 0,06 0,07 0,08

𝑅!"#! 0,02 0,02 0,03 0,04 0,05 0,05 0,07 0,07


76

Table 28: HM Model Sectorial Robustness of Commodities Metals and Composite Currencies Sectors to Chen and Liang (2007) Indicator



Constant -‐0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00

(0,77) (0,90) (0,99) (0,64) (0,08) (0,02) (0,02) (0,00)

Equity -‐0,01 -‐0,01 0,00 0,00 -‐0,01 -‐0,02 0,01 0,01

(0,03) (0,06) (0,67) (0,61) (0,12) (0,08) (0,52) (0,54)

Equity * D -‐0,01 -‐0,01 0,00 0,00 0,02 0,03 0,04 0,06

(0,30) (0,40) (0,79) (0,72) (0,16) (0,09) (0,02) (0,01)

Fixed Income 0,01 -‐0,00 0,01 0,01 0,05 -‐0,02 0,07 0,01

(0,68) (0,81) (0,29) (0,77) (0,15) (0,74) (0,04) (0,86)

Fixed Income * D -‐0,01 0,01 -‐0,01 0,00 -‐0,03 -‐0,02 -‐0,03 -‐0,02

(0,75) (0,84) (0,67) (0,91) (0,61) (0,81) (0,53) (0,73)

Comm. Agr. 0,00 0,00 0,00 0,01 -‐0,00 0,00 -‐0,00 0,00

(0,14) (0,19) (0,08) (0,12) (0,47) (0,93) (0,64) (0,73)

Comm. Agr. * D -‐0,01 -‐0,01 -‐0,01 -‐0,01 -‐0,00 -‐0,01 0,00 -‐0,00

(0,19) (0,21) (0,20) (0,22) (0,99) (0,62) (0,91) (0,69)

Comm. Energy -‐0,00 -‐0,00 -‐0,00 -‐0,00 -‐0,00 0,00 0,00 0,00

(0,64) (0,61) (0,88) (0,83) (0,87) (0,58) (0,90) (0,41)

Comm. Energy * D 0,00 -‐0,00 0,00 0,00 -‐0,00 -‐0,00 0,00 -‐0,00

(0,81) (1,00) (0,67) (0,87) (0,92) (0,73) (0,93) (0,86)

Comm. Metals 0,01 0,02 0,01 0,01 0,01 0,00 0,00 -‐0,00

(0,00) (0,01) (0,00) (0,02) (0,20) (0,58) (0,49) (0,99)

Comm. Metals * D 0,02 0,02 0,02 0,02 0,02 0,04 0,02 0,04

(0,02) (0,02) (0,02) (0,02) (0,02) (0,00) (0,02) (0,00)

TW USD -‐0,01 0,00 -‐0,01 0,00 -‐0,10 -‐0,08 -‐0,09 -‐0,08

(0,33) (0,86) (0,42) (0,76) (0,00) (0,03) (0,00) (0,04)

TW USD * D 0,01 0,00 0,00 0,00 0,00 -‐0,00 0,00 -‐0,01

(0,73) (0,93) (0,80) (1,00) (0,92) (0,96) (0,99) (0,89)

Equity * VIX -‐0,08 -‐0,11 -‐0,21 -‐0,26

(0,00) (0,00) (0,00) (0,00)

𝑅! 0,08 0,06 0,11 0,08 0,06 0,04 0,08 0,06

𝑅!"#! 0,08 0,05 0,10 0,07 0,06 0,04 0,08 0,06


77

Table 29: HM Model Sectorial Robustness of Equity and Fixed Income Sectors to the Exclusion of the Credit Crunch

Equity Fixed Income


Constant -‐0,00 -‐0,00 -‐0,00 -‐0,00 -‐0,00 0,00 -‐0,00 0,00

(0,00) (0,09) (0,00) (0,00) (0,13) (0,84) (0,16) (0,73)

Equity 0,07 0,13 0,07 0,14 -‐0,03 -‐0,04 -‐0,03 -‐0,04

(0,00) (0,00) (0,00) (0,00) (0,00) (0,00) (0,00) (0,00)

Equity * D -‐0,10 -‐0,20 -‐0,03 -‐0,07 -‐0,03 -‐0,03 -‐0,04 -‐0,05

(0,00) (0,00) (0,11) (0,03) (0,02) (0,06) (0,01) (0,01)

Fixed Income -‐0,01 -‐0,00 -‐0,01 0,00 0,13 0,47 0,13 0,47

(0,40) (0,89) (0,47) (0,99) (0,02) (0,00) (0,02) (0,00)

Fixed Income * D 0,04 0,05 0,02 0,02 -‐0,26 -‐0,24 -‐0,26 -‐0,23

(0,16) (0,25) (0,31) (0,53) (0,00) (0,03) (0,00) (0,03)

Comm. Agr. -‐0,00 -‐0,01 -‐0,00 -‐0,01 0,00 0,01 0,00 0,01

(0,27) (0,36) (0,16) (0,23) (0,36) (0,35) (0,36) (0,35)

Comm. Agr. * D -‐0,01 -‐0,02 -‐0,01 -‐0,01 -‐0,01 0,00 -‐0,01 0,00

(0,25) (0,22) (0,47) (0,51) (0,43) (0,86) (0,39) (0,97)

Comm. Energy 0,00 0,00 0,00 0,00 0,00 -‐0,00 0,00 -‐0,00

(0,46) (0,79) (0,23) (0,45) (0,97) (0,92) (0,99) (0,88)

Comm. Energy * D 0,01 0,01 0,00 0,00 0,00 0,00 0,00 0,01

(0,08) (0,09) (0,36) (0,37) (0,73) (0,57) (0,66) (0,48)

Comm. Metals 0,00 0,01 0,00 0,01 -‐0,00 -‐0,01 -‐0,00 -‐0,01

(0,47) (0,12) (0,93) (0,30) (0,28) (0,20) (0,30) (0,24)

Comm. Metals * D 0,01 0,02 0,01 0,02 0,01 0,00 0,01 0,00

(0,40) (0,11) (0,40) (0,09) (0,35) (0,78) (0,35) (0,76)

TW USD 0,04 0,07 0,04 0,08 -‐0,05 -‐0,08 -‐0,05 -‐0,08

(0,00) (0,00) (0,00) (0,00) (0,00) (0,01) (0,00) (0,01)

TW USD * D -‐0,03 -‐0,06 -‐0,02 -‐0,04 0,03 0,04 0,03 0,04

(0,03) (0,03) (0,11) (0,12) (0,15) (0,23) (0,16) (0,26)

Equity * VIX -‐0,75 -‐ 1,41

0,09 0,19

(0,00) (0,00) (0,29) (0,11)

𝑅! 0,16 0,19 0,29 0,32 0,11 0,22 0,11 0,22

𝑅!"#! 0,16 0,18 0,29 0,32 0,10 0,21 0,10 0,22


78

Table 30: HM Model Sectorial Robustness of Soft Commodities and Commodities Energy Sectors to the Exclusion of the Credit Crunch



Constant -‐0,00 -‐0,00 -‐0,00 -‐0,00 -‐0,00 -‐0,00 -‐0,00 -‐0,00

(0,00) (0,00) (0,00) (0,00) (0,00) (0,11) (0,00) (0,17)

Equity -‐ 0,00 0,00 -‐0,00 -‐0,00 -‐0,00 -‐0,00 -‐0,00 -‐0,00

(0,98) (0,94) (0,91) (1,00) (0,72) (0,95) (0,61) (0,82)

Equity * D -‐0,00 -‐0,00 -‐0,00 -‐0,01 0,00 0,01 -‐0,01 -‐0,01

(0,95) (0,89) (0,52) (0,54) (0,52) (0,42) (0,47) (0,48)

Fixed Income -‐0,01 -‐0,02 -‐0,01 -‐0,02 0,01 0,00 0,01 0,00

(0,20) (0,22) (0,19) (0,22) (0,73) (0,89) (0,74) (0,91)

Fixed Income * D -‐0,01 -‐0,01 -‐0,01 -‐0,01 -‐0,02 -‐0,03 -‐0,02 -‐0,03

(0,53) (0,64) (0,55) (0,66) (0,36) (0,49) (0,40) (0,54)

Comm. Agr. 0,01 0,02 0,01 0,02 -‐0,00 -‐0,01 -‐0,00 -‐0,01

(0,00) (0,00) (0,00) (0,00) (0,10) (0,20) (0,11) (0,21)

Comm. Agr. * D 0,01 0,01 0,01 0,01 0,02 0,03 0,02 0,03

(0,19) (0,48) (0,19) (0,49) (0,00) (0,01) (0,00) (0,01)

Comm. Energy 0,00 0,00 0,00 0,00 0,04 0,05 0,04 0,05

(0,23) (0,19) (0,24) (0,20) (0,00) (0,00) (0,00) (0,00)

Comm. Energy * D -‐0,00 -‐0,00 -‐0,00 -‐0,00 -‐0,03 -‐0,04 -‐0,03 -‐0,04

(0,12) (0,09) (0,16) (0,12) (0,00) (0,01) (0,00) (0,02)

Comm. Metals 0,00 0,00 0,00 0,00 0,00 0,01 0,00 0,01

(0,21) (0,32) (0,19) (0,30) (0,20) (0,18) (0,17) (0,15)

Comm. Metals * D 0,01 0,01 0,01 0,01 0,01 0,03 0,01 0,03

(0,09) (0,05) (0,09) (0,05) (0,03) (0,02) (0,02) (0,02)

TW USD -‐0,01 -‐0,02 -‐0,01 -‐0,02 -‐0,02 -‐0,04 -‐0,02 -‐0,04

(0,07) (0,20) (0,07) (0,19) (0,01) (0,02) (0,01) (0,02)

TW USD * D 0,01 0,02 0,01 0,02 0,03 0,05 0,03 0,05

(0,13) (0,26) (0,14) (0,28) (0,02) (0,02) (0,03) (0,02)

Equity * VIX 0,04 0,06

0,10 0,19

(0,26) (0,33) (0,04) (0,03)

𝑅! 0,11 0,10 0,11 0,10 0,27 0,22 0,27 0,22

𝑅!"#! 0,10 0,09 0,10 0,09 0,26 0,21 0,26 0,21


79

Table 31: HM Model Sectorial Robustness of Commodities Metals and Composite Currencies Sectors to the Exclusion of the Credit Crunch



Constant -‐0,00 -‐0,00 -‐0,00 -‐0,00 -‐0,00 -‐0,00 -‐0,00 0,00

(0,00) (0,00) (0,00) (0,00) (0,01) (0,14) (0,01) (0,14)

Equity 0,00 0,00 0,00 0,00 0,04 0,04 0,04 0,04

(0,76) (0,94) (0,67) (0,86) (0,02) (0,11) (0,02) (0,11)

Equity * D -‐0,01 -‐0,02 -‐0,01 -‐0,01 -‐0,04 -‐0,06 -‐0,04 -‐0,06

(0,00) (0,00) (0,12) (0,07) (0,07) (0,04) (0,14) (0,14)

Fixed Income -‐0,00 0,00 -‐0,00 0,00 -‐0,03 -‐0,11 -‐0,03 -‐0,11

(0,86) (0,92) (0,87) (0,91) (0,47) (0,05) (0,47) (0,05)

Fixed Income * D -‐0,00 -‐0,01 -‐0,00 -‐0,02 0,14 0,12 0,14 0,12

(0,78) (0,42) (0,72) (0,38) (0,03) (0,19) (0,03) (0,19)

Comm. Agr. 0,00 0,00 0,00 0,00 0,01 0,01 0,01 0,01

(0,03) (0,12) (0,03) (0,12) (0,18) (0,10) (0,18) (0,10)

Comm. Agr. * D 0,00 -‐0,00 0,00 -‐0,00 -‐0,01 -‐0,01 -‐0,01 -‐0,01

(0,84) (0,68) (0,75) (0,76) (0,31) (0,40) (0,31) (0,42)

Comm. Energy 0,00 0,00 0,00 0,00 0,01 0,01 0,01 0,01

(0,00) (0,01) (0,00) (0,01) (0,22) (0,13) (0,22) (0,13)

Comm. Energy * D -‐0,00 -‐0,01 -‐0,00 -‐0,01 -‐0,00 0,01 -‐0,00 0,01

(0,10) (0,08) (0,08) (0,06) (0,90) (0,62) (0,90) (0,63)

Comm. Metals 0,04 0,05 0,04 0,05 0,03 0,03 0,03 0,03

(0,00) (0,00) (0,00) (0,00) (0,00) (0,01) (0,00) (0,01)

Comm. Metals * D 0,00 0,00 0,00 0,00 0,01 0,01 0,01 0,01

(0,92) (0,91) (0,93) (0,91) (0,66) (0,49) (0,66) (0,49)

TW USD -‐0,02 0,01 -‐0,02 0,01 -‐0,17 -‐0,12 -‐0,17 -‐0,12

(0,00) (0,56) (0,00) (0,54) (0,00) (0,08) (0,00) (0,08)

TW USD * D -‐0,01 -‐0,03 -‐0,01 -‐0,03 -‐0,15 -‐0,18 -‐0,15 -‐0,18

(0,05) (0,00) (0,06) (0,00) (0,02) (0,04) (0,03) (0,04)

Equity * VIX -‐0,05 -‐0,06

-‐0,01 -‐0,04

(0,07) (0,15) (0,91) (0,86)

𝑅! 0,48 0,34 0,48 0,34 0,19 0,11 0,19 0,11

𝑅!"#! 0,48 0,34 0,48 0,34 0,18 0,10 0,18 0,10


81

9.2 Figures

Figure 1: Average Monthly Return of CTAs in Five Equity Market Regimes

Description: Figures depict the average monthly CTA return in five MSCI World monthly return quintiles.

Figure 2: Equity Market Crisis and Bear Market Identification

Crisis Market Identification Bear Market Identification

Description: Figures depict the evolution in the MSCI World and shaded areas reflect the identified crisis (left) or

bear market (right) regimes.

Figure 3: Fixed Income Market Crisis and Bear Market Identification


Description: Figures depict the evolution in the Barclays U.S. Aggregate and shaded areas reflect the identified crisis

(left) or bear market (right) regimes.

82

Figure 4: Commodities Agriculture Market Crisis and Bear Market Identification


Description: Figures depict the evolution in the S&P GSCI Commodities Agriculture and shaded areas reflect the

identified crisis (left) or bear market (right) regimes.

Figure 5: Commodities Energy Market Crisis and Bear Market Identification


Description: Figures depict the evolution in the S&P GSCI Commodities Energy and shaded areas reflect the


Figure 6: Commodities Metals Market Crisis and Bear Market Identification


Description: Figures depict the evolution in the S&P GSCI Commodities Metals and shaded areas reflect the


83

Figure 7: Trade-‐Weighted USD Market Crisis and Bear Market Identification


Description: Figures depict the evolution in the Trade-‐Weighted USD Exchange Rate and shaded areas reflect the


Figure 8: Overlapping Crisis Periods

Figure 9: CTA’s Time-‐Varying Equity Market Risk Factor Exposures

84

Figure 10: Managed Futures Dynamics in an Equity Market Crisis

Equity Market Cumulative Returns

RPM USD Equity Sector Position RPM USD Equity Sector TF Position

RPM USD Equity Sector Cumulative Return RPM USD Equity Sector TF Cumulative Return

RPM USD Composite Cumulative Return RPM USD Composite TF Cumulative Return

Description: Figures represent the equally weighted average evolution of a specific variable (blue line) throughout a

crisis event window spanning from 40 days before the start of a crisis to 160 days after. The start of a crisis is

indicated by the vertical line and the dark blue lines represent 1 standard deviation bands.

85

Figure 11: Managed Futures Dynamics in a Fixed Income Market Crisis

Fixed Income Market Cumulative Returns

RPM USD Fixed Income Sector Position RPM USD Fixed Income Sector TF Position

RPM USD Fixed Income Sector Cumulative Return RPM USD Fixed Income Sector TF Cumulative Return





86

Figure 12: Managed Futures Dynamics in a Commodity Agriculture Market Crisis

Comm. Agr. Market Cumulative Returns

RPM USD Soft Comm. Sector Position RPM USD Soft Comm. Sector TF Position

RPM USD Soft Comm. Sector Cumulative Return RPM USD Soft Comm. Sector TF Cumulative Return





87

Figure 13: Managed Futures Dynamics in a Commodity Energy Market Crisis

Comm. Ener. Market Cumulative Returns

RPM USD Comm. Ener. Sector Position RPM USD Comm. Ener. Sector TF Position

RPM USD Comm. Ener. Sector Cumulative Return RPM USD Comm. Ener. Sector TF Cumulative Return





88

Figure 14: Managed Futures Dynamics in a Commodity Metals Market Crisis

Comm. Met. Market Cumulative Returns

RPM USD Comm. Met. Sector Position RPM USD Comm. Met. Sector TF Position

RPM USD Comm. Met. Sector Cumulative Return RPM USD Comm. Met. Sector TF Cumulative Return





89

Figure 15: Managed Futures Dynamics in a Trade-‐Weighted USD Market Crisis

TW USD Market Cumulative Returns

RPM USD Comp. Curr. Sector Position RPM USD Comp. Curr. Sector TF Position

RPM USD Comp. Curr. Sector Cumulative Return RPM USD Comp. Curr. Sector TF Cumulative Return





90

9.3 MATLAB Code Crisis Identification Methodology

% Specify the selected data that you would like to run. % 1) Date % 2) S&P GSCI Agriculture % 3) S&P GSCI Energy (Note: start from row 2002 to end) % 4) S&P GSCI Metals (Note: start from row 5143 to end) % 5) MSCI World % 6) Barclays U.S. Aggregate Bond Index (Note: start from row 197 to end) % 7) Trade Weighted USD clear clc data=xlsread('Final Data Crisis identification clean'); data(:,1)=data(:,1)+datenum('30DEC1899'); data=data(197:end,[1 6]); u=60 b=0.41 %% Preliminary Coding: % IT: Market state indicator with the first column indicating the date and % the second been given a value of 1 if in a bull / non-crisis period state % Xmax & Xmin: refer to local minimum and maximum from which the actual % time series must deviate by a specified threshold. % tau: specifies the last date since the local minimum or maximum. % n: refers to how many different values the lambda 1 and 2 parameters are % allowed to take. E.g. If lambda 1 and 2 are allowed to vary between 0.01 % and 0.40 with steps of 0.01, then n=40. This logically leads to 1600 % different possible combinations of lambda 1 and lambda 2 that can be tested % in the loop below. % bear: bear is a variable that specifies the beginning and end of a % crisis / bear market respectively by the values 1 and 2. IT=data(:,1); IT(1,2)=1; xmax=data(:,1); xmin=data(:,2); xmax(1,2)=data(1,2); xmin(1,2)=data(1,2); tau=data(:,1); tau(1,2)=data(1,1); tau(1,3)=data(1,1); n=40 x=linspace(0.01,0.40,n)'; y=linspace(0.01,0.40,n)'; returns(:,1)=data(2:end,1); returns(:,2)=price2ret(data(:,2)); bear(:,1)=IT(:,1); bear(:,2)=0; % Create a n^2x2 vector of all possible combinations of lambda 1 and lambda 2 % given n.

91

for i=1:n for j=1:n z(i,:,j)=[x(i,1) y(j,1)]; end end h=z(:,:,1); for i=2:n h=vertcat(h(:,:,1),z(:,:,i)); end %% Optimization of the lambda parameters % J-loop: loop over all different possible combinations of parameters lambda % 1 and lambda 2 % i-loop: Loop over all values of the time series to determine the market % state. c=waitbar(0,'Please wait') for j=1:size(h,1) c=waitbar(j/size(h,1)); landa1=h(j,1); landa2=h(j,2); for i=2:size(IT,1) if IT(i-1,2)==1 if data(i,2)>xmax(i-1,2) IT(i,2)=1; xmax(i,2)=data(i,2); xmin(i,2)=xmin(i-1,2); tau(i,2)=data(i,1); tau(i,3)=tau(i-1,3); elseif data(i,2)<(1-landa1)*xmax(i-1,2) IT(find(data(:,1)==tau(i-1,2)):i,2)=0; xmax(i,2)=data(i,2); xmin(i,2)=data(i,2); tau(i,2)=data(i,1); tau(i,3)=data(i,1); elseif data(i,2)>(1-landa1)*xmax(i-1,2) IT(i,2)=1; xmax(i,2)=xmax(i-1,2); xmin(i,2)=xmin(i-1,2); tau(i,2)=tau(i-1,2); tau(i,3)=tau(i-1,3); end elseif IT(i-1,2)==0 if data(i,2)<xmin(i-1,2) IT(i,2)=0; xmax(i,2)=xmax(i-1,2); xmin(i,2)=data(i,2); tau(i,2)=tau(i-1,2); tau(i,3)=data(i,1); elseif data(i,2)>(1+landa2)*xmin(i-1,2) IT(find(data(:,1)==tau(i-1,3)):i,2)=1; xmax(i,2)=data(i,2); xmin(i,2)=data(i,2); tau(i,2)=data(i,1); tau(i,3)=data(i,1);

92

elseif data(i,2)<(1+landa2)*xmin(i-1,2) IT(i,2)=0; xmin(i,2)=xmin(i-1,2); xmax(i,2)=xmax(i-1,2); tau(i,2)=tau(i-1,2); tau(i,3)=tau(i-1,3); end end end % Determine the beginning and end of the bear/crisis state bear(:,2)=0; for i=2:size(bear,1) if (IT(i,2)==0) && (IT(i-1,2)==1) bear(i,2)=1; elseif (IT(i,2)==1) && (IT(i-1,2)==0) bear(i,2)=2; end end % Enforce the proper alteration between beginning and end % of a crisis period. In other words, if you end in a crisis state, % then there is a 1, but not a 2 leading to a dimension mismatch in the % summary matrix below. Thus, the bear state must be concluded, as well % as the fact that a start in a bear state must have a beginning. if IT(end,2)==0 bear(end,2)=2; end if IT(1,2)==0 bear(1,2)=1; end summary=zeros(size(find(bear(:,2)==1),1),2); summary(:,1)=bear(find(bear(:,2)==1),1); summary(:,2)=bear(find(bear(:,2)==2),1); for i=2:size(summary,1) summary(i,3)=summary(i,1)-summary(i-1,2); end for i=2:size(summary,1) if summary(i,3)<u IT(find(summary(i-1,1)==IT(:,1)):find(summary(i,2)==IT(:,1)),2)=0; end end % redetermine the beginning and end of the bear/crisis state bear(:,2)=0; for i=2:size(bear,1) if (IT(i,2)==0) && (IT(i-1,2)==1) bear(i,2)=1; elseif (IT(i,2)==1) && (IT(i-1,2)==0) bear(i,2)=2; end

93

end if IT(end,2)==0 bear(end,2)=2; end if IT(1,2)==0 bear(1,2)=1; end % Summary matrix that shows the start of a crisis, the end, the fall in % the market over a specific duration of the crisis period, the % intensity factor of the crisis and the standard deviation of the % return over the crisis period. summary=zeros(size(find(bear(:,2)==1),1),2); summary(:,1)=bear(find(bear(:,2)==1),1); summary(:,2)=bear(find(bear(:,2)==2),1); if size(summary,1)==0 IF(j,1)=0; IF(j,2)=0; IF(j,3)=0; IF(j,4)=0; else for i=1:size(summary,1) summary(i,3)=log(data(find(data(:,1)==summary(i,2)),2)/data(find(data(:,1)==summary(i,1)),2)); summary(i,5)=summary(i,2)-summary(i,1); summary(i,4)=std(returns(find(returns(:,1)==summary(i,1)):find(returns(:,1)==summary(i,2)),2))*sqrt(summary(i,5)); summary(i,6)=summary(i,3)/(summary(i,5)/365); end % Save the respective mean intensity factor over the crisis period % for a given lambda 1 and 2 parameter combination, the standard % deviation of these intensity factors, their intensity factor % adjusted for IF-volatility and the amount of crises identified by % the algorithm. IF(j,1)=mean(summary(:,6)); IF(j,2)=std(summary(:,6)); IF(j,3)=IF(j,1)/IF(j,2); IF(j,4)=size(summary,1); end end % Remove lambda parameters that lead to only a single crisis being % identified. This would lead to an infinite IF-adj. for i=1:size(IF,1) if IF(i,4)==1 IF(i,5)=0; else IF(i,5)=1;

94

end end % Enforce a severe enough intensity factor upon the series. In other words, % restrict the lambda parameters combinations only to those that provide an % intensity factor that is more severe than the overall average intensity % factor (in absolute value). IFadj=IF(find(IF(:,5)==1),:); z=mean(IFadj(:,1)) e=std(IFadj(:,1)) z=z for i=1:size(IF,1) if IF(i,1)<z IF(i,6)=1; else IF(i,6)=0; end end % Enforce a the rebound to be smaller than the fall in the market. for i=1:size(IF,1) if h(i,1)>h(i,2) IF(i,8)=1; else IF(i,8)=0; end end % Additional restriction only applying to equity markets. for i=1:size(IF,1) if h(i,1)<b IF(i,9)=1; else IF(i,9)=0; end end close(c) IFadj=IF(find(IF(:,5)==1&IF(:,6)==1&IF(:,8)==1&IF(:,9)==1),:); a=min(IFadj(:,3)) optimumparameters=h(find(IF(:,3)==a),:) %% Employ the identified parameters to detect crisis periods. landa1=optimumparameters(1,1); landa2=optimumparameters(1,2); c=waitbar(0,'Please Wait') % Preliminary Coding IT=data(:,1); IT(1,2)=1; xmax=data(:,1); xmin=data(:,2);

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xmax(1,2)=data(1,2); xmin(1,2)=data(1,2); tau=data(:,1); tau(1,2)=data(1,1); tau(1,3)=data(1,1); for i=2:size(IT,1) c=waitbar(i/size(IT,1)); if IT(i-1,2)==1 if data(i,2)>xmax(i-1,2) IT(i,2)=1; xmax(i,2)=data(i,2); xmin(i,2)=xmin(i-1,2); tau(i,2)=data(i,1); tau(i,3)=tau(i-1,3); elseif data(i,2)<(1-landa1)*xmax(i-1,2) IT(find(data(:,1)==tau(i-1,2)):i,2)=0; xmax(i,2)=data(i,2); xmin(i,2)=data(i,2); tau(i,2)=data(i,1); tau(i,3)=data(i,1); elseif data(i,2)>(1-landa1)*xmax(i-1,2) IT(i,2)=1; xmax(i,2)=xmax(i-1,2); xmin(i,2)=xmin(i-1,2); tau(i,2)=tau(i-1,2); tau(i,3)=tau(i-1,3); end elseif IT(i-1,2)==0 if data(i,2)<xmin(i-1,2) IT(i,2)=0; xmax(i,2)=xmax(i-1,2); xmin(i,2)=data(i,2); tau(i,2)=tau(i-1,2); tau(i,3)=data(i,1); elseif data(i,2)>(1+landa2)*xmin(i-1,2) IT(find(data(:,1)==tau(i-1,3)):i,2)=1; xmax(i,2)=data(i,2); xmin(i,2)=data(i,2); tau(i,2)=data(i,1); tau(i,3)=data(i,1); elseif data(i,2)<(1+landa2)*xmin(i-1,2) IT(i,2)=0; xmin(i,2)=xmin(i-1,2); xmax(i,2)=xmax(i-1,2); tau(i,2)=tau(i-1,2); tau(i,3)=tau(i-1,3); end end end %% Analysis of features of a crisis state % Define beginning and end of bear-crisis period bear(:,1)=IT(:,1); bear(:,2)=0;

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for i=2:size(bear,1) for j=2:size(IT,2) if IT(i,j)==0&IT(i-1,j)==1 bear(i,j)=1; elseif IT(i,j)==1&IT(i-1,j)==0 bear(i,j)=2; else 0; end end end % Additional restriction to make sure dimensions match for the next summary % matrix (specifically, if you find yourself in a bear-crisis period at the % end of the sample period than this needs to be ended, or the matrix % dimensions shall not match in the subsequent functions if IT(end,2)==0 bear(end,2)=2; end returns(:,1)=data(2:end,1); returns(:,2)=price2ret(data(:,2)); summary=zeros(size(find(bear(:,2)==1),1),2); summary(:,1)=bear(find(bear(:,2)==1),1); summary(:,2)=bear(find(bear(:,2)==2),1); % Defining the return over the entire crisis (bear) period, the duration, % the standard deviation of the returns over the period and the intensity % factor. for i=1:size(summary,1) summary(i,3)=log(data(find(data(:,1)==summary(i,2)),2)/data(find(data(:,1)==summary(i,1)),2)); summary(i,5)=summary(i,2)-summary(i,1); summary(i,4)=std(returns(find(returns(:,1)==summary(i,1)):find(returns(:,1)==summary(i,2)),2))*sqrt(summary(i,5)); summary(i,6)=summary(i,3)/(summary(i,5)/365); end %% add an additional restriction % Define how long each crisis (bear) period has been since the last one for i=2:size(summary,1) summary(i,7)=summary(i,1)-summary(i-1,2); end % Identify when this is smaller than 60 days for i=2:size(summary,1) if summary(i,7)<u IT(find(summary(i-1,1)==IT(:,1)):find(summary(i,2)==IT(:,1)),2)=0; end end %% Rerun code and make the period one, if it is less than 30 days since the

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former one bear2(:,1)=IT(:,1); bear2(1,2)=0; for i=2:size(bear2,1) for j=2:size(IT,2) if IT(i,j)==0&IT(i-1,j)==1 bear2(i,j)=1; elseif IT(i,j)==1&IT(i-1,j)==0 bear2(i,j)=2; else 0; end end end if IT(end,2)==0 bear2(end,2)=2; end summary2=zeros(size(find(bear2(:,2)==1),1),2); summary2(:,1)=bear2(find(bear2(:,2)==1),1); summary2(:,2)=bear2(find(bear2(:,2)==2),1); for i=1:size(summary2,1) summary2(i,3)=log(data(find(data(:,1)==summary2(i,2)),2)/data(find(data(:,1)==summary2(i,1)),2)); summary2(i,5)=summary2(i,2)-summary2(i,1); summary2(i,4)=std(returns(find(returns(:,1)==summary2(i,1)):find(returns(:,1)==summary2(i,2)),2))*sqrt(summary2(i,5)); summary2(i,6)=summary2(i,3)/(summary2(i,5)/365); end for i=2:size(summary2,1) summary2(i,7)=summary2(i,1)-summary2(i-1,2); end close(c) IT(find(IT(:,2)==0),2)=max(data(:,2)); IT(find(IT(:,2)==1),2)=0; t=datetime(datevec(data(:,1))); plot(t,data(:,2)) hold on area(IT(:,1),IT(:,2),'FaceColor',[0.7 0.7 0.7],'EdgeColor',[0.7 0.7 0.7]) plot(t,data(:,2),'k') hold off landa1 landa2 meanIF=mean(summary2(:,6)) stdIF=std(summary2(:,6)) Ncrisis=size(summary2,1)

masterproef_master_banking_and_finance_nicolas_dierick_pieterjan_tilleman

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