Research and investment strategies

#03 Low correlations, high volatility: big opportunity?

A cycle approach to assessing emerging markets macro risk

Fear versus fundamentals: Looking for long-term opportunity

in a troubled energy sector

#03

Chair: Dr. Henning Stein (Head of Institutional Marketing, EMEA) and Marlene Konecny (Senior Manager Marketing Institutional, Germany, Austria & Switzerland).Jutta Becker (Marketing Communications, Continental Europe), Carolyn Gibbs (Senior Strategist, Invesco Fixed Income), Ann Ginsburg (Senior Market Analyst, Invesco Fixed Income), Thomas Kraus (Head of Institutional Business, Germany, Austria & Switzerland), Harald Lohre (Senior Research Analyst, Invesco Quantitative Strategies), Kevin Lyman (Director, Global Investment Initiatives), Sarah Mumford (Head of Investment Marketing, Invesco Perpetual), Lisa Nell (Director – Marketing, Europe, Invesco Real Estate), Jodi Phillips (Marketing Editorial Director, US), Elena Zhmurova (Senior Manager, EMEA Institutional Strategy).

31 July 2016

Michael FraikinDo low intra-stock correlations and high cross-sectional volatilities make life easier for active managers, whether quantitative or otherwise? Our results are less clear-cut than we had expected.

Greg McGreevey, Rob WaldnerInvesco Fixed Income held its semi-annual Global Investor’s Summit in June, gathering around 50 of Invesco Fixed Income’s investment professionals from around the world to discuss key themes affecting global bond markets and determine our strategic views for the next 12-18 months. The following represents our current views and outlook.

Rashique Rahman, Jay RaolCredit cycle dynamics, in our view, provide critical insight into divergences between emerging market countries and their likely development in the coming years. In this article, we develop a heat map for emerging market countries, incorporating their respective credit cycles.

Kevin Holt, Shaia Hosseinzadeh, Norm MacDonald, Susanta Mazumdar, Dean Newman, Scott RobertsSince oil prices fell from more than USD110 a barrel in mid-2014 to below USD30 in January 2016, this dramatic plunge has reverberated through stock and bond markets worldwide. Although prices have recovered somewhat in recent months, oil prices are historically low. But, at the end of the day, what investors really want to know is where the opportunities lie. We will argue, that despite current uncertainties, the energy sector may hold great long-term potential for those who can look past shorter-term fears.

Dr. Bernhard PfaffIt is not always advisable to work with a time invariant regression formula. One solution is the so-called STAR Modell with its ability to change smoothly from one regime to another. Another far more flexible solution is a state space model which is based on as many states as time points instead of two regimes. Moreover, not all the explanatory variables must be observable.

Market Opportunities

It is often taken for granted that active management will be most successful if the market differentiates greatly between stocks. This frequently leads to assertions such as “when major events dominate markets, times are challenging for stock pickers”, “this risk-on, risk-off environment is difficult” or “this volatility creates big opportunities for stock pickers”. The majority of such statements refer to challenges rather than tailwinds – maybe because humans tend to blame failures on circumstances and ascribe success to their own virtues and actions.

In line with this thinking, opportunity is often described as stocks moving fairly independently of each other, i.e. in terms of low correlation between

stocks. In the same vein, opportunity may also be thought of as high volatility, since this usually means more differentiation between stocks. Low volatility, on the other hand, means little differentiation and therefore less opportunity.

It might, however, not be quite that straightforward: the existence of return factors (such as value and momentum) implies correlations between stocks, and high volatility might occur in times in which returns are dominated by unexpected shocks. In this article, we explore the relationship between correlations and volatility on short and medium term active manager returns – in order to find out how reliable this market lore is.

We examine a number of regions and treat systematic (overwhelmingly quantitative, factor based) managers as a special subgroup of the total manager universe, possibly adding a further angle. But we begin with the question of whether pairwise correlations and volatilities are telling us the same thing. In other words: are volatilities high when correlations are high, and vice versa?

Here and in the following we have defined average pairwise correlations as the average coefficient of correlation between the local currency returns over 20 day periods for all possible pairs of stocks in a region. The cross sectional volatility has been defined as the standard deviation of monthly local currency returns within a region. Quarterly and annual readings have been generated by averaging monthly values.

It might seem reasonable to expect that periods of high volatility are also periods in which stock returns are highly correlated. There is some evidence for this (figure 1).

But we can also see an increase in average pairwise correlations while this cannot be said for cross sectional volatility. Nor is this true for all markets and all periods. Broadly speaking, correlations have increased and were generally positive across the last 10 years, whereas prior to that there were positive and negative relationships. It would seem wrong to count on a stable and positive relationship between average pairwise correlations and cross sectional volatility.

For our analysis, we sourced manager returns from Mercers MPA (Global, Australia, eurozone, Europe, Japan, UK and US LC Core) and the index returns from MSCI. We then created two sub-groups within each manager universe: quantitative and other.

“Quantitative” managers are those that, on the basis of their process description, the product name or the firm description, indicate that their processes are overwhelmingly quantitative in nature. “Other”

Do low intra-stock correlations and high cross-sectional volatilities make life easier for active managers, whether quantitative or otherwise? Our results are less clear-cut than we had expected.

Cross sectional volatility Average pairwise correlation (RHS)

Volatility Average r2

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12/91 12/95 12/99 12/03 12/07 12/11 12/15

Volatility Average r2

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0.2

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0.6

0.7

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12/91 12/95 12/99 12/03 12/07 12/11 12/15

Volatility Average r2

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0.4

0.6

0.8

1.0

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12/91 12/95 12/99 12/03 12/07 12/11 12/15

Based on the global research universe of Invesco Quantitative Strategies comprising approx. 3000 securities. Source: Invesco Quantitative Strategies. Data as at 31 March 2016.

Market Opportunities

managers include managers that might have quantitative screens but have important judgmental elements and of course those that do not use quantitative elements in their processes. Unsurprisingly, Invesco Quantitative Strategies is included amongst the quantitative managers.

For those two groups and the regional universes we created monthly median and average active returns. For most months and universes, there was only little difference between the two, but especially in 2008 and 2009 average returns were skewed by fantastic outliers. We therefore consistently used median returns. It should also be borne in mind that the data set was to some extent subject to biases. Dead track records might have been removed, products with poor starts might not be included in the universes, poor returns of a product set to close might not be reported and the composites that form the basis of the reported figures might not be strictly representative, to name a few potential problems. It is therefore safe to assume that the active returns were somewhat exaggerated, especially in the more distant past.

One potentially interesting finding is that the active returns of both groups are positively correlated in all regions. Table 1 shows the correlation between the monthly active returns of quantitative and other managers in the various universes over the last ten years, i.e. over a comparatively recent period which may reflect current investment practices better than the full data history.

We now look at correlations between stocks. The monthly correlation within a market is defined as the average pairwise correlation (r²) of the daily stock returns of all the market’s stocks within a region. Even in a small universe like Australia, we

have millions of pairwise correlations, and globally we have well over a billion. We then move on to look at an ordinary least squares regression between the monthly, quarterly and annual results of the average pairwise correlations and the manager returns. This analysis has been performed four times: contemporaneous on absolute and ranked levels of returns and correlations, lagging the returns by one period and using the change in the level of average pairwise correlations. Table 2 shows the summary results of our analysis.

In some markets, average pairwise correlations are high (and usually negative), but the vast majority is not statistically significant. And whilst high or increasing correlations are often negatively related to active returns, there are a fair number of positive, albeit insignificant relationships. The strongest exception in this context is the World where a majority of correlations are significant. The lack of explanatory power of levels may be connected with the noticeable upward movement in the average pairwise correlations after 2000.

0.54

0.78

0.71

0.49

0.66

0.86

0.50

Source: Mercer MPA for manager returns and MSCI for index data, Invesco for calculations. Data history: 31 March 2006 – 31 March 2016

-0.07 -0.11 -0.26 -0.11 -0.13 -0.28 -0.06 -0.12 -0.10 -0.02 0.00 -0.28

0.00 -0.01 0.02 -0.06 -0.05 -0.09 0.02 0.06 -0.19 -0.15 0.32

0.03 0.03 0.06 0.05 0.04 0.06 0.05 0.11 0.19 -0.21

-0.03 -0.07 -0.15 -0.05 -0.10 -0.20 -0.01 -0.01 -0.19 -0.11 -0.13 0.06

-0.23 -0.08 -0.26

-0.04 -0.11 -0.10 -0.06 -0.12 0.04 -0.05 -0.08 -0.12 0.03 -0.04 0.05

-0.28 -0.28 -0.02 0.08 -0.02

Bold values are statistically significant at a 95% level.Source: Mercer MPA for manager returns and MSCI for index data, Invesco for calculations. Data history: 31 December 1991 – 31 March 2016 (from 31 December 1998 for eurozone).

0.34% 0.80% 0.63% 0.45% 0.22% 0.16% 0.31%

0.79% 0.34% 0.90% 0.28% 1.34% 0.57% 0.91%

0.63% 0.48% 0.53% 0.56% 0.49% 0.31% 0.57%

Average quarterly active returns in the 20% of quarters with the lowest and highest average pairwise correlations and in all quarters.Source: Mercer MPA for manager returns and MSCI for index data, Invesco for calculations. Data history: 31 December 1991 – 31 March 2016 (from 31 December 1998 for eurozone).

Market Opportunities

However, if we look at changes rather than absolute levels, the relationship between average pairwise correlations and active manager return becomes closer, and at least on a monthly or quarterly level it is often significant.

Another way of looking at the active manager returns is to group them into buckets. Table 3 shows results for five correlation quintiles, using our full data history. The pattern is not uniform. Japan, Australia, the US and the world show the lowest returns in the quintle with the highest correlations, but also below average returns in the periods with the lowest correlations. Europe, the UK and the eurozone do not conform to this picture.

Figure 2 shows recent active manager returns and average pairwise correlations for the eurozone as

an example. Over the last 10 years, the relationship between active manager returns and average pairwise correlations is usually rather weak, and added to this the relationships are more often positive than negative.

In a next step we segmented our active manager returns into two groups, “quantitative” and “other”. The findings were rather sobering. The lack of significant relationships between average pairwise correlations and active manager returns was not caused by the two subgroups behaving differently.

As evidenced by table 4, we can see that, for the most part, the relationships were very similar. There is little meaningful difference between quantitative and other managers, perhaps with the exception of the eurozone and Japan.

We then went on to analyze the relationship between cross-sectional volatilities and active manager returns. As noted above, cross sectional volatility has fluctuated considerably, but unlike pairwise correlation, there has not been any level change. Presumably our expectation should be that times of high cross-sectional volatility are opportunities for active managers. On the other hand, high cross-sectional volatility may indicate crisis and unexpected developments, which could catch active managers off-guard.

So what does the data tell us? As table 5 shows, there was generally a positive relationship between cross sectional volatility and active manager return, and occasionally it was also significant.

However, the picture became far more complicated when changes were considered rather than levels.

• Active return Average pairwise correlation (RHS)

% %

-25

0

25

50

-3

0

3

6

1999

2000

2001

2002

2003

2004

2005

2006

2007

2008

2009

2010

2011

2012

2013

2014

2015

Source: Mercer MPA for manager returns and MSCI for index data, Invesco for calculations. Data history: 31 December 1999 – 31 December 2015 (annual data).

Quant -0.06 -0.09 -0.26 -0.10 -0.10 -0.34 -0.06 -0.13 -0.21 0.02 0.09 -0.11

Non-quant -0.06 -0.11 -0.24 -0.11 -0.26 -0.06 -0.11 -0.08 -0.03 -0.01 -0.29

Quant -0.09 -0.17 -0.19 -0.07 -0.05 -0.33 -0.15

Non-quant 0.01 0.02 0.05 -0.03 -0.02 -0.09 -0.10 -0.10 0.39 -0.10 -0.15 0.35

Quant -0.06 -0.10 -0.08 -0.07 -0.08 0.00 -0.02 0.05 0.07 -0.27

Non-quant 0.03 0.04 0.08 0.06 0.05 0.10 0.06 0.12 0.18 -0.18

Quant -0.03 -0.04 -0.01 -0.02 0.00 -0.04 -0.01 0.02 -0.15 -0.11 -0.16 0.22

Non-quant -0.04 -0.10 -0.22 -0.05 -0.12 -0.22 -0.02 -0.05 -0.20 -0.10 -0.12 -0.03

Quant -0.05 -0.07 -0.18 -0.05 -0.07 -0.25 -0.06 -0.10 -0.15 0.05 0.07 -0.05

Non-quant -0.21 -0.09 -0.30

Quant -0.04 -0.10 -0.11 -0.02 -0.05 0.06 -0.03 -0.05 -0.02 0.02 -0.05 -0.09

Non-quant -0.02 -0.08 -0.05 -0.07 -0.14 0.05 -0.05 -0.08 -0.15 0.02 -0.03 0.11

Quant -0.32 -0.32 0.03 0.02 -0.07

Non-quant -0.15 -0.22 -0.12 -0.31

Bold values are statistically significant at a 95% level.Source: Mercer MPA for manager returns and MSCI for index data, Invesco for calculations. Data history: 31 December 1991 – 31 March 2016 (from 31 December 1998 for eurozone and Europe, 31 March 1996 or Japan, 31 December 1995 for Australia, 31 December 1994 for UK, since before the number of active managers was too small for a meaningful analysis).

Market Opportunities

Then we saw a number of significant relationships, positive and negative.

When separating the returns into buckets again, we found that active managers did better in periods of high cross-sectional volatility (table 6). But the picture was mixed relative to all periods. So high is better than low, but not necessarily good.

So far we have used real life active manager track records. But what would a factor-based portfolio look like? Obviously we cannot answer this for all possible portfolio set-ups, but we can look at a specific and in our view interesting case.

For this we deployed an equal-weighted blend of momentum, quality and value (based on the respective

global MSCI Indices with monthly rebalancing) and again looked at the correlations of cross-sectional volatilities and active returns (table 7).

We could conclude that, over one-month periods, the relationship between the cross-sectional volatility and the returns of the strategy was not significant. Over three or twelve month periods, however, we did find significant relationships between the change in cross-sectional volatility and returns.

Rising volatility was positive, at least during the last 10 calendar years, but we should not attach too much significance to this. There were only two years (2008 and 2009) of elevated volatility over that period, one of which was followed by an exceptionally poor year for the blended strategy (2009; -4.3%). The results over the full sample remained essentially unchanged,

0.07 0.04 0.10 0.07 0.05 0.08 -0.03 -0.19 -0.24

0.01 0.09 0.21 0.08 0.15 0.15 0.04 0.13 0.29 -0.04 -0.05 -0.09

0.04 0.06 -0.04 0.05 0.10 0.01 0.04 0.07 0.25 0.00 -0.01

0.34 0.09 0.22 0.23 -0.01 0.13

0.07 0.13 0.26 0.01 -0.01 -0.02 0.04 -0.13 0.03 0.06

0.09 0.22 0.04 0.11 0.14 -0.23 0.13

-0.02 0.04 0.13 0.01 0.03 0.04 0.06 0.12 -0.10 -0.12 -0.23

Bold values are statistically significant at a 95% level.Source: Mercer MPA for manager returns and MSCI for index data, Invesco for calculations. Data history: 31 December 1991 – 31 March 2016 (from 31 December 1998 for eurozone).

0.64% 0.28% 0.64% 0.48% 0.74% 0.49% 0.55%

0.53% 0.15% 0.22% 0.31% 0.60% 0.33% 0.27%

0.63% 0.48% 0.53% 0.56% 0.49% 0.31% 0.57%

Average quarterly active returns in the 20% of quarters with the lowest and highest cross-sectional volatilities and in all quarters.Source: Mercer MPA for manager returns and MSCI for index data, Invesco for calculations. Data history: 31 December 1991 – 31 March 2016 (from 31 December 1998 for eurozone).

-0.09 0.01 0.08 -0.11 0.05 -0.13

-0.06 -0.10 -0.30 -0.05 -0.25

-0.03 -0.07

Bold values are statistically significant at a 95% level.Source: MSCI for index data, Invesco for calculations. Data history: 31 December 1991 – 31 March 2016.

0.02% 0.28% 0.62%

0.10% 0.44% 1.50%

0.16% 0.49% 1.94%

Average active returns in the 20% of periods with the lowest and highest cross-sectional volatilities and in all periods.Source: MSCI for index data, Invesco for calculations. Data history: 31 December 1991 – 31 March 2016.

Market Opportunities

even if we neutralize 2008/9. We cannot prove a significant relationship between the absolute level of cross-sectional volatility and the relative return of our factor-based strategy.

We also analyzed whether possibly deviations from a “normal” level are meaningful, by dividing the months in our sample in buckets of 20%. Table 8 shows our findings.

The 20% of months with the highest cross-sectional volatility returned a slightly negative average active result while the least volatile 20% of periods showed an average relative return of 0.10 percentage points. This was both below the average (and consistent with quarterly and annual figures). It seems that high is indeed bad but low is slightly worse than average. No wonder linear regressions show a lack of significant relationships.

There is no clear evidence for a universal link between active managers’ returns and cross-sectional volatility or pairwise correlations of stocks. In addition, there is a lack of evidence for a strong differentiation between quantitative and other managers. Over monthly and quarterly periods, average pairwise correlations and active manager returns are generally negatively correlated, whereas the manager returns are positively correlated with cross-sectional volatility. For both measures, we find a negative correlation with changes in the measures. The results of our hypothetical factor example as well as differences between the regions warrant further research.

Michael Fraikin, Head of Global Research Invesco Quantitative Strategies

Market Opportunities

As events develop in the aftermath of the UK vote to leave the European Union (EU), we believe financial market volatility has the potential to feed through to consumption and domestic demand, adversely affecting growth in the UK and Europe.

Globally, we expect the direct impact of the Brexit vote on growth to be limited. It remains to be seen whether tighter financial conditions amid the fallout from the vote, including a potentially stronger US dollar, will dampen global growth. However, we believe uncertainty generated by the “Brexit” outcome is likely to curb investment, not only in the UK and the EU, but perhaps elsewhere, until the outcome of the complicated exit negotiations can clarify the trade and business landscape.

With heightened uncertainty and potential market volatility post-Brexit, we favor a market neutral stance. Though market dislocations such as this one can often present opportunities, we currently do not favor taking significant active risk-on positions in credit, currencies or interest rates. Catalysts for a reversal of the risk-off move are not yet clear, in our view, and uncertainties remain. In our view, this backdrop does not warrant significant risk taking.

We are watching global central banks closely. Both the Bank of England (BoE) and the European Central Bank (ECB) have announced that they stand ready to act as necessary. The BoE increased its liquidity measures by GBP250 billion immediately after the vote, and signaled that it expects to implement fresh stimulus measures in August. In the US, the bond market does not appear to be pricing in a Federal Reserve (Fed) interest rate hike until 2018. We believe that central bank action is only likely in the event of further market dislocations. The post-Brexit vote market reaction has been orderly thus far, in our view, and is unlikely to draw immediate central bank intervention.

While events in the UK and Europe are likely to command the spotlight for the foreseeable future, we are also closely watching developments in China as it seeks to stabilize growth. We believe China’s macro policy has pivoted away from monetary and fiscal stimulus toward supply side reform and efforts to curb leverage in the economy. We believe this shift marks a policy sea change which is likely to cap China’s growth momentum in the coming months.

In emerging markets (EM), several indicators suggest that EM generally has entered into a credit cycle downturn. We expect EM growth to slow as balance sheets are impaired and repaired and other risks associated with slow growth rise, including fiscal and financial sector strains.

We also see evidence of a late cycle emerging in global corporate credit markets. We place most global

credit sectors (US loans, US investment grade, US high yield, emerging markets and Asian credit) in the mid-to-late phases of their credit cycles. We believe European sectors (European loans, European investment grade and high yield) are in the early to mid-cycle expansionary phase.

In the financial sector, changes in global banking regulations have pushed capital, liquidity and asset quality metrics to their strongest levels in decades, but they have also impaired revenue growth and profitability. We believe credit quality differentiation among banks will play an increasingly important role as we enter a more challenged global growth environment.

• The global political backdrop is creatinguncertainty. Downward pressure on global growthis a risk.

• Financial market volatility is creating opportunitiesbut we are watching for catalysts beforeincreasing risk.

• The US Federal Reserve (Fed) is likely on hold.Political risk will likely play a key role in monetarypolicy globally going forward.

• In emerging markets, a potentially stronger USdollar and rising domestic leverage are continuedheadwinds to growth.

• We have downgraded our forecast of US GDPtrend growth in the coming year to 2.3% from2.5% to reflect softer than expected economicdata since the November Summit. While USconsumption and consumer confidence appearto be healthy, other important sectors havedisappointed.

• We expect Europe to grow by around 1.2% overthe next year. The risk is to the downside,however, due to the economic and politicaluncertainty created by the UK’s decision to leavethe EU.

• We expect China to grow by around 6% annuallyfor the foreseeable future, a bit below thegovernment’s target. Inflation is expected toremain at around 2%, also somewhat belowtarget.

• While there are some idiosyncratic bright spots,we believe that overall EM growth prospects arechallenged.

We have downgraded our forecast of US GDP trend growth for the coming year to around 2.3% from around 2.5% to reflect softer than expected economic data since the November Summit.

Invesco Fixed Income held its semi-annual Global Investor’s Summit in June, gathering around 50 of Invesco Fixed Income´s investment professionals from around the world to discuss key themes affecting global bond markets and determine our strategic views for the next 12-18 months. The following represents our current views and outlook.

Market Opportunities

We have seen consumer confidence, autos and some housing measures decline from their cyclical high levels. In addition, capital expenditures and productivity have posted lower than expected performance this year. We now expect capital expenditure to be flat while productivity growth remains highly uncertain. The bounce in the June payroll report brings the three-month moving average of job growth more in line with our 2.3% economic growth estimate.1 Given the decline in other measures of growth, we are not expecting the moving average to meaningfully surpass current levels.

There is good news on US inflation, which has been firming. While driven initially by rents, inflation has become more broad-based. We expect core consumer price inflation (CPI) to reach 2.4% over the next year. We are finally seeing signs of wage inflation, but not as much as we would have expected by this point in the cycle. However, the decline in labor force participation in the last few months and other measures of labor market slack now point to more positive signs of wage inflation after initially slowing over the last six months.

What does this moderate growth and inflation backdrop mean for Fed policy? Near-target levels of unemployment and inflation would typically point to Fed action to raise interest rates. However, the UK’s vote to leave the EU (Brexit) may cause the Fed to remain on hold until it sees greater clarity on the outcome’s impact on global growth, financial market volatility and the path of the US dollar. Tighter financial conditions following the Brexit vote could lower inflation expectations and dissuade the Fed from tightening. US bond markets do not appear to be pricing in a Fed rate hike until 2018. Based on our outlook for US growth and inflation, we expect the Fed to be comfortable raising interest rates in December, with risks to a later move.

We remain cautious on US interest rates, given their historically stretched valuations. The US 10-year Treasury (currently yielding around 1.5%) is the most expensive it has been since the 1960s, according to our estimates, but global deflationary forces are likely to keep some downward pressure on US interest rates.2

We now expect the eurozone to grow by around 1.2% over the next year (down from our previous estimate of around 1.5%), and expect inflation to measure 0-0.5% (current CPI is running at about 0%, well below the ECB’s 2% target).The risks to both growth and inflation are tilted to the downside, however, due to economic and political uncertainty created by the Brexit referendum result. While domestic demand has recovered somewhat over the past year, anemic growth had already reflected a host of constraints on potential growth, including Europe’s unfavorable demographics, a high debt burden, ongoing deleveraging, weak external demand for European exports and eurozone fiscal constraints. Even though the ECB has substantially expanded liquidity, market indicators suggest that investor confidence in the ECB’s ability to achieve full-fledged reflation remains low. Core government yield curves, for example, have collapsed and breakeven inflation rates remain at historical lows.

Beyond our central scenario of slower growth and lower inflation spilling over into the EU and eurozone from an increasingly likely UK recession, political challenges – as opposed to market-led financial risks – could constrain the ECB’s efforts to restore price stability and growth momentum. In addition to the formation of a new UK government and opposition leadership and eventual UK-EU negotiations around Brexit, Italy’s October referendum on Senate reform could be a major risk barometer. The referendum is ostensibly domestic rather than EU-oriented, however, Prime Minister Renzi has said he will resign if it does not pass. As such, the referendum could be interpreted as another protest vote or create relief, as the Spanish election did just after the Brexit referendum.

The run-up to the second quarter 2017 French presidential election and the October 2017 German federal election will also be monitored closely. Other countries that should be closely watched in terms of sentiment toward EU membership are Finland, the Netherlands and Denmark. Political signals about the direction of Europe from these political events and trends will likely influence business investment and household spending, especially on big-ticket items, and hence growth and inflation.

At the November Summit, we had expected monetary and fiscal stimulus to boost Chinese growth. Indeed, earlier this year, investors appeared to be pricing in a modest growth recovery. However, a May article in a major government newspaper, the ‘Peoples’ Daily’, suggested that China’s macro policy had pivoted away from stimulus toward supply side reform and efforts to curb leverage in the economy. We believe this article marks a policy sea change which is likely to cap future growth momentum.

We continue to expect Chinese GDP to grow by around 6% annually for the foreseeable future, a bit below the government’s target. Inflation is expected to remain below the government’s 3% objective at around 2%. Going forward, we expect a “zig-zag” policy approach to achieving desired growth. When GDP growth is below desired levels, we expect increased stimulus. Growth at or above desired levels is likely to bring focus on controlling leverage. Uncertainty around our view centers on two key issues: 1) low productivity growth amid high leverage; and 2) possible policy-maker personnel changes later this year. Low productivity growth suggests that leverage is becoming inefficient and that adding more leverage may not lead to higher growth outcomes. This may hinder the authorities’ ability to influence growth in the future. Policy-maker personnel changes could cause material changes in policy approach or direction.

We are cautious on Chinese bond markets. We believe there is limited room for additional monetary easing. At the same time, Chinese credit spreads have reached historically tight levels. As China pushes through supply side reform and deleveraging of its corporate and financial sectors, we expect some financial market volatility in the second half of this year. Given our expectations for continued deceleration in growth and a pick-up in corporate defaults, we expect credit spreads to widen from

Market Opportunities

current levels. We believe the central bank’s desire for financial market stability means it will carefully try to maintain renminbi stability against its target basket of foreign currencies.

While there are some idiosyncratic bright spots, we believe that overall EM growth prospects are challenged. We believe that EM, in general, is at the later stage of its credit cycle or into a credit cycle downturn. This implies a poor growth outlook, as balance sheets are impaired and repaired, and risks associated with slow growth rise, such as fiscal and financial sector strains. Our work suggests that there is quite a bit of differentiation regarding where countries are in their respective credit cycles - some continue a credit expansion, some are in repair/recovery and most are in the late-expansion/early downturn phase. This dynamic highlights the differentiation that we foresee in macroeconomic and market outcomes for EM countries.

Before the volatility generated by Brexit, the failure of much of EM to participate in the reprieve in financial market volatility fostered by stability in China, a commodity price bounce and a pause in Fed policy normalization is evidence of late credit cycle conditions in EM, in our view. We would have expected EM credit conditions to have shown improvement in that environment, but instead, they had deteriorated sharply. We believe this suggests that much of the EM universe may have entered a credit cycle downturn. The uncertainty and volatility due to the Brexit vote, especially with respect to US dollar strength, is likely to reinforce these conditions, in our view. That said, stability in the US dollar and global risk sentiment may help ease financial conditions and push out the turn in the cycle.

The downturn in the EM credit cycle tends to elevate macro-related risk, including uncertainty over policy direction, and will likely have adverse implications for EM assets, in our view. Markets have already priced in a fair amount of risk over the last year or so due to other factors, such as US dollar strength and concerns about Fed interest rate hikes and now Brexit. We believe the rise in risk premia has left EM markets generally fairly priced, but if credit cycle risks begin to be priced in, EM risk premia could become further elevated in the coming months and years. We are monitoring financial conditions in EM countries, including, for example, credit growth and non-performing loans. To the extent that EM financial conditions continue to tighten as the credit cycle advances, we would expect knock-on effects to growth and repercussions in terms of financial sector and fiscal stresses.

While low commodity prices have helped the commodity-consuming EM countries overall, we believe the best may be over as commodity prices stabilize, especially oil, although not at levels high enough to save commodity producers. Against this backdrop, we favor EM local duration (local government bonds) given its attractive yield potential. There is probably some scope for EM currencies to overshoot, but they have adjusted significantly in the last few years and, in many cases, have reached attractive levels, in our view. We believe EM credit markets have experienced the least in

terms of adjustment, and, going forward, we expect further adjustment in EM credit overall, given credit cycle dynamics.

In the US, we believe the credit quality of the banking sector relative to other countries is very strong. That said, tighter US regulations have squeezed profitability out of investment banking and mortgage businesses, leading to lower returns on equity compared to the past. In addition, loan quality metrics have started to normalize from record levels, so the release of credit loss reserves will no longer provide a boost to earnings. So while credit quality for the group as a whole is strong, it is unlikely to improve much going forward, in our view. For the remainder of 2016, we expect senior debt of US banks to perform broadly in line with the US corporate credit market, as strong fundamentals are offset by heavy potential supply and fair valuations. We still see potential for capital securities of high quality US banks to outperform given strong fundamentals, attractive yields in a low-yield environment and a much more benign supply outlook.

In Europe, we believe negative interest rate policy (NIRP) has constrained profitability in some cases and made it difficult for banks to grow their returns on equity (ROE) back to pre-financial crisis levels. We see Brexit’s impact on bank fundamentals as relatively muted in the short term, but over the longer term, the impact will likely flow through from an economic slowdown in the form of slower top line growth and weaker asset quality. Valuations are likely to be negatively impacted by volatility and more internationally – diversified banks are likely to fair relatively better. European banks have been reluctant to pass on negative interest rates to retail depositors. Rather, they have increased lending rates as interest rates drop further into negative territory. We expect this to impair broader credit creation and potentially economic growth. We favor the Scandinavian and Benelux banks and seek to avoid the southern European banks, such as Italian and Spanish banks, which are challenged by asset quality concerns, in our view.

In Asia, bank credit growth has decelerated, even in the more developed markets such as Hong Kong and Singapore where it has turned negative. However, capital ratios have improved sharply and Asian bank bonds have performed well, despite global market volatility in the first quarter. We believe this resilience was likely due to strong local investor support and the high proportion of lower beta Chinese banks in the Asian bank universe. In the second half of 2016, we expect continued slow loan growth but less regulatory pressure compared with European and US peers. We expect some deterioration in asset quality as economic growth slows, but do not foresee systemic-level stress. We anticipate heavy supply (in the form of senior and capital bonds) to potentially weigh on the market, especially in the investment grade space. We therefore expect general spread widening from current levels, but expect it to be contained by generally strong domestic and foreign demand. Relative stability in the Asia-Pacific region could attract more investment flows to the region post-Brexit vote.

Market Opportunities

We believe determining where economies are in their credit cycles provides insight into their current stage of economic formation and the potential performance of risk assets. We observe that banking sector-induced financial crises tend to elongate credit cycles and, following a financial crisis, we observe that cycles can last about twice as long as the typical cycle (around 65 months from peak to trough). According to our estimates, the current cycle has lasted about 84 months. We believe that most global credit sectors (US loans, US investment grade, US high yield, emerging markets and Asian credit) are in the mid-to-late phases of their credit cycles. European sectors (European loans, European investment grade and high yield) appear earlier on, in our view, in the early-to-mid expansionary phase.

In the US investment grade sector, flat earnings growth and higher leverage in response to debt-financed mergers and acquisitions (M&A) and other shareholder-friendly initiatives are some indicators that suggest a late cycle. Energy remains in a downturn but appears to be past the bottom of its cycle, based on the recent rebound in crude prices and due to an increased focus on balance sheet repair in the sector. A host of other macro and credit indicators suggest that several other US sectors are moving into late cycle: slowing US GDP growth,

bottoming unemployment, slowing corporate revenue growth and flattening profit margins, low corporate credit risk premia compared to fundamentals and rising corporate default rates. Debt-to-GDP among non-financials is approaching cycle highs and the high volume of M&A, some characterized by mega deals and rich valuations, suggests late cycle behavior, in our view. In terms of overall credit quality, we also see the US and Europe displaying a trend toward more credit downgrades compared to upgrades, a further sign of late cycle conditions, in our view.

In the US, strong labor market performance has supported consumption, which has underpinned our above-trend growth outlook. Deterioration in US labor market conditions could pose risks to consumer spending overall, feeding through to weaker growth. Financial market volatility due to increased global growth uncertainties could also dampen US consumer confidence and spending.

Risks out of Europe now pose perhaps the most significant global economic and financial event risks as China devaluation fears recede. If risks of political fragmentation rise, the eurozone is likely to

Expect 2.0 - 2.3% growth in coming year. Labor market improvement on track.

Expect annual growth of 0.8 – 1.2% over the next year with risks skewed to downside.

Expect 0.7% growth in 2016. Investment weak and wage growth insufficient to boost demand.

Expect growth to moderate to around 6%. Growth appears to be stabilizing, but risk of further slowdown.

Expect core inflation to near 2.4% by the end of 2016, barring further drops in energy prices.

Expect annual inflation of 0.0 – 0.5% over the next year with risks skewed to downside.

Expect 0.3% inflation in 2016 due to soft oil prices and stronger yen

Expect 1.5 - 2.0% inflation, below central bank’s 3% objective

Expect first 2016 Fed rate hike in December. Fed continues to be data dependent and risk sensitive through 2016.

Expect greater chance of ECB increases in asset purchases if downside risks to growth materialize. We do not rule out rate cuts but believe they are less likely.

Expect further easing from Bank of Japan at July or October monetary policy meetings.

Large-scale monetary easing is unlikely. Targeted easing measures are being adopted.

Neutral Currently neutral, but likely to change to expansionary.

Expansionary Easy

Expect US dollar to continue to appreciate, but at more modest pace than previously.

Expect euro depreciation if more political risks materialize but solid fundamentals should offer support.

Expect yen to trade between JPY100 - 115 per US dollar this year. A yen below 100 will likely be unwelcome by Japanese authorities due to its deflationary impact.

Expect the Chinese currency (RMB) to move generally in line with target basket of currencies.

Market Opportunities

underperform our baseline scenario of weaker growth and inflation. Anti-EU and/or anti-eurozone political forces could exacerbate headwinds, causing declines in consumer confidence and animal spirits in both the corporate and financial sectors.

As China focuses more on supply side reform and controlling private sector leverage, we could see greater than expected financial market volatility and/or downside pressure on Chinese economic growth. Shifts in policy direction due to possible personnel changes among key policy makers could also affect economic outcomes. Chinese capital outflows and associated volatility were some of the drivers of Q1 risky asset underperformance. Renewed volatility in China is likely to have impacts on the global financial markets.

Destabilizing geopolitical events could have systemic implications for developed market and EM countries. Following the surprising “leave” result in the UK referendum, a push for additional referenda across Europe could pose significant risks to financial markets and sentiment.

Greg McGreevey, CFA, Chief Executive Officer Rob Waldner, CFA, Chief Strategist, Head of Multi-Sector Invesco Fixed Income

1 Source: US Department of Labor, Invesco, 8 July 2016.2 Source: Bloomberg L.P., 13 July 2016.

Market Opportunities

Emerging market (EM) economies and financial markets have recently been going through a period of intense volatility. The common notion is that this EM volatility is due to the US Federal Reserve’s (Fed) desire to raise interest rates with the attendant risk of capital outflows and the build-up of external debt; we are reminded of the taper tantrum of 2013. Add to this the more recent oil and commodity price declines and concerns around China, related to its high levels of indebtedness in the face of moderating growth. Some of this is true, but does not speak to the full story.

Our view is that EM countries are, by and large, at late-expansion/downturn phases of their respective credit cycles. Owing to the buildup of private sector leverage and, in most cases, a concomitant decline in productivity, EM country balance sheets (both public and private) are likely to become increasingly impaired. This outcome is likely to place strains on future growth – and in the process elevate overall macro uncertainties and risk.

Indeed, EM countries are undergoing a process of macroeconomic adjustment, an adjustment needed in order to reduce domestic and external imbalances (see Appendix). These imbalances were generated by a period of sustained and rapid domestic credit growth – that fueled consumption and a build-up in leverage – with little in the way of underlying productivity gains to support future growth.

Gauging where a country is in its respective credit cycle is important; it has implications for assessment of overall macro-related risk and how that risk should be priced by markets. From an investing standpoint, we would want to ensure that we are being properly compensated in the markets of countries where macro conditions suggest higher risk – that is, uncertainty as to economic and market outcomes as a result of where a country is in its respective credit cycle.

But how do we gauge where a country is in its credit cycle? And overall macro conditions? We cover each of these subjects in turn.

It is hardly an exact science, but based on academic work and our own analysis, we have isolated a number of factors that provide guidance on where a country is likely to be in its respective credit cycle. These factors are reflected in our Credit Cycle Index (CCI).

The CCI is constructed by looking at real housing prices as well as credit-to-GDP – in two different but complimentary ways. We first examine the current credit-to-GDP ratio relative to its historical trend.2 When the current value exceeds its trend, this would indicate an excess of credit.

However, unlike many of the developed market countries examined in the literature, the rapid pace of financial deepening in EM countries makes looking only at credit/GDP problematic, given that rising levels of credit reflect maturing credit markets and deepening financial intermediation. Therefore, we augment this by looking at changes on a cross-country basis. When a country experiences credit growth in excess of GDP greater than its peers, this would additionally indicate an excess buildup of credit.

But it could very well be that the CCI is rising for a country where credit growth is decelerating but GDP growth is decelerating even faster. In this case the CCI would be rising where, in fact, credit growth itself is slowing. We therefore supplement the index with two other indicators:

The first is the trajectory of credit growth itself, on an annual basis. To capture the extent of misallocation, we analyze the excess credit growth relative to nominal GDP growth.

Second, we gauge the duration of the prevailing CCI expansion (figure 1).

Credit cycle dynamics, in our view, provide critical insight into divergences between emerging market countries and their likely development in the coming years. In this article, we develop a heat map for emerging market countries, incorporating their respective credit cycles.1

56

55

45

44

43

39

36

36

34

31

24

23

22

19

19

16

16

16

4

0 20 40 60

Thailand

Malaysia

Indonesia

Hungary

Philippines

South Korea

Chile

Poland

Czech Republic

India

Turkey

China

Brazil

Average cycle

South Africa

Colombia

Mexico

Russia

Peru

Quarters

Source: Invesco. Data as at 30 June 2016. Average cycle is the average of five CCI expansions since 1970.

Cycle phase

Repair/recovery Contracting Declining and negative

–

Expansion Rising Rising and positive

Lower than average

Late expansion/downturn

Rising Declining and positive

Higher than average

Downturn Declining Declining and negative

Higher than average

Source: Invesco. For illustrative purposes only. *Average is 16 quarters in duration.

Market Opportunities

We look at the duration of expansion in the CCI for each country relative to the average of the five CCI expansions for EM in aggregate since 1970, which we find to be 16 quarters.3

Based on these factors, we bucket EM countries as in expansion, downturn, repair or recovery phases of their respective credit cycles (table 1). To the extent that the CCI has either peaked or has extended beyond the prior cycle peak (credit growth is slowing and the credit expansion is longer than 16 quarters in duration), we would expect the credit cycle expansion to be relatively advanced, that is, more likely to enter a downturn. In contrast, to the extent that the CCI has either troughed or has extended below the prior cycle trough (credit growth is rising and the expansion is shorter than 16 quarters in duration), we would expect the credit cycle to be relatively nascent.

Countries can be in early, mid- or late-expansion depending on the duration of the prevailing cycle. A repair/recovery phase suggests the country is in the beginning stages of a renewed credit cycle expansion but may yet have work to do in improving bank and private-sector balance sheets.

To be clear, mapping to the cycle is an inexact science and we will continue to refine our approach and work. In this report, we attempt to classify countries based on developments in the CCI and its underlying components, specifically credit growth and the duration of the prevailing expansion. We have less assurance of where a country may be in its respective cycle when we may be at a cycle turning-point. A country late into an expansion may, in fact, be at the initial stages of a downturn or we may see a continuation of the expansion. That said, when a country extends beyond the prior cycle peak as indicated by CCI, there is more likelihood that it enters a downturn.

With these caveats in mind, for EM as a whole, we are in what we believe to be the late expansion/early downturn phase. For one, the aggregate EM CCI is above the two prior peaks, EM excess credit growth has been slowing and the duration of the current credit expansion is beyond the historical average. Figure 2 shows the CCI and excess credit growth for EM in aggregate.

However, this outcome masks considerable variation across countries. Even amongst Brazil, China and India, credit cycle dynamics are quite varied. Where the CCI for China and Brazil indicate the countries are late-expansion/early downturn, for India it indicates the country is in its repair/recovery phase. Credit growth in Brazil is slowing markedly, for India it is expanding, albeit marginally (figure 3).

Table 2, column 4 shows our classification of the different EMs. There are some important differences between the countries:

• Colombia, Mexico, Peru and South Africa appearto be in the midst of an ongoing expansion.

• The Czech Republic, Malaysia and Poland appearto be in a downturn.

Excess credit growth CCI (RHS)

% Index level

-8

-5

-2

1

4

7

-5

0

5

10

15

20

Q1/01 Q1/03 Q1/05 Q1/07 Q1/09 Q1/11 Q1/13 Q1/15

Source: Invesco, IMF, BIS, EM central banks. Data as at 31 December 2015. Excess credit growth is the difference between annual credit growth and annual nominal GDP growth.

Excess credit growth CCI (RHS)

% Index level

-7

0

7

14

21

-15

-10

-5

0

5

10

15

20

25

Q1/00 Q1/03 Q1/06 Q1/09 Q1/12 Q1/15

% Index level

-15

-10

-5

0

5

10

15

20

25

-15

-10

-5

0

5

10

15

20

25

Q1/00 Q1/03 Q1/06 Q1/09 Q1/12 Q1/15

% Index level

-8

-6

-4

-2

0

2

4

6

-15

-10

-5

0

5

10

15

20

Q1/00 Q1/03 Q1/06 Q1/09 Q1/12 Q1/15

Source: Invesco, IMF, BIS, EM central banks. Data as at 31 December 2015. Excess credit growth is the difference between annual credit growth and annual nominal GDP growth.

Market Opportunities

• Several countries in Asia appear to be in veryadvanced stages of their credit cycles.

• Hungary, India and Indonesia appear to be in arepair/recovery phase.

The phase in which a country is has implications for prospective economic and financial market outcomes; it will likely influence the outcome of policy action and orientation as well. The early credit cycle upturn is characterized by the repair/recovery phase. It occurs before the full benefit of a credit expansion can be seen on economic growth momentum. Contrast this with countries in the late-expansion/downturn phase, where we would expect to see early signs of slowing economic growth momentum. During a credit cycle downturn, balance sheets are impaired and, in time, repaired to health – all of which tends to have an adverse impact on economic growth. Credit cycle downturns – from peak to trough – tend to last several years.

Beyond considerations of economic growth, how is the credit cycle tied to macro vulnerabilities?

Macro vulnerability is likely to be a reflection of

(1) policy responsiveness;

(2) policy flexibility;

(3) initial economic conditions.

With respect to initial conditions, arguably a country with greater fiscal flexibility and ability of the banking system to absorb loan losses is better positioned to weather a credit cycle downturn than a country with less. We consider a country late in its credit cycle with limited financial and fiscal flexibility and

a weaker banking system to be more vulnerable from a macro perspective.

Oftentimes credit busts are associated with financial crisis. However, it is important to note that this occurs in only one third of cases, since 1960.4 More often than not, countries experience a sustained period of sub-par economic growth. This outcome, in itself, may induce more macro-related stresses such as social unrest or political uncertainty, serving to exacerbate the economic outcome.

It is in this context that we consider macro vulnerability – defined here as economic, financial or politicalconditions that raise the overall level of investmentuncertainty. High levels of macro uncertainty reducethe confidence of investment, whereas low levels ofmacro risk raise the confidence of investment. Highlevels of macro vulnerability do not imply highlikelihood of economic or financial crisis, ratheruncertainty related to economic outcomes. Similarly,low levels of macro vulnerability do not imply lowrisk of crisis, rather more certainty related toeconomic outcomes.

We’ve compiled a heat map of macro conditions highlighting financial flexibility, fiscal flexibility and indicators of banking system soundness for EM countries (table 2). We measure financial flexibility as the capacity for paying down accumulated debt. This is based on the excess of domestic debt/GDP relative to income per capita (productivity). Fiscal flexibility is based on the level of consolidated government debt/GDP; and bank soundness is considered based on the combination of the loan/deposit ratio, tier 1 capital ratio and nonperforming loans (NPLs).

Most EM countries currently exhibit a measure of credit-cycle vulnerability, based on these criteria.

Brazil Rising Declining/positive Longer Late expansion/downturn Lower 74% Lower 0.8 12.4 3.1 Fair

Chile Declining Stable/positive Longer Late expansion/downturn Lower 17% Lower 1.0 9.9 2.0 Fair

China Rising Declining/positive Longer Late expansion/downturn Lower 44% Lower 0.7 11.3 1.7 Fair

Colombia Rising Stable/positive Shorter Expansion Moderate 49% Moderate 1.0 7.3 3.1 Less sound

Czech Republic Declining Declining/negative Longer Downturn Moderate 41% Lower 1.0 17.3 5.6 Fair

Hungary Stable Stable/negative Longer Repair/recovery Lower 76% Moderate 1.0 12.0 13.0 Less sound

India Contracting Stable/negative - Repair/recovery Higher 67% Moderate 0.8 10.1 5.9 Less sound

Indonesia Contracting Declining - Repair/recovery Higher 27% Higher 1.0 18.8 2.4 More sound

Malaysia Declining Declining/negative Longer Downturn Lower 57% Lower 0.9 13.9 1.6 Fair

Mexico Rising Rising/positive Shorter Expansion Higher 54% Moderate 0.7 14.7 3.0 More sound

Peru Rising Rising/positive Shorter Expansion Moderate 23% Higher 1.6 11.1 4.1 Less sound

Philippines Contracting Declining/positive Longer Repair/recovery Moderate 37% Higher 0.7 13.6 1.9 More sound

Poland Declining Declining/positive Longer Late expansion/downturn Lower 51% Moderate 0.9 13.5 7.1 Fair

Russia Declining Declining/positive Shorter Late expansion/downturn Lower 17% Lower 0.9 8.8 3.7 Less sound

South Africa Rising Rising Shorter Expansion Moderate 50% Moderate 0.9 12.3 3.2 Fair

South Korea Rising Rising Longer Late expansion/downturn Lower 36% Lower 1.0 11.7 1.7 Fair

Thailand Contracting Declining/positive Longer Repair/recovery Lower 43% Lower 1.1 13.9 2.7 Fair

Turkey Rising Declining/positive Longer Late expansion/downturn Lower 33% Lower 1.2 12.5 2.7 Fair

Excess credit = trend in private sector credit growth relative to nominal GDP growth; duration = duration of CCI expansion relative to historical average; domestic = domestic credit/GDP relative to Income/Capita; fiscal = gross general government debt/GDP; loan/dep = loan/deposit ratio; NPL = non-performing loans to total loans (%).Source: Invesco, IMF. Data as at 15 December 2015.

Market Opportunities

• US subprime crisis • Euro Greek crisis • 1 October 2015

-1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

Brazil

China

Eurozone

Indonesia

India

Mexico

Malaysia

Russia

South Africa

Singapore

Thailand

USA

Financial conditions index, 0 = normal

Source: Bloomberg, Invesco calculations. Data as at 31 March 2016.

Colombia, Mexico, Peru and the Philippines exhibit what we would characterize as low to, at most, moderate macro-related credit-cycle vulnerability.

As the US dollar weakening since 2004 (figure 4) tended to reinforce the upturn in the credit cycle via capital inflows and currency appreciation, what is likely exacerbating the downturn in the credit cycle for a number of EM countries is the recent appreciation in the US dollar.

Though the emphasis tends to be on external vulnerabilities related to US dollar strength, we are more concerned about the impact on EM domestic dynamics. US dollar appreciation and the concomitant depreciation in EM currencies serve to tighten domestic financial conditions, which may be manifested in a more-pervasive downturn in the credit cycle. EM currency depreciation serves not as a means of loosening domestic monetary conditions but, in fact, tightening them. Similarly, we witness the pass-through of higher short-term interest rates via currency depreciation.

In contrast to developed markets, where the policy interest rate matters, arguably, overall monetary conditions in EM are largely a function of (1) the policy rate; (2) the exchange rate; and (3) long-term local bond yields. In some countries, the policy rate has more influence, whereas, in others, the exchange rate is decidedly more important as the nominal anchor. Those countries more sensitive to the exchange rate will tend to see higher pass-through of currency depreciation to higher local bond yields – and at the same time tighter domestic financialconditions.

That said, we are likely in the late stage of the currency adjustment, evidenced by a tightening in overall domestic financial conditions, which is likely to suppress domestic demand and, in the process, materially suppress imports.

The upshot of all this tightening in credit and financial conditions is that it serves to rebalance the economy both domestically and externally. Moreover, as the currency depreciates and economic activity and wage growth slows, external competitiveness is increasingly restored and current account balances improve as imports slow and exports grow.

However, in contrast to a normal business cycle downturn, an unfortunate outcome at this stage in the credit cycle for many countries is that we may see a measure of private-sector balance sheet impairment that exacerbates and extends the downturn as balance sheets are gradually repaired.

This is likely to depend on where a country is in its respective credit cycle, macroprudential measures and the extent of capital buffers to absorb loan losses. For countries at the latter stages of their credit cycles, the above responses may not be sufficient; the government may need to take more drastic steps to avert deterioration in private sector balance sheets – including transferring losses to its own balance sheet.

There are two dynamics that we are watching to assess the pace and magnitude of macro adjustment at this stage in the credit cycle:

As a gauge of overall competitiveness, we are watching trends in real effective exchange rates. Since 2011, real effective exchange rates for EM countries have declined, largely reflecting trade-weighted depreciation in their nominal exchange rates (figure 4). We expect that moderation in domestic prices and wages will increasingly contribute to the real exchange rate adjustment going forward, to the extent that currency depreciation fosters a tightening in overall domestic financial conditions.

We monitor overall domestic and external financial conditions to detect countries that may be transitioning from a growth slowdown to a more disorderly deleveraging. Our financial conditions index summarizes the risk appetites of the domestic financial system.

We had been seeing an overall tightening in domestic financial conditions in EM countries, suggesting that tighter credit conditions would likely follow (figure 5).

80

85

90

95

100

105

110

Q1/94 Q1/99 Q1/04 Q1/09 Q1/14

Source: BIS. Data as at 31 December 2015.

Market Opportunities

Restoring domestic and external rebalance

The ‘fragile five’ were not so much countries running large current account deficits as much as they were – and are – countries struggling with varying degreesof domestic and external imbalance; they just happento be more-sensitive to capital flows than othercountries suffering from the same maladies. Arguably,the rise in domestic leverage – supporting, as it has,domestic demand – has at the same time beencontributing to macro imbalance.

What is at issue is restoring internal and external balance via necessary macro adjustment. As we will show, the necessary adjustment is a combination of fiscal expenditure reduction combined with currency depreciation.

A frame of reference for thinking about macro adjustment for an open economy is internal and external balance. Internal balance refers to ‘full employment’ and external balance to ‘balance of payments equilibrium’ (balance of inflows and

outflows). The concept of domestic and external balance is a longstanding one, popularized in the 1960s by T.W. Swan. The Swan diagram (figure 7) is a useful visualization that allows us to gauge the types of adjustments required to restore both domestic and external balance for an economy. How does an economy achieve internal and external balance in this construct?

Based on initial conditions and policy action, a country can move towards or away from this optimal balance. Policy response can be classified as expenditure-changing, expenditure-switching or direct controls. Expenditure-changing impacts domestic demand and, as a result, imports, which alters the trade balance; think of this as fiscal policy. Expenditure-switching impacts the exchange rate and, as a result, the demand for domestic relative to foreign goods; think of this as monetary policy. Direct controls relate to trade barriers, price or wage or exchange controls.

The impact is likely to be validated by deterioration in domestic demand conditions, indicated by slowing retail sales and import growth.

Indeed, credit conditions had been worsening in EM, broadly, in recent quarters (figure 6). Based on the Institute of International Finance (IIF) EM bank lending survey, we had been seeing a trend toward tightening in lending standards and softening loan demand with an upturn in NPLs. According to this data, deterioration in credit conditions had been broad-based across countries and regions.

Though this reflects conditions that prevailed in Q1 2016, to the extent that tighter domestic financial conditions in EM countries prevail, we expect this trend to be sustained. Moreover, traditional monetary policy tools may become less effective in reversing the moderation in credit growth given late-credit cycle dynamics – particularly if we are faced with tighter US monetary policy. It suggests that slower growth conditions in EM are likely to persist for some time.

Arguably then, the weakening of the US dollar in early 2016 – amid concerns on the part of the Fed relating to the generalized tightening in global financial conditions – may serve to at least push out, if not begin to reverse for a time, ongoing tightening in EM domestic financial conditions that had persisted over the last several quarters. However, given that we believe we are in the late credit-cycle phase for many EM countries, we believe that the positive impact is only likely to be temporary. Moreover, a resumption of US policy interest rate normalization is likely to further facilitate the process of EM domestic rebalancing.

In fact, based on available evidence, the period of US dollar stabilization in H1 2016 did little to reverse ongoing deterioration in credit conditions across EM countries; the IIF survey indicated further tightening in EM credit conditions. This suggests to us that the credit cycle in EM is relatively advanced and, with it, prospects of moderating growth have increased as domestic rebalancing proceeds.

Rashique Rahman, Head of Emerging Markets Jay Raol, Senior Macro Analyst Invesco Fixed Income

Contributions from Arnab Das, Head of Emerging Markets Macro Research and Sovereign Analysis, and Yi Hu, Senior Credit Analyst, Invesco Fixed Income

1 This article is the second part of a three-part series on emerging market debt. The first part, „Understanding the emerging market credit cycle”, was published in Risk Reward Q1/2016. The third and final part will follow in a later edition.

2 Similar to Drehmann, Borio and Tsatsaronis, 2012.3 See Credit Booms and Macroeconomic Dynamics: Stylized Facts

and Lessons for Low-Income Countries, IMF Working Paper (January 2015); How Do Business and Financial Cycles Interact?, IMF Working Paper (April 2011); Financial Cycles: What? How? When?, NBER International Seminar on Macroeconomics, Chapter 7 (September 2011).

4 Source: Policies for Macroeconomic Stability: How to Deal with Credit Booms, IMF Staff Discussion Note (June 2012).

Diffusion index

0

10

20

30

40

50

60

70

Q4/09 Q4/10 Q4/11 Q4/12 Q4/13 Q4/14 Q4/15

Contractionary

Expansionary

Source: IIF. Data as at March 2016. Diffusion index (50 = neutral) is average of answers to 14 questions. Values above 50 indicate easing lending conditions relative to previous quarter and vice versa.

Market Opportunities

Domestic demand

External balance

Internal balance

C/A deficit,inflation

C/A surplus,inflation

C/A surplus, unemployment

C/A deficit,unemployment

Domestic demand

External balance

Internal balance

Real exchange rate Real exchange rate

‘Fragile Five’

(a)

(c)

(b)

C/A = current account. ‘Fragile Five’ are Brazil, India, Indonesia, South Africa and Turkey.Source: Invesco. For illustrative purposes only. The x-axis represents domestic demand (absorption) and the y-axis the real exchange rate. The blue line represents external balance (EB) and the green line the internal balance (IB). The four quadrants represent various internal and external states, with the intersection of EB and IB being the optimal point, that of internal and external balance.

Arguably, fiscal policy will have more impact on domestic demand and should be the preferred route to achieving internal balance; monetary and exchange-rate policy will have more impact on the real exchange rate and should be the preferred route to achieving external balance. The convergence path to internal and external balance, based on this framework, requires a combination of domestic demand moderation to induce disinflation, coupled with (real) exchange rate depreciation to improve external competitiveness.

Markets may be doing the adjustment in lieu of active policy response. As we argue, US dollar strength and EM currency depreciation may be inducing not only the needed real exchange rate adjustment for restoring external balance but also – via tightening in domestic financial conditions – moderation in domestic demand to restore internal balance as well.

Market Opportunities

Oil prices are volatile, and have always been volatile. Real or expected supply shortages can lead to huge jumps in the oil price, with the oil crises of the 1970s and 1980s being well-known examples. During recessions, on the other hand, oil suddenly becomes cheap, sometimes extraordinarily so. But today, there is no recession. And, untypically, market participants have not greated low oil prices with unbroken enthusiasm. So what is different this time?

At first glance, two things in particular appear new: the shale oil revolution in the US and the fact that China, the world economy’s newest player, is undergoing structural change. Add in Saudi Arabia’s new production policy, and prices suddenly plunge with no major recession, but only slightly weaker growth in sight. But are these really the most important factors?

Since the global financial crisis, Asia has contributed between 50% and 80% of global incremental oil

demand, and the region has added 1.33 million barrels a day of incremental demand in 2015 versus 0.5 million barrels in 2014.2 This represents around 70% of global incremental demand of 1.9 million barrels a day in 2015, versus less than 50% in 2014. Obviously, demand has not been a problem.

And it is likely to remain high: 70% of oil is used for transportation,3 and there’s no greater stimulus for commodity consumption than low prices. For example, on a year-on-year basis, sport utility vehicle (SUV) sales year to date are up 10% in the US, and 63% in China, following 50% growth in 2015 and 2014.4 In China alone, almost 800.000 SUVs have been sold newly registered in December 2015 (figure 1). Furthermore, miles driven in the US have been trending steadily higher, and have now reached record growth of 4% year on year.5 Per capita air travel in China is growing at one of the highest rates we’ve seen over the last five to seven years, and that there is a large number of people who are transitioning from commuting by bicycle to taking buses and cars. Those are secular growth drivers that should sustain some level of baseline demand growth even as overall GDP growth attenuates. Furthermore, compared to other commodities, oil demand is less reliant on China. The country consumes just 12% of the world’s oil, versus more than half of the iron ore, aluminium, copper, nickel and zinc produced around the world.6 So, whatever happens in China, the consequences should be less severe for oil than for other commodities. When it comes to oil, China does not have to grow at 7% to 8% to prevent demand from collapsing.7

To summarise, there has been no evidence of demand declines, in China or elsewhere. And, even if this changes, cuts in capital expenditure would likely fix any massive hiccup.

So if demand is stable, are we seeing a supply glut? The answer is yes – but for reasons other than often assumed. The shale oil revolution in the US has certainly been an important factor. Recently, however, US supply has gone into decline (figure 2). What has really pushed the market off the rails is Saudi Arabia’s determination to drive competition out of the market – even if that means operating at a loss.

Traditionally, Saudi Arabia and other OPEC8 members have cut their production as a way to prop up falling oil prices. But, as oil prices plummeted throughout 2015, Saudi Arabia kept its oilfields pumping: in November 2014, Saudi Arabia pumped 9.584 million barrels of oil a day, while in November 2015, it upped production to 10.130 million barrels a day.9 The country has approximately USD600 billion in currency reserves10, allowing it to bear the brunt of lower prices for a few more years yet. Nevertheless, in our view, even Saudi Arabia cannot flood the market with

Since oil prices fell from more than USD110 a barrel in mid-2014 to below USD30 in January 2016, this dramatic plunge has reverberated through stock and bond markets worldwide. Although prices have recovered somewhat in recent months,1 oil prices are historically low. But, at the end of the day, what investors really want to know is where the opportunities lie. We will argue that, despite current uncertainties, the energy sector may hold great long-term potential for those who can look past shorter-term fears.

Low oil prices seem to be stimulating consumption

Number of motor vehicles (SUV) newly registered with a government authority

0

100,000

200,000

300,000

400,000

500,000

600,000

700,000

800,000

1/10 1/11 1/12 1/13 1/14 1/15 1/16

Source: Bloomberg. Data as at 30 June 2016.

The falloff comes after several years of production increases

5,453

5,597

5,991

7,081

7,874

9,429

9,262

0 2,000 4,000 6,000 8,000 10,000

December 2009

December 2010

December 2011

December 2012

December 2013

December 2014

December 2015

Thousand barrels per day

Source: US Energy Information Administration, February 2016. Production of crude oil and lease condensate in the US.

Market Opportunities

cheap oil forever. The government said in December that it plans to gradually cut subsidies that people receive on oil, water and electricity. Over time, moves like this could lead to pressure on the government to stop producing oil at a loss and help firm up oil prices. In our view, the current supply glut is a relatively short-term problem. According to the US Energy Information Administration, production will rise only modestly (figure 3).

Coupled with the relatively stable demand, this is good news for the energy sector. However, an important question for investors is when and whether rising prices will also lead to rising capex. After all, the sector does not only consist of the few well-known oil majors, but also of lots of smaller oilfield suppliers and equipment manufacturers whose fortunes depend on oil producers’ investments.

In 2013 and 2014, global capex in the oil sector was over USD600 billion each year, before dropping to just over USD500 billion in 2015 (table 1). We’re already hearing from exploration and production (E&P) companies that the number will be even lower in 2016. It is quite possible we have not seen the bottom yet – given the storage overhang, the strong US dollar and, last but not least, the uncertainties surrounding the oil price. With oil at USD30 per barrel, oil production loses all pretence of profitability, and capex would have to come down further. But at USD60, the picture could look quite different.

In December 2015, we began to see production declines on a month-over-month and a year-over-year basis as earlier capex curtailments were starting to take hold. Often, big offshore projects were shelved, decisions which cannot be reversed easily once oil hits USD60 again. These are long-term deferments in projects that have implications for future supply – but will nevertheless help to stabilise oil prices and thus lead to renewed capex later.

And, even though global capex has come down, there are regional hotspots of activity. For example, drilling activity in Russia was relatively robust in 2015, and is expected to remain so this year, helped

by a much weaker rouble. Do not underestimate the potential of weaker petro currencies to withstand these lower oil prices. And in Saudi Arabia – perhaps in pursuit of volume over value – the number of active drill rigs has steadily increased since the downturn began two years ago.

In addition, one must differentiate between short-cycle and long-cycle oil supply. US shale has responded to lower prices with significant cuts to capex. But longer-dated barrels from multi-year, multi-billion dollar projects in deep offshore or Canadian oil sands are harder to stop and start. In fact, the investment overhang could be rather severe and it is possible to see US shale oil shift from being part of the problem to part of the solution in terms of the global supply/demand balance.

Bad news also comes from Asia, where capex has yet to decline in real terms. For most national oil

World petroleum and other liquids production is projected to rise by 1 million barrels per day from 2015 to 2017, while non-OPEC production is expected to drop overall. There are exceptions, however: The US Energy Information Administration notes Canadian production is expected to increase by almost 0.2 million barrels a day in both 2016 and 2017, as several oil sands projects begin production.

• Non-OPEC production • Total world production

57.55

57.19

56.68

95.74

96.44

96.70

0 20 40 60 80 100

2015

2016E

2017E

Million barrels per day

Source: US Energy Information Administration, Short-Term Energy Outlook, 8 March 2016. Includes production of crude oil (including lease condensates), natural gas plant liquids, biofuels, other liquids, and refinery processing gains.

The Middle East is the only region to increase spending during that time

(USD mn) (USD mn) (USD mn) (%) (%)

North America 176,612 194,090 125,754 9.9 -35.2

Middle East 3,477 40,180 42,550 15.5 5.9

Latin America 73,934 76,553 69,901 3.5 -8.7

Russia/FSU 48,211 44,320 35,491 -8.1 -19.9

India, Asia & Australia 108,111 106,370 91,360 -1.6 -14.1

Europe 45,788 45,770 35,314 0.0 -22.8

Africa 23,383 25,726 20,916 10.0 -18.7

Majors (international) 104,946 100,897 84,487 -3.9 -16.3

NAM independents (international) 15,172 14,635 11,250 -3.5 -23.1

Other E&P (international) 4,045 5,127 4,166 26.7 -18.7

International spending total 458,367 459,578 395,495 0.3 -14.0

Worldwide E&P spending

Source: Barclays Research and Company Reports, 2015. NAM = North American. A = actual, E = estimate.

Market Opportunities

companies, the 15% to 20% drop we saw in 2015 was related to cost deflation.11 We will probably see real capex decline in 2016, likely by a further 20% (or USD75-95 billion), not least due to cost deflation. No new projects are being taken on. All new liquefied natural gas (LNG) projects are likely to be postponed indefinitely.

Thus, all in all, the outlook for capex is mixed. Investors must therefore be selective.

Even for long-term investors, short-run developments matter – or, to quote John Maynard Keynes, “in the long run, we are all dead”. Thus, even for optimists, it pays to avoid short-term risks. There have already been some bankruptcies among small companies. And we believe there are more to come. Ultimately, however, this could turn out to be a healthy development that will allow companies with strong balance sheets to pick up good assets at fire sale prices.

One reason we have increased our default expectations is our belief that a number of troubled US companies have adopted a new attitude about formally filing for bankruptcy. We think we are about to see a new trend, whereby US company managements will weigh the merits of a so-called “pre-emptive default” or “strategic bankruptcy.” What’s interesting about this process is that many stressed US companies today may have 12 to 18 months of liquidity on hand, yet may decide to file for Chapter 11 protection much sooner than some market participants expect.

Importantly though, we don’t think investors should become overly pessimistic about rising defaults. This may sound counterintuitive, but default is a lagging indicator. We would ask investors to recall what happened in the high yield markets of 2008 and 2009: defaults rapidly increased in 2009, and yet the asset class generated its best-ever total return.

Indeed, for investors, financial distress is not always bad. In North America and particularly in Canada, the oil sector is highly dependent on bank financing. These commercial banks are now asking their borrowers to sell assets to repay debt. This is squeezing many producers who suffer from a mismatched term structure between assets that are long-term users of capital and funding that is short-term. The US Office of the Comptroller of the Currency (OCC) is now keeping a close eye on energy lending and we are seeing a diminished appetite on the part of traditional providers of the reserve-based credit facilities that were once the lifeblood of the industry. As a result, we see a growing backlog of classic distressed opportunities involving good companies with high quality assets facing constrained liquidity.

From a purely economic standpoint, oil prices are based on how much money it costs to get that resource out of the ground. At the end of the day, there are certain costs for extracting oil, which must be accommodated. We believe the price per barrel should come back to a meaningfully higher level over the longer term.

We work with an average holding period of about five to seven years, we’re willing to buy stocks that others are ignoring – or fleeing – when we believe that their prices don’t reflect their fundamentals. We’re looking for energy companies with good assets and strong balance sheets that can weather an extended oil price downturn. Lots of fear is priced into the market right now. For investment managers like us, that signals opportunity.

We also try to invest in the best companies, those operating in the most economically viable basins, and right now we’re very focused on companies that are operating in the Permian Basin.12 We prefer companies that have moderate to low leverage, strong management and assets that are attractive in today’s low oil price environment.13

In 20 years of natural resources investing, oil prices have never been this volatile and disconnected from business fundamentals. The market wants to value equities at a level that’s unsustainable. For us as long-term value investors, this is an attractive situation. With the ability to sift through asset quality and acquire good companies that get better with time, we believe the market is handing us a truly unique opportunity.

Kevin Holt, Chief Investment Officer, Invesco US Value Equities Shaia Hosseinzadeh, Managing Director and Head of Energy, WL Ross & Co. Norm MacDonald, Portfolio Manager, Natural Resources, Invesco Canada and Invesco US Susanta Mazumdar, Investment Director, Invesco Asia Pacific Dean Newman, Head of Emerging Market Equities, Invesco Perpetual Scott Roberts, Co-Head of High Yield, Invesco Fixed Income

1 Spot price per barrel Brent, USD49 as at 29 May 2016.2 Sources: Goldman Sachs Asia Securities Ltd., BP World

Statistics, June 2016.3 Source: EIA Monthly Energy Review, February 2016.4 Sources: Bloomberg, China Automotive Information Net, Ward’s

Automotive Group, February 2016.5 Sources: US Energy Information Administration, US Department

of Transportation, January 2016.6 Sources: CRU, Wood Makenzie, February 2016.7 India’s oil demand, on the other hand, surged by 8% in 2015,

contributing 16% of incremental global demand. India is now second largest contributor to global oil demand. From January to May 2016, India’s demand has risen by a further 10%.

8 Organization of the Petroleum Exporting Countries.9 Source: “Saudi Arabia won’t change oil production policy,” Wall

Street Journal, 30 December 2015.10 Source: International Monetary Fund, 25 February 2016.11 Sources: Morgan Stanley Asia Securities Ltd., Invesco Asset

Management.12 The Permian Basin, also known as the West Texas Basin, is a

large sedimentary basin in western Texas and southeastern New Mexico. It contains rich petroleum, natural gas, and potassium deposits and is one of the most well-studied geologic regions of the world. Source: Encyclopaedia Britannica.

13 An alternative could be buying some cheap gas utilities which got de-rated significantly in 2015 along with the upstream sector reflecting reverse substation from gas to liquid. Most of these gas distributors have strong earnings, cash flows and returns even at lower oil prices. As oil prices stabilise, gas consumption has started to grow at double digit pace in 2016, particularly in China and India. Asia’s gas demand is also benefitting from lower prices of imported liquefied natural gas (LNG).

Methodology

State space models were developed in the 1960s for the engineering sciences.1 At the end of the 1980s, they found their way into econometrics as structural time series models.2 However, contrary to what the name implies they are not restricted to the structural representation of usual time series. They are equally suitable for ARIMA models (i.e. the Box-Jenkins model), dynamic linear models, cubic spline models and stochastic volatility models as shown in the empirical application at the end of this article.

A linear state space model consists of two equations,3 the observation equation:

1a) y Zt t t t= +α ε

and the state equation:

1b) α α ηt t t t tT R+ = +1

The observation equation corresponds to the regression equation of a classic regression model, but is far more flexible. It explains yt, the (p × 1) vector of the dependent variables, as product of Zt, the (p × m) system matrix of the independent variables, and t, the (m × 1) state vector. The (p × 1) error process t is also part of this. Unlike the variables, the “states” are not directly observable.

The state equation models its development. It explains the change in the time-variable state vector

t with the states of the past and the (k × 1) error process t. The matrix Tt is also termed system matrix.4

A starting value – an initial distribution – is also needed for 1.5

One of the objectives of state space modelling is to derive one-step forecasts for the non-observable state vector. The Kalman filter is normally used for this.

Based on the information available at time point t, the following one-step forecast of the state vector is derived at time point t + 1:

2a) a Ta Kvt t t t t t+ = +

1

which can be calculated through the recursive use of the formulas (2b) – (2f).

2b) v y Z at t t t= −

2c) F Z PZ Ht t t tT

t= +

2d) K TPZ Ft t t tT

t= −1

2e) L T K Zt t t t= −

2f) P TPL RQRt t t t t

Tt t t

T+ = +1

vt denotes the observation error and Ft and Pt+1|t the accompanying covariance matrices. Matrix Kt is referred to as the Kalman filter gain.6 The one-step forecasts are formed from the product of this matrix and the observation error as well as the term Ttat.

Because the recursion equations (2) and (3) will pass forward from the oldest to the most recent observation, this process is also called forward pass.

The state vector and its covariance matrix at time point t are then:

3) a a PZ F v

P P PZ F Z P

t t t t tT

t t

t t t t tT

t t t

= +

= −

−

−

1

1

Because allowance is only ever made for the information available at time point t, reference is made to a filtered estimate.

Another possibility is not to estimate the state vector at time point t on the basis of information available at that time but on the basis of all information, including that also only known in the future. As this results in lower fluctuations of the state vector, the estimate of the state vector is said to be smoothed:

4a) αt t t ta Pr= + −1

with

4b) r Z F v Z rt tT

t t tT

t−−= +11

4c) N Z F Z L N Lt t t t tT

t t−−= +11

4d) V P PN Pt t t t t= − −1

As the recursion formulas are now used in the reverse order, the process is also termed backward pass.

Until now we have worked on the assumption that the system matrices were known. But usually this is not the case. They can, however, be determined by means of forecast-error variance decomposition. The corresponding log likelihood function is:

5) ln ln lnynp

F v F vt tT

t tt

n

ψ π( )=− ( )− +( )−

=∑

22

1

21

1

with all unknown model coefficients included in the parameter vector . Based on the normal distribution assumption, this estimate function is efficient, i.e. no other estimate function exists with a lower variance. Equation (5) is then also maximized using numerical optimization.

Stochastic volatility models (SV models) were introduced by Taylor.7 They assume that volatility is not observable (i.e. it is “latent”) and that it follows a

It is not always advisable to work with a time invariant regression formula. One solution is the so-called STAR Modell with its ability to change smoothly from one regime to another. Another far more flexible solution is a state space model which is based on as many states as time points instead of two regimes. Moreover, not all the explanatory variables must be observable.

Methodology

stochastic process of log variances. Returns are explained by a multiplicative approach:

6) r ut t t=σ

rt denotes the continuous returns (for t = 1,…,T) and ut = ii (0, 1) denotes an independently identical standard normally-distributed random variable that is multiplied by the time-variant standard deviation of the process, t. The logarithm of the variance is to be explained:

7) ln ,σ γ ψ ν ν σνt t t t th h21

20= = + + ( )−

with E[ut s s t. In the SV model, it follows a non-observable stochastic process which for | | < 1 is strictly stationary with expected value /(1 − ) and variance 2, /(1 − 2).8

With equation (7), the explanation can also be written as r u et t

ht= ( )12 . The fact that we are dealing

with a state space model becomes evident if we use the log squared returns, yt = lnr2

t, as explanatory variable. In this case the equation is (6):

8) y r h u t Tt t t t= = + =ln ln , ,...,2 2 1

The transformed random variable lnu2t shows an

expected value of -1.27 and a variance of 2/2.9

The log squared returns are explained by the sum of two stationary processes. For | | < 1, they therefore also follow a stationary process.10

Using equations (7) and (8), the SV model can be formulated as a state space model:

9) y h iid

h h iid

t t t t

t t t t

=− + + ( )= + + ( )−

1 27 0 2

0

2

12

. , ,

, ,

ζ ζ π

γ ψ ν ν σ

ζ

ν

E tt tν⎡⎣ ⎤⎦ =0

With t = (-1.27, , ht)T as state vector, the system

matrices in accordance with the specification equation (1) are:

10) Z Zt t t= = ⎡⎣ ⎤⎦ =1 0 1 , ε ζ

11) T T R Rt t= =

⎡

⎣

⎢⎢⎢⎢⎢

⎤

⎦

⎥⎥⎥⎥⎥

= =

⎡

⎣

⎢⎢⎢⎢⎢

⎤

⎦

⎥⎥⎥⎥⎥

1 0 0

0 1 0

0 1

1 0 0

0 1 0

0 0 1ψ, ,

εεν

t

t

=

⎡

⎣

⎢⎢⎢⎢⎢

⎤

⎦

⎥⎥⎥⎥⎥

0

0

12) H H Q Qt t= = ⎡⎣⎢⎤⎦⎥ = =

⎡

⎣

⎢⎢⎢⎢⎢

⎤

⎦

⎥⎥⎥⎥⎥

πσν

2

2

2

0 0 0

0 0 0

0 0

,

The distribution parameters for 1 ~ ( 1, P1) are:

13) a P1 1

1

1 27

1

0 0 0

0 0 0

0 02

2

=−

−( )

⎡

⎣

⎢⎢⎢⎢⎢

⎤

⎦

⎥⎥⎥⎥⎥

=

⎡

⎣

⎢⎢⎢⎢⎢⎢

⎤

−

.

/

,γγ ψ σ

ψν

⎦⎦

⎥⎥⎥⎥⎥⎥

The unknown parameters, = ( 2)T, can be estimated by maximizing equation (5).

Because t is not normally distributed, this estimate is no longer efficient but it does at least deliver the linear estimator with the smallest quadratic error. SV models are therefore quasi maximum likelihood estimates.11

Based on the examples used in previous articles, we now apply the stochastic volatility model to the fluctuations of the log squared gold price changes.

The upper part of figure 1 shows the daily gold price data from 31 December 1999 to 28 November 2014. Until around 2005 the gold price rises moderately. This was followed by phases of volatility clustering, as can be seen in the changes in the gold price (lower part of figure 1). The return process evidently does not reveal any constant variance, in other words it is not homoscedastic.

To adjust the SV model to the data12, we have squared and logarithmized the continuous returns differing from zero. Figure 2 shows the thus transformed returns as well as the filtered and the smoothed volatility estimate. As the state variable ht is the log variance of the process, both volatility estimates were transformed into a daily standard deviation by means of exponenting and calculating the square root.

The volatility peaks are clearly recognizable. As expected, the filtered estimate of the state variables fluctuates more strongly than the smoothed estimate.

Gold price

US Dollar/troy ounce

0

500

1000

1500

2000

12/99

12/00

12/03

12/05

12/07

12/09

12/11

12/13

Continuous returns

%

-12

-8

-4

0

4

8

12/9

9

12/0

0

12/0

3

12/0

5

12/0

7

12/0

9

12/1

1

12/1

3

Source: London Bullion Market, Invesco. Daily data as at 31 December 1999 to 28 November 2014.

Methodology

The estimates of the unknown variables are ˘ .γ =−0 0014 , ˘ .ψ=0 9939 and ˘ .σν

2 5 0404=− . The estimate for lies just below one so that, formally speaking, a stationary variance process exists that, however, has been almost integrated from degree 1. This can also be clearly seen in the

autocorrelations. The only gradually declining values (figure 3) signal a long memory quality. The expected value for ht (expressed as daily volatility) is 0.891 and is calculated as

exp ˘ / ˘γ ψ1−( )( ) .

Finally we use the empirical SV model for a pseudo ex ante forecast for the 23 trading days in December 2014. For this we use the forecast equation (2a).

Figure 4 shows the progression forecast and the previously calculated smoothed volatilities. With this, a point forecast can be made, for example, for the expected monthly volatility in December.

This article dealt with state space models and their solution using the Kalman filter. Many econometric approaches can be formulated as state space models. Unlike the classic regression approach, the explanation variables here are not restricted to observable variables but can also include unobservable (“latent”) variables. An example of such a state space model is the stochastic volatility model (SV model) that we have used on the daily gold price fluctuations.

The next articles will continue the theme of state space models. The focus will be on diagnostic tests and alternative estimation methods.

Dr. Bernhard Pfaff, Portfolio Manager, Invesco Global Asset Allocation

1 Kalman (1960), Kalman and Bucy (1961), Anderson and Moore (1979).

2 Harvey (1991).3 The observation equation is also known as the measurement

equation, due probably to the model's origins in engineering; the state equation is also known as the transition equation. There are a large number of notations for state space models. The following explanation is based on Durbin (2012).

4 If the normal distribution is assumed for the error processes, with t ~ (0t, Ht) and t ~ (0, Qt) applying, we talk of a linear Gaussian state space model with the additional system matrices Ht and Qt. If they are specified as time-variable, a dynamic state space model is said to exist. By specifically setting the (m × k) matrix Rt the time variation can be restricted to a subset of the state vector.

Absolute returns

%

12/99

12/00

12/03

12/05

12/07

12/09

12/11

12/130

4

8

12

Daily volatility

Filtered Smoothed

%

0.0

0.5

1.0

1.5

2.0

2.5

12/99

12/00

12/03

12/05

12/07

12/09

12/11

12/13

Source: Invesco. Daily data as at 31 December 1999 to 28 November 2014.

Autocorrelation ACF

-0.25

0.00

0.25

0.50

0.75

1.00

0 10 20 30 40 50 60Lag

Partial autocorrelation ACF

-0.25

0.00

0.25

0.50

0.75

1.00

0 10 20 30 40 50 60Lag

Source: Invesco. Daily data as at 31 December 1999 to 28 November 2014.

Smoothed daily volatility Forecast 2- -band

%

0.0

0.5

1.0

1.5

6/14

7/14

8/14

9/14

10/14

11/14

12/14

Source: Invesco. Daily data as at 30 June 2014 to 31 December 2014.

Methodology

5 In the Gaussian state space model, the starting value is

1 ~ (a1, P1).6 The “filter gain” measures the willingness to adjust the forecast

for the following state after an observation (and the accompanying forecast error). If the observation error shows a high variance, the observation is not considered to be particulary reliable so that – all other factors being equal – the willingness to adjust the forecast for the future state is correspondingly lower. If, on the other hand, the variance of the observation errors is low, they are considered to be reliable; the willingness to adjust the one-step forecast is greater. The reverse can be seen with the covariance matrix of the state vector. If the variance of the vector is high, the forecast for the state vector would also have be changed more than in the case of a projection based on the autoregressive term. If, on the other hand, the variance of the state vector is low (or even zero), the optimal forecast is the simple projection of the current state. The filter gain is then zero. The plus or minus signs of the observation error determine the direction of the forecast correction. If the observation is underestimated, the one-step forecast for the future state is raised in relation to the autoregressive projection and in the event of an overestimation it is reduced. The forecast improvement thus flows into the filter gain while allowing for the variance of observation error and state vector.

7 Taylor (1982), see also Harvey et al. (1994).8 An SV model thus differs from a GARCH(1, 1) model in so far as

the conditional variance is modelled as 2t = + r2

t–1 + 2t–1

with the parameter restrictions > 0 and + < 1 and does not follow a stochastic but a deterministic process.

9 Cf. Abramowitz and Stegun (1970), Harvey et al. (1994).10 For = 1 the variance process follows a random walk. In this

case, the best linear predictor for ht would be an exponentially-weighted mean of the log squared returns (see Harvey et al., 1994).

11 The first two elements of the state vector are not time-variable; only the variance process is modelled as the latent time-varying variable. If the Kalman filter is used, the constant elements of the state vector (expected value of and ) are written over by setting their error influences/variances to zero.

12 All calculations were conducted using the free statistical programming environment R 3.3.0 (see R Core Team, 2016) as well as the CRAN packages dlm (see Petris et al, 2009), and timeSeries (see Würtz et al., 2015).

• Abramowitz, M. and N. Stegun (1970). Handbookof Mathematical Functions. New York: DoverPublications Inc.

• Anderson, B. and J. Moore (1979). OptimalFiltering. Englewood Cliffs, NJ: Prentice-Hall.

• Durbin, J. (2012, 8). Time Series Analysis byState Space Methods (Oxford Statistical Science)(2nd revised ed.). Oxford University Press, USA.

• Harvey, A., E. Ruiz, and N. Shephard (1994,April). Multivariate stochastic variance models.The Review of Economic Studies 61(2), 247–264.

• Harvey, A. C. (1991, 4). Forecasting, StructuralTime Series Models and the Kalman Filter.Cambridge University Press.

• Kalman, R. (1960). A new approach to linearfiltering and prediction problems. Transaction ofthe ASME, Series D, Journal of Basic Engineering82, 30–45.

• Kalman, R. E. and R. S. Bucy (1961). New resultsin linear filtering and prediction theory.Transaction of the ASME, Series D, Journal ofBasic Engineering 83, 95–108.

• Petris, G., S. Petrone, und P. Campagnoli (2009).Dynamic Linear Models with R. useR! Springer-Verlag, New York.

• R Core Team (2016). R: A Language andEnvironment for Statistical Computing. Vienna,Austria: R Foundation for Statistical Computing.

• Taylor, S. (1982). Time Series Analysis: Theoryand Practice, Chapter Financial Returns Modelledby the Product of Two Stochastic Processes: AStudy of Daily Sugar Prices 1691–79, pp. 203–226. Amsterdam: North-Holland.

• Würtz, D., T. Setz, und Y. Chalabi (2015).timeSeries: Rmetrics - Financial Time SeriesObjects. R package version 3022.101.2.

Specialized investment capabilities globally

We believe the best investment insights come from specialized investment teams with discrete investment perspectives, operating under a disciplined philosophy and process with strong risk oversight and quality controls.

Source: Invesco, as at 31 July 2016. The listed investment teams do not all provide their products or services globally. Not all funds and strategies listed are available in all jurisdictions. Please refer to the appropriate internet site or your local Invesco office. All entities listed are wholly owned, indirect subsidiaries of Invesco Ltd., ex-cept Invesco Great Wall in Shenzhen, which is a joint venture between Invesco and Great Wall Securities, and the Huaneng Invesco WLR Investment Consulting Company Ltd. in Beijing, which is a joint venture between Huaneng Capital Services and Invesco WLR Limited.

AtlantaAustinBostonChicagoDallasHoustonLouisvilleNew YorkNewport BeachPalm HarborSan DiegoSan FranciscoToronto

FrankfurtHenleyLondonMadridMilanMunichParisPragueWarsaw

BeijingHong Kong

MumbaiSeoul

ShanghaiShenzhenSingapore

TaipeiTokyo

MelbourneSydney

• Asia ex-Japan• Greater China• Japan• Australia

Beijing, Hong Kong, Melbourne, Mumbai, Shenzhen, Singapore, Sydney, Taipei, Tokyo

• Canadian, regional, sector and global equity• Canadian and global fixed income• Balanced portfolios

Toronto

• Global liquidity• Stable value• Global and US broad fixed income• Global alternatives and bank loans

Atlanta, Chicago, Hong Kong, London, Louisville, New York, Palm Harbor (FL), San Diego

• US, global and non-US growth equity• US value equity• Sector equity• Balanced portfolios

Austin, Houston, San Francisco

• Global macro• Risk parity• Commodities• Active balanced solutions

Atlanta, Frankfurt

• Emerging markets• Global and non-US equity• US equity

Atlanta, San Francisco

• Global and regional equities, including UK, European, Asian, Japanese and emerging markets

• Multi-asset• Fixed income

Henley

Index-based ETFs and actively managed ETFs• US and non-US equity• Taxable and tax-free fixed income• Commodities and currencies

Chicago

• Private equity funds of funds• Customized portfolios

London, New York, San Francisco

• US, global, regional and emerging equity• Long/short strategies• Active low volatility • Balanced solutions

Boston, Frankfurt, Melbourne, New York, Tokyo

• Global direct real estate investing• Global public real estate investing

Atlanta, Beijing, Dallas, Hong Kong, London, Madrid, Milan, Munich, New York, Newport Beach, Paris, Prague, San Francisco, Seoul, Shanghai, Singapore, Sydney, Tokyo, Warsaw

• Equity trusts• Closed-end trusts• Tax-free fixed-income trusts• Taxable fixed-income trusts

Chicago

• Private Equity: Contrarian buyouts, distressed and special situations

Beijing, New York, Tokyo

Source: Invesco, data as at 30 June 2016.

Exploring the world for high quality results. Invesco is a leading independent global investment management company, dedicated to helping people worldwide achieve their financial objectives. With USD 779.6 billion of assets under management, more than 750 investment professionals worldwide and an operational network spanning more than 20 countries, Invesco has the global capability to deliver our best ideas to investors around the world.

Our investment solutions range from major equity and fixed income asset classes to more non-traditional asset classes including real estate and private equity. These are delivered through a diverse set of investment vehicles for our clients such as open-ended funds, ETFs, cash products and more.