symmetric and asymmetric us sector return volatilities in
TRANSCRIPT
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Symmetric and Asymmetric US Sector Return Volatilities
in Presence of Oil, Financial and Economic Risks
Shawkat Hammoudeha
Yuan Yuanb
Thomas Chiangc
Mohan Nandhad, *
Abstract. This paper examines the impacts of world, country, and sector-specific variables on the stock return volatility of twenty-seven US sectors in the short-and long-run, accounting for the asymmetric shocks based on GARCH models. In the standard GARCH model the two world variables, oil and MSCI (Morgan Stanley Capital Index), have differing impacts on the US equity sector returns’ volatility, with oil price dampening it while MSCI heightening it for most sectors. This result underlines the need for hedging more against world capital market risk relative to oil risk which is probably hedged by many sectors. The world and country factors’ impacts are not as pervasive across the board, compared with the sector-specific impacts of the P/B ratio and trading volume which affect almost all sectors. Increases in the P/B ratio would reduce the aggregate volatility, while increases in the trading volume would heighten it for all sectors. Asymmetry of factor impacts on volatility is also found for most sectors. Most of the GARCH factor results are confirmed in the CGARCH model with the exception of the impact of interest rate on the short-lived transitory volatility. Finally, interesting econometric results on the inclusion or exclusion of trading volumes are discussed. JEL Classification: C22, G12
Key words: Volatility, GARCH; Trading Volume a,b,c LeBow College of Business, Drexel University, Philadelphia, PA, U.S.A. a [email protected] b [email protected] c [email protected] d Accounting and Finance, Monash University, Melbourne, Australia. Phone : +613 9904 4610 ; E-mail: [email protected] * Corresponding author.
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I. Introduction
In the last two decades, world financial markets have been experiencing erratic
volatility at certain times as witnessed by the stock market crash in 1987, the Asian
crisis in 1997, the collapse of dotcom stocks in 2000, and the recent Chinese market
spillover in 2007. To address these unpredictable excess risks, both financial
institutions and regulatory agencies have developed various risk management
techniques to deal with extreme market movements in order to protect investors’
portfolios.
In attempting to provide better explanations of the stock volatile movements and
better predictions of the volatility, several approaches have been advanced in the
empirical studies. First, conditional variance models have been developed to fit
clustering volatility (Bollerslev et al., 1992; Nelson, 1991, Glosten et al., 1993, Ding
et al., 1993, Engle, 1995, 2002). A more recent brand of these models pays particular
attention to the asymmetrical impact on stock return volatility.1 Second, a larger set of
economic variables and more efficient econometric techniques are employed in
modeling stock return series in order to reduce the model uncertainty. For instance, in
explaining the stock return, Avramov (2001) and Ludvigson and Ng (2007) construct
some risk factors that comprise a large amount of information by using Bayesian
approach to gain estimation efficiency. Third, in addition to the conditional volatility
that employs the GARCH-type models, attempts have been made to link stock
volatility to various economic fundamental risks, including sector, industry or firm
risks (Fama and French, 1992, 1995) and macro economic volatility (Schwert, 1989;
Errunza and Hogan, 1998; Flannery and Protopapadakis, 1999). The fourth approach
is to find a better measurement of the risk variables to validate the test equation.
1 See Engle (1995) for a collection of ARCH models
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Andersen el al. (2004) and Ghysels et al (2005) suggest the use of high frequency
data, while Andersen et al (2003), Andersen et al (2004), and Engle et al. (2006)
suggest employing alternative definitions to measure volatility.
Motivated by the established literature particularly the approach that links stock
volatility to various economic fundamental risks, this paper’s purpose is to extend the
research by linking sector stock volatility to a broader scope of information set
pertinent to policy analysis and global environment. Particularly, the paper
emphasizes the role of the oil risk on return volatility of equity sectors of the US
economy, given the recent surge in oil prices. Moreover, in addition to the sector-
specific factors, price-book ratio and liquidity effect (Fama and French, 1996;
Lamoureux and Lastrapes, 1990), we add macro economic variable (Schwert, 1989),
and global market volatility (Engle et al., 1990, 1995; Hamao, 1990) into the model.
Thus, the model incorporates sectors’ volatility, country factors (macroeconomic
variables), and world factors into a unified framework. Our empirical research is
connected to a large body of the literature examining the relationship between the
stock return volatility and the underlying economic fundamentals. Thus, this paper is
not an exercise that tests new techniques.
In sum, the paper provides empirical evidence on stock return volatility behavior
by incorporating the presence of world, country and sector risks. Specifically, the
purpose of the paper is five-fold:
1. to examine the responsiveness of the stock return volatility of twenty seven
US sectors to the common variables: oil price, world market index, and short-
term interest rate;
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2. to measure the impacts of the fundamental (sector-specific) variables, namely
book/price ratio and trading volume, on the return volatility of those US
sectors;
3. to examine the significance of trading volume and whether including trading
volume reduces the volatility persistence rate;
4. to assess whether the volatility-volume relationship is significant for both the
transitory and permanent components of volatility; and
5. to assess the asymmetric effects in oil price, federal funds rate and trading
volatility on the transitory component of stock return volatility.
This paper is organized as follows. Following this introduction, section II
describes the variables’ selection and related literature, and section III discusses the
data. Section IV presents the methodology. Section V presents the empirical findings
and analyzes the results. Section VI concludes.
II. Variables’ Selection and Literature Review
The rationales for the variable selection are briefly stated as follows. The Price-
Book ratio (P/B) provides a measure to assess the value of a stock.2 A high P/B ratio
reflects that investors have high expectations for the company. A lower P/B ratio may
signify that the stock is undervalued or something is fundamentally unfavorable with
the company. Fama and French (1995) find correlation between P/B ratio, future
ROE, and future stock return. Danielson and Dowdell (2001) further confirm that a
firm’s P/B ratio can predict the future cash flow pattern earned by a firm. In other
2 P/B is calculated by dividing the current price of a company's stock times its shares outstanding (market capitalization) by its last quarter's book value. Book value is assets less liabilities which is equivalent to book value of equity. A P/B ratio represents the market value for every dollar of tangible assets.
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studies, Fama and French (1993, 1996) and Avramov (2002) consistently show that
P/B has significant information content for predicting stock return.
In a related literature, it has been documented that the return volatility is positively
related to trading volume. Clark (1973) observes that the variances of stock returns
and trading volumes are both driven by the same latent variable measuring the
number of information arrivals hitting market. The arrivals of news generate price
changes which are accompanied by changes of trading-volume in the market as the
volume adjusts to new equilibrium. A more recent study of volatility-volume behavior
is based on the GARCH model. Lamoureux and Lastrapes (1990) insert the
contemporaneous trading volume in the variance equation of the GARCH model for
20 openly traded individual stocks and find this variable to have a significant
additional explanatory power in determining volatility. Additional evidence is
supported by Wagner and Marsh (2005) who show that surprise volume has a
significant power in predicting stock return volatility. However, as expounded by
Longin (1997), return volatility, volume, and liquidity are all positively related to
each other, although these variables may be associated with different trading
processes. To some extent, the trading volume can be set up as a proxy of liquidity,
which has the advantage of being easy to measure. Based on information we
observed, it is appealing to incorporate trading volume in test equations.
The interest rate has long been considered as an effective financial variable that
affects the discount factor, costs of borrowing, liquidity, and portfolio allocation. In
addition to its function as an indicator of liquidity of financial markets, it is frequently
used by the Fed as a policy instrument to control and stabilize the financial markets
and economic activity. As evident by Fama’s research, the short-term interest rate
can also be used as a proxy for the prediction of future inflation rate. As a result,
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change of interest rate will have an effect on the discount factor and/or future cash
flows. McQueen and Roley (1993) argue that macroeconomic news such as interest
rate may also have a nonlinear effect on stock returns. Therefore, it would be
interesting to discern how this macro factor affects volatility at the sector level.
With rapid advancement of high-tech and IT devices, any economic news or
financial announcements in a particular agent will be disseminated to global markets
shortly, causing volatility spillover. Ross (1989) argues that market volatility is
related to the information flows, suggesting that information from one stock market
can be incorporated into the volatility process of another stock market. King and
Wadhwani (1990) propose a “market contagion” hypothesis and argue that trading of
stocks in one market per se affects stock prices in other markets, even if the source of
the trading is purely noise. Hamao et al (1990), Karolyi and Stulz (1996), and Chen et
al (2004) find evidence consistent with this interpretation. It is of interest to point out
that the evidence derived from the cross market studies is mainly from the US market
to foreign markets (Masih and Masih, 2001). No significant evidence is found for the
feedback from foreign markets to the US sector markets. In our model, however, we
focus on whether the world stock returns have significant effect on the US sector
markets by employing more recent data. 3
The daily headline news suggests that oil price movements have a significant
effect on production as oil products are related to a huge array of by-products ranging
from aviation, plastic, to medicine. Thus, a rise in oil prices causes higher production
costs, jeopardizing future profits. The oil price also has a direct impact on consumer
spending; its fluctuations would further affect consumer confidence, future income
3 On February 28, 2007, the Chinese stock market dropped by about 8.5 percent. The next day the US Dow Jones Industrial Index dropped by about 420 points.
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streams and portfolio allocations, leading to stock return volatility. Mork et al (1994)
contend that a rise in oil price produces a negative impact on real output. Jones and
Kaul (1996) also find that a rise in oil price negatively influences the aggregate stock
market returns in Canada, Japan, United Kingdom and the United States due to its
adverse effect on their economies. Using the GARCH model, Hammoudeh et al
(2004) examine the effect of oil price shocks on five US S&P oil sector index
volatilities and report that that oil prices have strong impact on the oil sectors’
volatility. Similar results are found in the studies on the firm’s level by Faff and
Brailsford (1999) and Boyer and Filion (2006), among others. In light of the above
reported evidence, it would be interesting to determine how the oil shocks affect the
return volatility, sector by sector.
In addition to the search for appropriate variables to be used to explain sector
stock return and volatility, this study also addresses to the issues that grasp recent
empirical attention. First, it is recognized that financial market stability depends very
much on the persistence of volatility. It is natural to inquire whether the volatile
movement of stock return is temporary or permanent. This motivates us to construct
a conditional model based on the component GARCH (CGARCH) features as
proposed by Engle and Lee (1999). Second, as we observed investors’ behavior, the
reaction to a negative shock is often more profound than to an equal amount of
positive shock. This asymmetrical effect has become an empirical regularity in
studying stock return volatility series. Evidence from Nelson (1991), Engle et al
(1993), Glosten et al (1993) and Bekaert and Wu (2000) well justifies this market
phenomenon.
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III. The Data
In this paper, we use daily DataStream ‘total return’ indices for twenty seven US
sectors as classified by the Industrial Classification Benchmark (ICB) which is based
on a 4-tier hierarchy4. The sample covers the daily period from January 2, 1989
through October 3, 2006. Total return indices' series measure growth in value of a
vector of assets holding over a specified period of time, assuming that dividends are
re-invested to purchase additional units at the closing price applicable on the ex-
dividend date. As indicated in the introductory section, the regressors in the estimated
equations include two world variables: the oil price and the Morgan Stanley Capital
Index; one country index, the federal funds rate; and two domestic sector variables,
the price–to-book value and the trading volume. The spot price for oil (OIL, hence
after) is the price quoted for immediate delivery of WTI crude at Cushing, Oklahoma,
and is expressed in U.S. dollars per barrel. Data for the WTI price is accessed from
the EIA website. The daily federal funds rate (FFR) is obtained from the database of
the Federal Reserve Bank of Saint Louis. The financial ratio P/B (PB) and the trading
volume (VO) are obtained from DataStream.
The descriptive statistics reported in Table 1 suggest that the General Finance
equity sector has the highest average return, while Support Services has the lowest
return among all the domestic equity sectors considered during the sample period. On
the other hand, the highly cyclical Technology Hardware & Equipment has the
greatest return volatility, while Electricity, Food Producers, and Real Estate have the
lowest volatility as measured by the standard deviation.
4 Industries, supersectors, sectors and subsectors. The inclusion of sectors is bounded by the availability of data on P/B ratio. DataStream provides the “price indices” and the “total return indices”; the latter assumes the incorporation of dividend re-investment and thus is the better measurement. Total return index is not return index
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Table 1: Descriptive Statistics of 27 Sector Stock Indices
Industries RETURN DPB DVO Mean SD Kurt. C.V. Mean SD Kurt. Mean SD Kurt.
Beverages 5.01E-04 0.012 7.11 24.31 1.80E-04 0.014 13.21 6.30E-04 0.305 5.28
Chemicals 3.91E-04 0.012 7.18 30.76 1.27E-04 0.014 37.16 4.58E-04 0.259 6.68
Construction & Materials 3.85E-04 0.013 6.94 34.48 1.67E-04 0.047 678.55 6.97E-04 0.339 4.93
Electronic & Electrical Eq. 5.90E-04 0.014 7.47 23.93 1.10E-04 0.015 10.79 6.44E-04 0.276 6.24
Electricity 3.93E-04 0.009 11.46 23.52 1.58E-04 0.010 13.46 3.93E-04 0.257 6.66
Food & Drug Retailers 4.13E-04 0.011 11.45 26.89 -6.79E-05 0.013 16.74 7.42E-04 0.299 5.86
Food Producers 4.42E-04 0.009 8.97 20.50 5.18E-05 0.011 22.09 5.68E-04 0.262 6.28
Fixed Line Tele. 2.84E-04 0.013 7.81 45.54 1.23E-04 0.017 81.84 8.16E-04 0.308 7.78
General Financial 6.61E-04 0.014 6.37 21.62 1.38E-04 0.016 12.17 7.39E-04 0.269 6.21
Gas, Water & Multiutilities 3.69E-04 0.011 10.57 30.01 1.14E-04 0.010 12.57 7.49E-04 0.314 5.84
Healthcare Eq. & Services 5.86E-04 0.011 7.36 18.94 2.10E-04 0.012 18.54 8.76E-04 0.263 6.89
Industrial Engineering 5.11E-04 0.012 5.96 22.81 1.80E-04 0.014 13.43 5.02E-04 0.295 6.39
Industrial Transportation 3.96E-04 0.012 9.12 30.73 1.58E-04 0.013 22.04 6.18E-04 0.288 6.05
Industrial Metals 3.86E-04 0.017 6.25 43.34 1.82E-04 0.020 103.38 9.65E-04 0.343 5.17
Leisure Goods 3.94E-04 0.011 7.83 28.20 1.35E-04 0.017 95.58 4.28E-04 0.279 5.43
Life Insurance 6.24E-04 0.012 8.57 19.18 1.60E-04 0.014 30.98 7.81E-04 0.353 5.68
Nonlife Insurance 5.11E-04 0.010 8.46 20.39 9.84E-05 0.013 56.96 7.43E-04 0.329 172.58
Oil & Gas Producers 4.92E-04 0.012 5.63 25.31 1.06E-04 0.014 43.19 7.38E-04 0.265 6.65
Oil Eq. & Services 4.58E-04 0.017 4.95 37.08 1.46E-04 0.019 8.72 1.04E-03 0.337 5.65
Personal Goods 5.44E-04 0.012 29.79 21.69 1.70E-04 0.012 17.87 4.80E-04 0.307 11.00
Pharm. & Biotech. 5.38E-04 0.013 6.34 24.07 1.67E-05 0.015 33.26 7.96E-04 0.258 6.19
Real Estate 4.95E-04 0.009 7.90 19.07 1.49E-04 0.010 107.86 1.02E-03 0.375 5.87
Software & Computer Services 5.99E-04 0.017 7.02 29.09 2.10E-04 0.018 14.39 8.27E-04 0.263 7.48
Support Services 2.49E-04 0.011 10.52 45.94 1.27E-04 0.013 21.84 9.17E-04 0.318 9.32
Tech Hardware & Eq. 4.22E-04 0.019 7.57 45.82 1.72E-04 0.022 12.64 8.84E-04 0.255 6.55
Tobacco 6.27E-04 0.018 17.31 28.06 1.06E-04 0.019 26.43 8.19E-04 0.390 5.53
Travel & Leisure 4.40E-04 0.014 13.85 32.21 1.86E-04 0.014 31.82 1.06E-03 0.293 6.36
DOIL 2.66E-04 0.025 24.41 92.43
DFFR -1.17E-04 0.051 25.85 -438.86
DMSCI 2.21E-04 0.008 14.15 37.44
Notes: The data consist of 27 sector stock indices. Mean is average value, SD stands for standard deviation and Kurt for kurtosis. The daily sample period is from January 2, 1989 to October 3, 2006.
PBD denotes the change in the ( P/B) ratio, VOD is the change in trading volume SD is standard deviation and Kurt is Kurtosis.
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If P/B value is of interest, the Software & Computer Services equity sector has the
highest average positive percentage change, whereas the defensive Food & Drug
Retailers sector has the lowest average percentage increase. These figures reflect
different valuation expectations by investors on different sectors. When it comes to
sectoral volatility of the P/B ratio, Technology Hardware & Equipment has the
highest volatility as against the lowest volatility from the Gas, Water & Multiutilies
sector.
With respect to the trading volume change, the Travel & Leisure equity sector has
the highest average percentage increase, while Electricity has the lowest increase.
Additionally, trading volume has the highest volatility among all of the variables
under investigation. Note that the stocks in the Tobacco sector have the highest
volume volatility, whereas Electricity has the lowest. It would be interesting to see
how the percentage changes in trading volume affect those sectors’ return volatilities.
MSCI has both lower average return and volatility as compared with US sectors’
stock returns. The oil average return is close to the lowest return of all the domestic
sectors, but its volatility is higher than those in other sectors.
For the federal funds rate the average rate return is negative, indicting that a
relatively easy monetary policy has been adopted for most of the sample period.
However, its volatility is double that of the oil price. This ironically signifies this
source of uncertainty on stock return volatility.
Most of the industries’ returns and the independent variables have a kurtosis that
is substantially greater than 3, indicating high excess kurtosis. Personal Goods has the
highest return kurtosis (29.79) followed by Tobacco (17.31), while Oil Equipment &
Services has the lowest. The financial ratio P/B percentage change has the highest
kurtosis in Construction & Materials. The P/B’s kurtosis is generally much higher
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than that of the average change in the trading volume which has its highest kurtosis in
Non Life Insurance. Oil price and federal funds rate have almost the same kurtosis.
Overall, the kurtosis statistics imply that volatility persistence is present in most
sectors, which informally points to the possibility of using the GARCH models to
examine volatility.
IV. The Models
As described in the introductory section, the purpose of the paper is to
examine the characteristics of the return volatility behavior of the US domestic equity
sectors in response to the sector financial fundamentals, interest rate, oil shocks, and
world stock return based on GARCH-type specifications5,6. To learn the marginal
impact, empirical work will be carried out by adding incremental variables as well as
changing econometric specifications. We start the models by specifying mean-
equation for each of the sector return series as:
R it = 0ip + tiitiiti ZR epp +D+- 211 , (1) where itR is the return on the ith sector stock between day t-1 and t; 0ip is the long-term
drift; 1ip and 2ip are constant parameters; AR(1) is added to the mean equation to
capture the partial adjustment of some degree of market friction. Empirically, it is
based on the AIC criterion to decide the lag length. DZit represents the first difference
of the exogenous variables that include common economic factors and sector-specific
5 We tried to estimate the EGARCH to detect the presence of leverage effect in daily sectoral data. The MlE did not converge for eleven of the twenty seven industries. We found the leverage effect present in ten of the remaining sixteen industries. Due to the convergence problem and space consideration, we opted not to include the EGARCH model in this study. 6 Before we estimate any of the GARCH family models we must check for the presence of the ARCH effect. We started these models by estimating the PGARCH which should nest GARCH. The results indicate that most of the industries have a power of 2, which justifies using GARCH.
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variables; and ite is the error term for the ith sector return at day t.7 DZit is partitioned
into two subsets (DZ1t, DZ2it), where the former subset contains the world and country
factors DMSCIt, DOILt and DFFRt, while the latter includes the sector-specific
variables DPBit and DVOit. In expression, we write:
DZit = (DR w
t , DOILt ; DFFRt, DPBit, DVOit) (2)
where DR w
t is world stock return, which is proxied by DMSCIt, the first log-difference
of Morgan Stanley Capital Index; DOILt is the first log-difference of the spot price
WTI crude oil; DFFRt denotes the first difference of the federal funds rate,
representing the monetary policy effect; DPBi is the difference of the P/B ratio that
captures Tobin-Q effect; DVOi is the first log-difference of trading volume; ite | It – 1 ~
N(0, 2its ); N ( . ) represents the conditional normal density with mean 0 and variance
2its , and It –1 is the information set available up to time t –1.
To highlight different features of the volatility, we consider an Asymmetric Power
GARCH (APGARCH) proposed by Ding et al (1993) because of its generality. This
model is expressed as:
iti
ds , = iw + 1 1( ) ii t i t
da e g e- -- + itii
dsb 1, - + i itZl D (3)
where iti
ds , stands for the conditional variance for sector i, 1, -tie is the shock term
from the previous period, di denotes the power of conditional variance to measure
volatility duration, ai and bi are the constant coefficient effects for ARCH and
GAECH, gi denotes the asymmetric effect of lagged shock on the conditional variance,
7 The unit root tests show that all the variables including the trading volume are integrated of degree one based on the ADF and PP tests. Therefore we will use the first log differences.
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and DZit represents a vector of exogenous variables stated in Eq. (2). If di = 2, ig = 0,
and 0=il , this model collapses to GARCH(1,1)8. Further, if di = 2 and il = 0, this
model reduces to GJR- GARCH(1,1) model. In this variance equation, the sum of the
coefficients of GARCH components measures the degree of convergence to long-run
equilibrium or volatility persistence of the ith sector in this model.
V. Empirical Results
We present in this section the estimation results of the variance equation in each of
the two GARCH type models for the twenty seven US sectors. In the standard
GARCH model, we focus on the general behavior of the sector aggregate volatility
relative to multiple risks and on the econometric implications of adding the trading
volume to the variance equation in terms of MLE convergence, predictive power and
volatility persistence. In the CGARCH model, we distinguish between the
fundamental factors-induced permanent and shocks-induced transitory components of
volatility and we also examine the implications of excluding changes in trading
volume. Additionally, we examine the impacts of the asymmetric shocks of the
common variables on the return volatility for each sector. Finally, we test the
robustness of the estimations of the models for all sectors by dividing the sample
period into two subperiods: January 2, 1989 - December 31, 2003 and January 2, 2004
- October 3, 2006. These additional estimations also allow us to test whether the
conventional wisdom that oil price has negative effects on equity sector return
volatility holds in those two different subperiods. There are those who contend that in
1990's oil price was driven by supply factors, and in turn influenced economic
8 Our estimates indicate that the power in the PARCH model is 2 for most of the sectors. Thus we will move directly to GARCH(1,1).
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activities. But, from 2004 and before the collapse in 2008 oil price has been affected
more by demand than supply factors. Thus, the contention presumes that in the recent
period oil price moves together with economic indices (stock price index, exchange
rate, etc) and other commodity prices.
V.a. The GARCH results
The results of the estimated sector return volatility for the whole sample are
reported in Table 2. As anticipated, the two global variables, oil price and MSCI,
have differing impacts on volatility across different sectors. Interestingly, increases
in the oil price whether favorable or not to sectors9 reduce the return volatility for
most sectors, including the oil sectors, at the 5 percent level of significance, with the
General Finance sector is the most responsive to those increases. However, exceptions
are found for those sectors that use oil intensively. In these sectors, including
Industrial Transportation, Leisure &Travel, Software & Services (at 5% level of
significance), Leisure Goods and Real Estate (at 10% level), an increase in oil price
leads to high volatility. This result was upheld for both subperiods. Results for the
subperiods are available on demand. The dominant (negative) result implies that most
sectors may be able to pass-through the oil price increases to consumers because the
producers in those sectors posses market power in less competitive business
environments, particularly during rising oil prices associated with high economic
growth or due to low price elasticities of demand.
9 An increase in the oil price is usually favorable to returns of the oil-producing and serving sectors, while it is unfavorable to oil-consuming sectors.
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Table 2: The Sectors’ Stock return Volatility for GARCH(1,1) –Whole Sample INDUSTRIES a b a+b DOIL DMSCI DFFR DPB DVO R2
Beverages 0.15 a
0.58 a
0.73 1.02E-05
8.27E-05
-6.73E-06
-5.18E-05 a
2.23E-05 a
0.83
Chemicals 0.14 a
0.57 a
0.71 -4.10E-05
7.64E-05
-4.72E-05 a
1.01E-05
3.50E-05 a
0.74
Construction & Materials 0.09 a
0.49 a
0.57 -3.57E-04 b
-1.97E-04
-2.79E-05
-3.93E-06
9.35E-05 a
0.23
Electronic & Electrical Eq. 0.07
a
0.93
a
1.00 8.13E-06
1.29E-04
a
-4.33E-06
-8.59E-05
a
4.99E-06
a
0.59
Electricity 0.10 a
0.64 a
0.75 6.95E-06
4.40E-07
-9.02E-07
-3.57E-05 a
4.72E-06 a
0.84
Food & Drug Retailers 0.12 a 0.52 a 0.64 2.88E-05 -5.66E-05 1.05E-06 -2.10E-04 a 3.71E-05 a 0.55
Food Producers 0.00 0.82 a 0.82 -1.55E-06 -1.53E-06 4.13E-06 a -2.23E-05 a 4.34E-06 a 0.68
Fixed Line Tele. 0.09 a 0.76 a 0.84 -3.13E-05 a 1.41E-05 -1.47E-05 a -1.40E-05 a 1.48E-05 a 0.59
General Financial 0.14 a
0.57 a
0.71 -3.08E-05
8.19E-05 b
4.73E-06
-1.61E-04 a
2.10E-05 a
0.85
Gas, Water & Multiutilities 0.13 a
0.52 a
0.65 -1.08E-04
-8.18E-04 a
-5.51E-05 a
-2.40E-04 a
4.90E-05 a
0.38
Healthcare Eq. & Services 0.11 a
0.81 a
0.93 -2.83E-05 b
6.18E-05 b
-1.67E-05 a
-8.87E-05 a
9.86E-06 a
0.59
Industrial Engineering 0.18 a
0.45 a
0.62 -4.64E-05 b
9.93E-05 b
1.91E-05 b
-1.07E-04 a
1.02E-05 a
0.74
Industrial Transportation 0.13 a
0.55 a
0.67 7.46E-05 c
1.53E-04 b
-8.94E-06
-2.45E-04 a
3.12E-05 a
0.70
Industrial Metals 0.11 a 0.50 a 0.62 -3.35E-04 a 4.80E-04 a -8.38E-06 -2.56E-05 6.68E-05 a 0.70
Leisure Goods 0.02 a 0.95 a 0.98 4.17E-05 a -2.50E-05 -5.27E-06 -1.80E-05 c 2.22E-05 a 0.41
Life Insurance 0.10 a 0.51 a 0.61 -9.01E-05 a 7.19E-05 a -3.08E-05 a -3.09E-04 a 3.34E-05 a 0.59
Nonlife Insurance 0.14 a
0.57 a
0.72 -5.99E-05
-2.51E-04 c
-1.85E-05
-2.81E-04 a
8.65E-06 a
0.66
Oil & Gas Producers 0.00 b
0.94 a
0.94 -1.20E-05 b
-4.33E-06
-1.38E-05 a
-3.84E-05 a
9.71E-06 a
0.70
Oil Eq. & Services 0.10 a 0.52 a 0.63 -6.79E-06 c 1.29E-04 a 6.69E-07 -5.14E-05 a 5.84E-06 a 0.84
Personal Goods 0.12 a
0.52 a
0.63 -1.72E-06
-1.04E-04
-5.71E-05 c
-4.11E-04 a
4.31E-05 a
0.49
Pharm. & Biotech. 0.63 a
0.48 a
1.11 5.87E-07
8.48E-07
4.17E-06
-3.59E-05 c
5.53E-06 a
0.63
Real Estate 0.16 a
0.50 a
0.66 5.71E-05 b
1.12E-04 a
4.18E-05 a
-8.41E-05 a
1.27E-05 a
0.40
Software & Computer Services 0.12
a 0.52
a 0.63 3.89E-04
a 2.15E-04
6.23E-05
1.74E-05
6.67E-05
a 0.72
Support Services 0.03 a
0.97 a
1.00 -1.45E-05
5.75E-05 c
4.69E-06
-6.25E-05 b
7.54E-06 a
0.48
Tech Hardware & Eq. 0.10 a
0.87 a
0.97 2.45E-06
-1.27E-06
4.90E-06
-1.61E-05 a
2.72E-06 a
0.84
Tobacco 0.15 a
0.59 a
0.74 -1.65E-04 a
2.28E-04
-1.13E-06
-3.23E-04 a
3.32E-05 a
0.81
Travel & Leisure 0.17 a
0.81 a
0.98 2.58E-05 c
1.62E-04 a
-6.96E-06
-2.08E-04 a
1.05E-05 a
0.43
Notes: Due to space limitation in the table, we use the following significance notation: a for 1 percent, b for 5, and c for 10 percent levels of significance. We only included twenty seven sectors because of data availability and MLE convergence problems during the models’ estimations. α is the impact of lagged shocks, b is the effect of lagged variance capturing volatility clustering. The sum of α and b measures the volatility persistence. DOIL is the differenced WTI oil price, DMSCI is the differenced Morgan Stanley Capital index, DPB the differenced price to book value and DVO the differenced volatility volume.
16
It is also likely that companies in most sectors are able to hedge against oil price
risk. But the unfavorable positive oil price shocks raise aggregate volatility for the
oil-using sectors that involve largely travel, leisure and transportation. It does not
seem that the sectors in this group are able to pass through the higher cost of oil to
consumers because of media awareness and more competitive environment.
Not surprisingly, increases in MSCI have more wide-spread impacts on the
sectoral return volatility than those of the oil price. MSCI represents the mood of the
world’s stock markets and can have a dynamo effect on the US domestic returns.
Increases in MSCI lead to increases in US sectors’ GARCH volatility across the
board, with Industrial Transportation and Life Insurance experiencing the highest
elevation in volatility. This may result from spillovers, cross market hedging, and
increases in the markets’ speeds of processing information. The domestic sectors that
experience a decline in return volatility in response to increases in MSCI are Utilities
and General Finance. These results have implications for constructing diversified
sector portfolios with net low volatility. Therefore, we can have a mosaic of sectors
that can be combined as a diversified portfolio to reduce volatility in response to
increases in MSCI. Interestingly when the sample period is divided into two
subsamples, the impact of MSCI on sector volatility is mixed, with lower impact in
the first subperiod than in the second period. In the second period, the impact on
sector volatility is different, with more sectors experiencing lower than higher
volatility (results are available on demand). Probably, most of the speculations were
in the commodity markets than in the stock market.
Changes in the US federal funds rate has less impact on the magnitude of US
sector return volatility than changes in the world variables (oil price and MSCI). The
impacts of changes in monetary policy on sector stock return volatility have mixed
17
signs, ranging from negative correlation for the Chemical sector to positive
correlation in Real Estate industry, but more sectors exhibiting dampened than
heightened volatility. The diverse and less significant signs of the monetary policy
may stem from that fact that in most of time, changes in the Fed policy are
anticipated; it renders less significant impact on the volatility. The evidence points to
the direction that Real Estate sector should have more active risk management
strategies to deal with volatility during the rising interest rate periods. The
heightening volatility is pronounced in more sectors in the second period than in the
first one. This is perhaps due to the increases in inflation expectations in reaction to
higher commodity prices.
Unlike the world and country variables, the impact of the sector-specific variables,
P/B ratio and trading volume, are more uniform and statistically significant across the
board. The evidence shows that the sign of P/B ratio is negative, meaning that an
increase in P/B ratio (or the M/B value) is associated with a decrease in stock return
volatility. The is consistent with the phenomenon that markets with higher P/B ratios
tend to have higher P/E ratios on equity, higher returns on assets, or higher growth
rates. These healthy attributes would perhaps produce investment confidence and
project further future growth, creating stability of market volatility.10 This result is
reinforced in the subperiods.
Consistent with Lamoureux and Lastrapes (1990), increases in trading volume
give rise to higher volatility. This result holds true for all sectors. This can be seen
from the positive sign of the estimated coefficients on this variable, which are highly
10 The current empirical findings in time series studies and their interpretations are not completely in agreement with the cross sectional study of expected stock returns by Fama and French (1992). Their work is based on efficient market hypothesis in that higher expected return is required for compensating higher risk, which is associated with the value stocks with a lower P/B ratio.
18
significant across all sectors, giving credibility to the positive contemporaneous
correlation rationalized by the mixture of distributions hypothesis by Clark (1973).
This positive relationship between volatility and the change in volume is the clearest
directional relationship among all the common and sector-specific variables across
sectors.
In slightly departing from Lamoureux and Lastrapes (1990), which argue that
adding the trading volume to the variance equations substantially increase the
explanatory power of the GARCH model11, our results show that adding the change in
this variable instead of the volume gives mixed results for the explanatory power. It
significantly increases the explanatory power (see adjusted R2) for fifteen sectors,
while it reduces it for six sectors. These mixed results are somewhat more in line with
those of Ané and Ureche-Rangau (2006) who found “mitigated” results than that of
Lamoureux and Lastrapes (1990). It is interesting to note that the positive
relationships between volatility and changes in trading volumes endure in both
subperiods for almost all sectors. The only difference is that the relationships
decreased some for most of the sectors during the subperiods relative to the whole
sample.
Another distinguishing feature of the trading volume which we faced during the
estimation is that excluding it from the models disabled the MLE convergence during
estimation for seven sectors and reduced the statistical significance of the world and
country variables across the board. We believe that excluding this variable makes the
models mis-specified because they would suffer from the “missing variable”
phenomenon.
11 Due to the very large sizes of the tables, we have opted not to include the tables that contain the estimations of the models that do not have the changes in the trading volume. Those tables are available upon requests.
19
Another discrepancy with some studies in the literature is related to the impact of
trading volume on the long-run persistence of return volatility. In contrast to those
studies, our results indicate that including changes in volume led to a reduction in the
degree of persistence for thirteen out of twenty seven sectors, while it increases it for
five sectors. The remaining did not converge when changes in trading volume were
excluded.
In terms of convergence to long-run equilibrium when changes in trading volume
are accounted for, only seven out of the twenty seven sectors show slow decay or
convergence, while the others converge in significantly less time. Only one sector
(Pharmaceutical & Biotechnology) displays explosive behavior, and three sectors
(Electronic & Electrical Equipment, Oil & Gas Producers, and Supporting Services)
demonstrate volatility clustering.
At the end, it is interesting to note that the most and least return volatile sectors
based on unconditional standard deviation are Tobacco and Food Producers,
respectively as provided in Table 1. If the unconditional coefficient of variance is
used, the most and least volatile sectors are Support Services and Health Care
Equipment & Service, respectively. If the sectoral generated GARCH series are used,
then the most and least conditional volatile sectors based on standard deviation are
Travel & Leisure, and Oil & Gas Producers, respectively. These sectors are selected
as examples based on the unconditional coefficient of variance
V.b. The asymmetric results
In light of analyzing risk-averter’s behavior, it is crucial to make a distinction
between the impacts of positive and negative shocks on the sector return volatility in
the standard GARCH model. In this subsection, we examine the impacts of
asymmetric shocks emanating from oil price, MSCI and federal funds rate on the
20
standard GARCH volatility for the whole sample and the two subperiods. 12
Following the literature (Pettengill et al 1995), the impacts of the explanatory
variables are split into up and down patterns in their markets. The estimated results
for the whole sample are reported in Table 3.
Table 3: World and Country Variables’ Asymmetric GARCH Impacts -Whole Sample
INDUSTRIES DOIL DFFR DMSCI
Positive Negative Positive Negative Positive Negative
Beverages -1.19E-04 a 8.67E-05 a -6.18E-05 a 3.97E-05 a -5.28E-04 a 5.83E-04 a
Chemicals -2.72E-04 a 1.94E-04 a -1.21E-04 a 7.44E-05 a 6.71E-05 a -2.51E-05
Construction & Materials -1.01E-03 a 6.37E-04 a -1.91E-04 a 2.02E-04 a -8.70E-04 a -4.12E-04
Electronic & Electrical Eq. -6.28E-04 a 3.55E-04 a -2.14E-04 a 2.02E-04 a 1.46E-04 b 4.83E-05
Electricity -8.28E-05 a 5.95E-05 a -3.52E-05 a 3.62E-05 a 1.23E-04 a -1.07E-04 b
Food & Drug Retailers -3.32E-04 b 2.88E-04 a -1.07E-04 a 8.25E-05 a 4.90E-04 a -1.99E-04 b
Food Producers -1.32E-04 b 1.08E-04 a -4.11E-06 -2.30E-06 2.09E-04 a -1.06E-04 a
Fixed Line Tele. -4.10E-04 b 2.79E-04 a -1.23E-04 a 1.35E-04 a 9.43E-05 b -1.97E-04 a
General Financial -2.35E-04 a 1.63E-04 a -3.87E-05 a 6.72E-05 a 2.58E-04 a -6.57E-05
Gas, Water & Multiutilities -2.92E-04 a 1.54E-04 a -1.18E-05 -9.29E-06 -7.65E-04 a -1.16E-04
Healthcare Eq. & Services -3.50E-04 a 3.04E-04 a -1.17E-04 a 1.04E-04 a 1.22E-04 b 4.42E-05
Industrial Transportation -2.70E-04 a 2.44E-04 a -1.46E-04 a 3.74E-05 2.08E-04 b -1.14E-04
Industrial Metals -5.37E-04 a 3.66E-04 a -1.18E-04 a 1.83E-04 a -5.08E-04 a 2.93E-04 a
Leisure Goods 5.23E-05 a 3.26E-05 b 8.77E-06 -3.75E-06 1.18E-03 a -1.11E-03 a
Life Insurance 1.55E-06 9.62E-06 1.37E-05 1.36E-06 4.90E-05 a 7.41E-05 a
Nonlife Insurance -2.45E-04 a 2.12E-04 a -1.07E-04 a 9.26E-05 a -4.14E-04 a 6.62E-04 a
Oil & Gas Producers -2.77E-04 a 1.13E-04 a 9.22E-07 -7.95E-06 3.23E-04 a -7.33E-05 a
Oil Eq. & Services 7.07E-06 7.76E-06 1.09E-04 a -1.05E-04 a -4.20E-05 1.65E-04 a
Personal Goods -3.49E-04 3.48E-04 a -4.39E-05 c 1.75E-04 a -1.38E-03 a 1.08E-03 a
Pharm. & Biotech. -3.04E-04 a 2.63E-04 a 6.25E-05 a 4.93E-06 b 1.15E-05 -2.64E-05
Real Estate -1.78E-04 a 1.78E-04 a -2.53E-05 1.19E-04 a -1.18E-03 a 7.41E-04 a
Software & Computer Services -3.51E-04 a 5.24E-04 a 1.77E-04 a -1.25E-04 a 4.46E-04 a 4.23E-04 a
Support Services -2.26E-05 c -4.03E-06 -1.84E-04 a 1.35E-04 a 1.69E-05 4.57E-05
Tech Hardware & Eq. -3.63E-04 a 2.29E-04 a 1.07E-05 b -3.92E-06 -2.06E-06 4.03E-06
Tobacco -4.05E-04 a 2.62E-04 b -1.05E-04 a 1.39E-04 a -9.63E-04 a 1.44E-03 a
Travel & Leisure -5.47E-04 a 5.30E-04 a -7.78E-05 c 2.36E-04 a 3.47E-04 a -1.26E-04
Notes: The Wald test indicates that up and down shocks have symmetric impacts for three sectors in case of the oil price, 4 sectors for FFR, and 7 sectors for MSCI.
12 It is not our intention to examine the asymmetric impacts for the sector-specific variables, P/B ratio and changes in trading volume, since those variables are non-exogenous macro shocks and they have already demonstrated strong impacts across almost all sectors.
21
The evidence shows that those variables have more significant outcomes across
the board when the impacts are separated by ups and downs patterns than in the
aggregate GARCH case. Particularly and interestingly, in the upward case an increase
in the oil price, whether it occurs favorably or unfavorably to sectors, reduces
conditional volatility for most of the sectors, including the oil-producing and oil-
consuming sectors, with the cyclical Construction & Building Materials sector
cooling off the most. The other sectors that also cool off more than the average level
include Electronic & Electrical Equipment, Industrial Metals, Telecommunications,
Software & Computer Equipment, and Multi-utilities. These volatility results are
consistent in their cooling direction with those obtained at the aggregate level
although with a stronger degree, all in all suggesting that companies in most sectors
hedge against the oil price risk. They also imply that in an environment of rising oil
prices, coupled with low price elasticity, most sectors manage to pass the price
increases to the consumers. These oil results also hold for the two subperiods,
showing greater impact volatility for most sectors than for the whole sample (Table
4). We must also add that the impacts were greater in the second subperiod than in the
first subperiod, which is not surprising.
Additionally, decreases in the oil price also reduce volatility for all sectors in all
periods. But the volatility impact in this case is not as strong as when the oil market is
moving upward for most sectors, with the cyclical sectors Construction & Materials,
and Software & Computer Services are the most sensitive to the oil price moving
downward. This result suggests that companies during declines in oil prices
associated with declining economy are not as able to maintain profitability and/or they
tend to engage less hedging. The Wald test demonstrates that the positive and
negative oil shocks are asymmetric except for three sectors.
22
Table 4-a: World and Country Variables’ Asymmetric GARCH Impacts-Subperiod 1/2/1989-12/31/2003
INDUSTRIES DOIL DFFR DMSCI
Positive Negative Positive Negative Positive Negative
Beverages -1.56E-04 a 1.38E-04 a -6.74E-05 a 4.50E-05 a -6.26E-04 a 6.54E-04 a
Chemicals -2.93E-04 a 2.05E-04 a -1.29E-04 a 8.07E-05 a 2.22E-04 a -1.21E-04 a
Construction & Materials -9.90E-04 a 6.24E-04 b -1.43E-04 a -2.94E-04 a 1.47E-05 -2.76E-03 a
Electronic & Electrical Eq. -6.77E-04 a 3.86E-04 a 1.98E-05 5.74E-05 a 8.46E-05 c 6.68E-05
Electricity -9.83E-05 a 6.90E-05 b -3.68E-05 a 3.78E-05 a 1.34E-04 a -1.08E-04 b
Food & Drug Retailers -3.72E-04 b 3.02E-04 b -1.45E-04 a 9.12E-05 a 7.11E-05 -2.60E-04 b
Food Producers -1.49E-04 b 1.20E-04 a -6.46E-05 a 5.74E-05 a 1.94E-04 a -1.51E-04 a
Fixed Line Tele. -4.89E-04 a 3.09E-04 a -1.44E-04 a 1.53E-04 a 7.76E-05 -3.31E-04 a
General Financial -2.57E-04 a 1.82E-04 b -4.39E-05 a 7.78E-05 a -7.29E-04 a 4.99E-04 a
Gas, Water & Multiutilities -5.98E-04 a 4.01E-04 a -5.84E-05 c -5.01E-05 b -6.68E-04 a -1.03E-03 a
Healthcare Eq. & Services -3.58E-04 a 3.16E-04 a -1.30E-04 a 1.00E-04 a 3.02E-05 -5.37E-05
Industrial Transportation -3.17E-04 a 2.69E-04 a -1.65E-04 a 3.39E-05 2.12E-04 b -1.91E-04 c
Industrial Metals -1.24E-04 a 1.85E-04 a -5.05E-05 b 1.54E-04 a 1.17E-04 -1.61E-04 b
Leisure Goods -5.48E-04 a 4.92E-04 a 5.22E-06 6.74E-06 2.28E-03 a -1.85E-03 a
Life Insurance -4.06E-04 a 3.12E-04 a 2.24E-05 a 2.21E-05 a 2.69E-05 5.81E-05 a
Nonlife Insurance -2.64E-04 b 2.29E-04 a -1.07E-04 a 1.05E-04 a -9.96E-04 a 7.45E-04 a
Oil & Gas Producers 1.71E-05 -6.52E-05 a 4.17E-06 5.72E-06 c 2.29E-04 a -1.28E-04 a
Oil Eq. & Services -1.05E-04 a 1.75E-04 a 5.58E-05 b -4.76E-05 c 6.91E-06 2.01E-04 a
Personal Goods -3.78E-04 3.85E-04 a -4.40E-05 1.80E-04 a -1.41E-03 a 1.10E-03 a
Pharm. & Biotech. -3.06E-04 a 2.93E-04 a 4.31E-05 c 2.18E-07 1.04E-04 -1.04E-04
Real Estate -3.11E-04 a 2.51E-04 a -3.45E-05 1.38E-04 a 1.57E-04 c 1.88E-05
Software & Computer Services -4.61E-04 a
5.54E-04 a
-7.45E-05 b
1.01E-04 a
5.27E-05
2.19E-04 a
Support Services 7.15E-06 3.04E-05 b -2.00E-04 a 1.55E-04 a -1.46E-05 4.21E-05
Tech Hardware & Eq. -4.61E-04 a 2.68E-04 a -1.24E-04 a 1.78E-04 a -1.15E-04 -1.07E-04
Tobacco -3.70E-04 a 2.57E-04 a -1.05E-04 a 1.26E-04 a -9.00E-04 a 1.40E-03 a
Travel & Leisure 1.65E-05 -1.37E-06 -3.32E-05 a -1.09E-05 -7.32E-05 -9.88E-05
Notes: The Wald test indicates that up and down shocks have symmetric impacts for 1 sector in case of the oil price, 6 sectors for FFR, and 7 sectors for MSCI.
23
Table 4-b: World and Country Variables’ Asymmetric GARCH Impacts- Subperiod 1/2/2004-10/3/2006
INDUSTRIES DOIL DFFR DMSCI
Positive Negative Positive Negative Positive Negative
Beverages -5.30E-05 a
-2.68E-05 c
-9.41E-06 a
4.85E-07
-2.31E-04 a
2.57E-04 a
Chemicals 1.98E-05 c
7.70E-07
5.88E-05 a
1.35E-05 b
-1.72E-04
2.58E-04 a
Construction & Materials -1.22E-03 a
9.92E-04 a
6.79E-04 a
-2.33E-04
-2.00E-04
-8.76E-05
Electronic & Electrical Eq. -1.52E-04 a
1.39E-04 a
5.74E-05 b
-1.26E-04 a
1.31E-04 a
1.62E-04 a
Electricity 2.43E-05
-3.33E-05
1.76E-05
-2.86E-05
-1.79E-04 a
1.09E-05
Food & Drug Retailers -4.23E-04 a
3.72E-04 a
-8.88E-06
3.51E-04 a
-1.58E-03 a
1.14E-03 a
Food Producers 2.72E-05 b
-5.46E-06
9.75E-05 a
-6.85E-05 b
1.90E-04 c
-1.84E-05
Fixed Line Tele. 2.07E-05
-1.82E-05
4.40E-05 a
-1.01E-05
-5.77E-04 a
3.52E-04 a
General Financial -9.80E-05 a
7.53E-05 a
2.86E-06
2.82E-05 a
1.09E-05
1.01E-05
Gas, Water & Multiutilities -2.91E-04 a
2.18E-04 b
4.40E-05
-4.88E-05
1.86E-04 b
4.15E-05
Healthcare Eq. & Services -2.55E-04 a
1.88E-04 a
-7.80E-06
7.80E-05 a
-3.22E-04 a
4.88E-04 a
Industrial Transportation -3.23E-04 a
3.22E-04 a
7.71E-05
1.46E-04 a
-1.21E-03 a
6.08E-04 a
Industrial Metals -2.86E-04 a
1.55E-04 a
-6.97E-06
4.19E-05
2.03E-04
1.21E-05
Leisure Goods -5.14E-04 a
2.29E-04 c
2.26E-05
1.17E-04 b
-1.50E-03 a
1.25E-03 a
Life Insurance -4.08E-04 a
1.31E-04
-2.86E-06
-1.42E-05
-1.22E-03 a
8.80E-04 a
Nonlife Insurance -7.24E-05 a
4.37E-05 a
-6.72E-07
3.25E-05 a
-4.75E-04 a
2.76E-04 b
Oil & Gas Producers -6.16E-04 a
3.00E-04
-8.00E-06
9.67E-05
-2.14E-03 a
1.51E-03 a
Oil Eq. & Services -3.48E-04 a
2.54E-04 a
5.86E-05 a
-1.32E-05
-1.12E-03 a
6.93E-04 a
Personal Goods -4.18E-04 a
3.57E-04 a
-1.17E-04 c
1.66E-04 b
-9.23E-04 a
1.00E-03 a
Pharm. & Biotech. -7.18E-05 a
4.59E-05 a
2.18E-05 b
6.50E-06
-2.87E-04 a
1.35E-04 a
Real Estate -2.90E-05 c
1.94E-05
1.03E-06
2.38E-05 a
-2.29E-04 a
2.03E-04 a
Software & Computer Services -3.28E-04 a
3.32E-04 a
-3.32E-05
2.34E-04 b
-6.11E-04 a
1.92E-04
Support Services -1.13E-04 a
8.46E-05 a
-2.12E-05
6.23E-05 c
-8.23E-05
2.21E-04 a
Tech Hardware & Eq. -4.72E-05 a
4.62E-05 a
3.94E-05 b
-2.30E-05
-1.41E-04
2.06E-04 a
Tobacco -2.09E-04 a
6.31E-05
-3.57E-05
8.57E-05
-7.19E-04 a
9.51E-04 a
Travel & Leisure -1.64E-04 a
1.81E-04 a
2.19E-05 a
1.67E-05
-2.96E-04 a
2.88E-04 a
Notes: The Wald test indicates that up and down shocks have symmetric impacts for 4 sectors in case of the oil price, 10 sectors for FFR, and 6 sectors for MSCI
24
Similar volatility-dampening results hold true for D FFR when this variable is
in an upward regime, with the exceptions of the four sectors: Oil Equipment &
Services, Technology Hardware & Equipment, Pharmaceutical & Biotechnology, and
Travel & Leisure sectors (at 10%) that display increases in return volatility (at 10%)
concurrent with a restrictive monetary policy. These sectors are highly sensitive to
downturn in the economy, and thus their companies should hedge against interest rate
risk more than others.
The dampening results also hold when the D FFR move is in the downward
regime. The exceptions are Gas, Water & Multi-utilities, Oil & Gas Producers, Oil
Equipment & Services, Pharmaceutical & Biotechnology, and Technology Hardware
& Equipment. These sectors experience increases in volatility during monetary policy
easing. The Wald test shows that the positive and negative in the FFR shocks are
asymmetric except for four sectors. Those results also hold for the two subperiods, but
with greater impacts on sector volatility and more in the second period than in the first
one.
The results are more different for MSCI than for the other two variables, and
are also relatively mixed when MSCI moves both up and down. Thirteen versus nine
sectors exhibit increases in volatility when MSCI moves up, while ten versus six
sectors show decline in volatility when MSCI moves down. This result shows that the
US stock market sectors are part of the world stock markets, co-move with the world
movements and are subject to global volatility spillovers.
To sum up, Software & Computer Services is the only sector that is sensitive
to the three factor variables almost when they move up and when they move down.
Movements, whether up or down, in the oil price dampen this sector’s volatility,
whereas increases or decreases in D FFR heighten its volatility. Upward movement in
25
MSCI also increases its volatility, while as is the case for oil; downward movement in
MSCI reduces its volatility. This has to do with the very cyclical nature of this sector.
V.c. The CGARCH results
The empirical analysis of employing the standard GARCH model allows us to
discern a general relation between the conditional variance and the exogenous
variables in modeling the volatility clustering phenomenon. However, we would have
a richer and more informative insight if we investigate the parametric impacts of
exogenous shocks on volatility by employing a CGARCH model. This model allows
us to distinguish the short-lived transitory impact from the long-run effect on
(permanent) volatility. The representation is given by:
tiq , = iw + )( 1, itii q wr -- + )( 21,
21, -- - titii sef (4)
2,tis tiq ,- = iw + )( 2
1 tti q--ea + )( 21, itii q--sb + titi Z ,, Dh , (5)
where itq long-run components of volatility; it is assumed to be slowly mean
reverting; 2,tis tiq ,- , is the temporary component and will be more volatile. Now
CGARCH model allows mean reversion to a varying level tiq , . When
,1)(0 <+< ba short run volatility converges to its mean of 0, while if 10 << r , the
long run component converges to its mean of iw /(1- ir ) with the restriction of
.0>> ii fb
The CGARCH results are reported in Table 5. The increase in the daily oil price
risk dampens the short-lived transitory volatility for most sectors, while it heightens
the volatility for three sectors only (wherever impacts are statistically significant at
5% or better). The oil result is similar to those obtained in Table 2 for the standard
GARCH model.
26
Table 5: The Sectors’ Stock Return Volatility - CGARCH Model
INDUSTRIES r f a b DOIL DMSCI DFFR DPB DVO R2
Beverages 0.54 a 0.05 a 0.04 a 0.11 b 1.87E-05 a 5.20E-05 a -2.98E-06 a -2.54E-05 a 2.44E-06 a 0.81
Chemicals 0.58 a 0.05 0.12 0.46 9.82E-06 c 2.23E-05 a 4.70E-07 -1.44E-05 a 4.89E-06 a 0.66
Construction & Materials 0.51 a 0.07 0.05 0.02 -1.13E-04 1.13E-04 2.77E-05 2.09E-06 5.04E-05 a 0.23
Electronic & Electrical Eq. 0.98 a 0.03 a 0.04 a 0.21 a 9.57E-06 1.95E-04 a 1.58E-05 -8.92E-05 a 1.52E-05 a 0.60
Electricity 0.99 a 0.00 a 0.13 a 0.39 a 6.40E-06 1.11E-05 3.67E-06 -3.63E-05 a 3.72E-06 a 0.84
Food & Drug Retailers 1.00 a 0.00 a 0.00 0.84 a -4.20E-05 b 3.07E-04 a -1.18E-05 -2.38E-04 a 2.78E-05 a 0.48
Food Producers 0.86 a 0.01 a -0.01 a 0.85 a 3.18E-07 -8.53E-06 2.90E-06 -1.25E-05 b 4.38E-06 a 0.68
Fixed Line Tele. 0.99 a 0.00 a 0.07 a 0.78 a -1.35E-05 1.15E-05 -2.92E-06 -1.27E-05 a 1.04E-05 a 0.58
General Financial 0.80 a 0.18 a -0.18 a 0.99 a -7.21E-06 4.23E-05 1.12E-05 -4.96E-05 a 8.43E-06 a 0.83
Gas, Water & Multiutilities 0.99 a 0.04 a 0.01 0.86 a 3.24E-05 1.90E-04 a 2.20E-05 -1.45E-04 a 1.92E-05 a 0.37
Healthcare Eq. & Services 0.97 a 0.08 a 0.05 a 0.18 -1.54E-05 1.40E-04 a -8.73E-06 c -9.78E-05 a 8.41E-06 a 0.59
Industrial Engineering 0.69 a -0.47 a 0.65 a 0.02 -5.10E-05 b 9.31E-05 b 1.94E-05 b -1.04E-04 a 1.06E-05 a 0.74
Industrial Transportation 1.00 a 0.00 a 0.06 a 0.75 a 1.85E-05 2.29E-05 8.18E-06 -9.13E-05 a 1.38E-05 a 0.68
Industrial Metals 0.46 a 0.00 b 0.15 a 0.00 -2.12E-05 b 3.09E-05 1.13E-05 a -3.01E-05 a 4.12E-06 a 0.59
Leisure Goods 0.99 a 0.01 b 0.01 0.94 a 2.41E-05 2.94E-05 -2.56E-06 -6.69E-05 a 2.31E-05 a 0.41
Life Insurance 0.98 a 0.01 a 0.10 a 0.59 a -5.17E-05 a 1.64E-04 a -5.86E-06 -2.07E-04 a 1.92E-05 a 0.56
Nonlife Insurance 0.09 a 0.11 a -0.01 -0.05 -9.82E-06 c 6.64E-05 a 9.42E-06 a -1.19E-04 a 1.09E-06 a 0.50
27
Table 5 continue..
INDUSTRIES r f a b DOIL DMSCI DFFR DPB DVO R2
Oil & Gas Producers 0.87 a -0.40 a 0.40 a 0.47 a -2.32E-05 a 1.85E-07 -4.02E-06 -3.14E-05 a 1.02E-05 a 0.70
Oil Eq. & Services 0.33 a -1.25 b 1.52 a -1.19 b 6.35E-06 4.37E-05 2.62E-06 -2.77E-05 3.79E-06 b 0.84
Personal Goods 0.94 a 0.06 a 0.07 a 0.35 a -8.72E-05 a -1.85E-05 -3.69E-05 a -2.87E-04 a 1.74E-05 a 0.49
Pharm. & Biotech. 0.82 a 0.42 a -0.18 a 0.97 a 8.85E-07 1.42E-05 c -1.61E-07 -3.61E-05 a 2.72E-06 a 0.64
Real Estate 0.63 a 0.12 a 0.08 a 0.17 a 3.02E-05 -5.86E-06 4.09E-05 a -8.42E-05 a 1.07E-05 a 0.41
Software & Computer Services 0.56 a 0.13 a 0.05 b 0.06 1.79E-04 a 9.04E-05 c 3.58E-05 a -6.58E-06 2.36E-05 a 0.71
Support Services 1.00 a 0.02 a 0.04 a 0.87 a -2.78E-06 1.56E-04 a 1.53E-05 -1.26E-04 a 8.09E-06 a 0.48
Tech Hardware & Eq. 0.98 a 0.03 a 0.05 a 0.79 a 1.25E-05 c 5.04E-05 b 1.28E-05 a -2.57E-05 a 2.80E-06 a 0.84
Tobacco 0.50 a 0.05 c 0.05 0.02 -7.49E-05 a -1.66E-04 a 3.65E-05 a -1.74E-04 a 9.46E-06 a 0.80
Travel & Leisure 0.97 a 0.08 a 0.06 a 0.24 c 6.29E-05 b 1.93E-04 a -2.45E-05 -3.49E-04 a 1.75E-05 a 0.44
Notes: Due to space limitation in the table, we use the following significance notation: a for one percent, b for five, and c for 10 percent levels of significance instead of using *, ** and ***. r measures the degree of permanent volatility, while α + b captures the degree of transitory volatility. The common and industry characteristics variables in this table are related to the transitory volatility equation and not to the permanent volatility equation which exhibits similar volatility attributes like the standard GARCH equation. and is not reported.
28
The CGARCH’s oil finding that oil dampens volatility for most sectors is
consistent with the above assertion that many sectors manage to pass the oil risk
shocks into the consumers because of less competitive environment or low price
elasticity of demand, and many sectors hedge against the oil price risk in the short
run, as are the results in the table are for the transitory volatility. However, some
sectors such as Software & Computer Services and Travel & Leisure are unable to
hedge, and/or pass the oil price risk even in the short run as indicated in our data.
Software & Computer Services and Travel & Leisure are highly cyclical sectors, and
changes in the oil price increase their risk-sensitive volatility as they slide over the
business cycle together with the oil prices.
Consistent with the GARCH model, all of the exogenous variables in CGARCH
have similar performance. MSCI shocks increase the transitory volatility of all
sectors (except Tobacco) because of the mood and spillover dynamo effects of this
world variable which reflects snow balling of information as a result of globalization
and improvement in communication technology. The Tobacco result may have
something to do with the addiction nature of demand for smoking which is highly
inelastic.
Checking the relationship between transitory volatility and monetary policy, the
results indicate that the sign of D FFR is positively related to the volatility in many
sectors. This means that a tight monetary policy leads to a rise in the transitory
volatility, with the exceptions of the defensive sector Beverages and Personal
Goods13. The evidence suggests that changes in monetary policy tend to aggravate
the volatility in most sectors, perhaps because they are seen to be more risky from
13 These two sectors have low price elasticity of demand and they operate in a highly competitive and un-concentrated environment.
29
investors’ point of view. In this sense, changes of monetary policy introduce
uncertainty to the sectors that are particularly sensitive to changes in the interest rate.
The impacts of changes in sector-specific variables, P/B ratio and trading volume
on the transitory volatility are also similar to their impacts in the GARCH model
above. Thus increases in the daily volume raise the transitory return volatility for all
sectors, a result that is also consistent with the mixture of distributions hypothesis
(MDH). Increases in the P/B ratio moderate the transitory volatility as investors
become more cautious of high financial valuations in the short-run.
From an econometric point of view, the evidence suggests that adding daily change
trading volume to the variance equations increases the explanatory power as noted by
the adjusted R2 for sixteen sectors, reduces R2 for three sectors, and makes no change
for rest of sectors as compared to the results by excluding trading volume. Other
CGARCH findings also suggest that adding the changes in trading volume increases the
persistence of the transitory component (and thus reduces the speed of convergence to
long-run equilibrium) for fourteen sectors while it reduces it for nine others. This result
indicates the importance of shocks on slowing down the transitory convergence when
trading volume is controlled for14. Other persistence results indicate that the CGARCH
model clearly shows that the short-run persistence is still lower than the long-run
persistence for almost all sectors even when changes in the trading volume is accounted
for. Moreover, there is volatility clustering in the transitory and permanent volatilities
for some sectors. The persistence of permanent volatility is strong for twelve sectors,
14 In fact, the lack of MLE convergence during the estimation problem without trading volume is detected for two sectors. This problem is due to a specification problem across sectors when trading volume is omitted.
30
and for the transitory volatility it is strong for only two sectors (Leisure Goods and
Support Services) only.
VI. Conclusions
The results of the impacts of the different sector-specific fundamentals and global
and domestic variables on conditional volatilities, defined in a family of GARCH
models, for 27 US equity sectors can be used to construct a mosaic of diversified
portfolios to fit investors’ diverse needs. The results are given for the whole sample
period 1/2/1989 - 10/3/2006 and for two subperiods, with the breaking point defined
by the surge in commodity prices after the start of the 2003 Iraq war. The results for
the subperiods underline the robustness of the estimations for the whole period.
The GARCH estimations suggest that the two global factor variables, oil price and
MSCI, have differing impacts on standard GARCH volatility for the equity sectors
over the whole sample, with oil price dampening volatility and MSCI heightening it
for most sectors. They both, however, have greater and more sector-pervasive impacts
on this volatility than the domestic country variable, interest rate. The results
demonstrate similar but greater impacts when the sample period is divided into two
supberiods. It seems it is hard for firms to pass risks to consumers when the world
environment is affected by several factor risks, but firms seem to hedge successfully
against the oil price risk Sectors such as the cyclical sectors Construction & Materials
and Industrial Metals are particularly the most responsive and prepared to unfavorable
oil price shocks. But Software & Services is the most upwardly oil sensitive volatility-
prone. This sector should design more effective hedging or pricing strategies to
reduce their extra sensitivities to the unfavorable positive oil shocks. A sector
portfolio that combines stocks from Construction & Materials and Industrial Metals
31
on one hand, and Software & Services on the other hand may bring some balance to
the oil-caused volatility.
In the case of bullish world capital markets, increases in MSCI heighten many
sectors’ volatilities, with the Industrial Metals sector being the most sensitive by
displaying the highest increase in volatility. However, the Gas, Water and Multi-
utilities sector is the most responsive in reducing volatility. One way traders can
reduce the sector upward volatility sensitivity to increases in MSCI is by diversifying
into sectors (such as the Utilities) which experience simultaneous reduction in
volatility concurrent to increases in MSCI. This is a strategy that balances different
sectors or employs sector diversification-based hedging to dampen volatility in
response to rising MSCI.
Since the two global variables affect sector volatilities differently, they may offset
each other’s impacts, depending on the sectors. It is possible that when oil prices are
rising and the world markets are flourishing certain sectors may experience a decline
in volatility while others witness an increase, leading to basically very little change in
the portfolio volatility. Combining in a sector-diversified portfolio, sectors with
differing volatilities to the oil and MSCI variables would be another strategy to reduce
the overall volatility, amounting to balancing factor sensitivities across sectors.
Examples of such sectors include Industrial Metals, Tobacco, Health Care Equipment
& Services and Industrial Engineering.
The results also show that increases in the federal funds rate can reduce volatility
in certain sectors, giving monetary policy and indirect role in calming market
volatility. To complete the volatility balancing mosaic, rising oil prices, increasing
interest rate and rising the world’s stock markets may work in concert to reduce
volatility in some sectors. Examples of such sectors are Industrial metals, Health Care
32
Equipment & Services, and Life Insurance which have different factor sensitivities.
Sectors that should be heeded off in such an environment include Real Estate whose
market is particularly sensitive to unfavorable interest rate shocks.
Increases in the P/B ratio (or the M2B value) would reduce the aggregate
volatility as investors become more conservative and demand higher risk premium for
the more expensive stocks. This variable can be used as a criterion for selecting
sectors that reduce portfolio volatility at time of increases in MSCI. Sectors that are
particularly sensitive to this ratio include the defensive sectors: Personal Goods,
Tobacco and Food and Drug Retailers.
The most important factor variable in affecting volatility is the trading volume.
Increases in this volume elevate volatilities for all sectors because it signifies
increases in liquidity. Diversification in this case will not reduce return volatility
because there is no sector to hide in as changes in trading volume affect all sectors.
Thus, hedging by using financial derivatives on part of the risk-averse investors is a
panacea for dealing with the liquidity-induced increases in volatility.
Excluding the trading volume from volatility equations has also econometric
implications. Models that do not account for this variable may have MLE
convergence problems during estimation, lower explanatory power, and less statistical
significance for the independent variables. Therefore, excluding this variable subjects
the GARCH models to the missing variable issue. Further, our results show that the
inclusion of this variable in the models reduces the rate of volatility persistence for
most but not all sectors.
The impact of increases in the oil price on the transitory volatility in the
CGARCH model is similar to the one obtained in the GARCH model and has similar
implications. This CGARCH finding confirms the GARCH result that many sectors
33
manage to pass the oil risk shocks to consumers and also to hedge against oil price
risk in the short run, while a few (such as Software & Computer services, and Travel
& Leisure) face a more competitive environment or do not hedge, and thus are unable
to do so. Similar to the differing impact of MSCI relative to oil in the GARCH model,
positive MSCI shocks in the CGARCH model increase the transitory volatility of all
sectors (except Tobacco) because of the significance of the mood and dynamo
spillover effects of this world variable. However when it comes to interest rate, most
sectors in the CGARCH model unlike in the GARCH model show an increase instead
of a decrease in the transitory volatility in reaction to monetary policy tightening.
Monetary policy-makers should be forward-looking and have their efforts aim at the
fundamental factors such as inflation and interest rates and not on the short-lived
return volatility shocks which vanish rapidly. The CGARCH model demonstrates
convincingly that the transitory volatility has lower persistence and shorter duration
than the permanent volatility at the sector level.
Software & Computer Services is the only sector that is sensitive to all three
world and country factor variables whether when they move up or move down.
Similar to other sectors, movements whether up or down in the oil price dampen this
sector’s volatility, but increases or decreases in FFR heighten its volatility which is
contrary to most other sectors. Also contrary to other sectors, upward movements in
MSCI also increase its volatility, while downward movement in MSCI reduces its
volatility as is the case for oil shocks. This has to do the very cyclical nature of this
sector.
34
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