Masters in Finance
Asset Management
Master Thesis
Title: “Oil price volatility and its predictive power on stock returns”
Konstantinos Varvakis
11801964
July 2018
Supervisor: Dr. Raphael Ribas
Statement of Originality
This document is written by Student Konstantinos Varvakis who declares to take full responsibility for the contents of this document.
I declare that the text and the work presented in this document are original and that no sources other than those mentioned in the text and its references have been used in creating it. The Faculty of Economics and Business is responsible solely for the supervision of completion of the work, not for the contents.
Table of Contents
ABSTRACT ... 3
1.INTRODUCTION... 4
2. LITERATURE REVIEW ... 6
2.1PREDICTING STOCK MARKET RETURNS ... 6
2.2OIL PRICE VOLATILITY AND STOCK MARKET RETURNS ... 8
3. DATA ... 9
3.1CRSP DATA ... 9
3.2FAMA AND FRENCH MODEL... 10
3.3OIL DATA ... 11
4. DESCRIPTIVE STATISTICS ... 12
5. EMPIRICAL METHOD ... 14
5.1MEASUREMENT OF OIL PRICE VOLATILITY ... 14
5.2IN-SAMPLE REGRESSIONS ... 17
5.2.1 In-Sample Regression Results ... 19
5.3OUT-OF-SAMPLE REGRESSION ... 20
5.3.1 Out-of- Sample Results ... 22
5.4TRADING STRATEGY ... 24
5.4.1 Rce and Risk aversion... 29
6. ROBUSTNESS CHECK ... 30
7. CONCLUSION ... 32
Abstract
This thesis examines whether oil price volatility can predict stock market returns and can be used to construct a trading strategy that increases the utility of investors. The proposed explanatory variable, which is constructed to incorporate both the unanticipated component and the time-varying conditional variance of oil price change (forecasts), found to be highly significant in explaining stock market returns. Furthermore, in an out-of-sample frame the variable found to be a better predictor than the Historical Mean model and lead to utility gains for investors.
1.Introduction
Oil is still the primary energy source in most of the countries. In 2017, United States consumed 19.88 million barrels of petroleum products per day. People and industries use it in their daily activities. Thus, its price level and its fluctuations are strong determinants of their welfare. Changes in oil price, which can be proxied by oil price volatility, have an effect on firms’ expected cost and as a result on their output (Ferderer, 1996). By generalizing this premise, we can observe that oil price changes are strong predictors for the future GDP.
Moreover, stock markets historically reflect the economic growth and well-being of nations (Ake, 2010). Therefore, given the big fluctuations in oil prices that have been observed during the last 30 years, a question is raised; Can oil price volatility predict stock returns?
To answer this question, I need first to establish the existence of a significant relation between those two variables. This paper’s first hypothesis illustrates this question
Hypothesis 1: The oil price volatility has a negative statistically significant effect on stock returns.
My results agree with those of Sardorsky (1999). He found that oil price fluctuations Granger-cause a reduction in stock market returns in U.S, using data from 1947 to 1996. On the other hand, Lee, Ni and Ratti (1995) showed that real oil price volatility has insignificant explanatory power on GNP and stock returns in U.S after 1986. However, both of these studies conclude based on in-sample regressions which is not sufficient to give us reliable results. In my research the predictive power of oil price volatility is tested using both in-sample and out-of-in-sample regressions, method that has not been applied in this topic before. In addition, I contribute to the existing literature by constructing a trading strategy to
investigate the value of this variable for the mean investor.
Most of the related existing literature investigates the relationship between oil prices and the macroeconomy. The effect of changes in oil prices and stock market returns has only been seen from the frame of oil shocks which include only significant increases in oil prices (Hamilton, 1983). I chose oil price volatility as a predictor because it incorporates positive and negative changes in oil prices. This is important because some studies, where oil price fluctuations are divided into positive and negative, give insignificant results for effect of the negative movements of oil price. In addition, oil price volatility depicts the uncertainty for the future of the economy. Fluctuations in oil prices lead agents to cease their economic activity in
order to figure out whether these fluctuations are signals for recession or not (Bernanke,1983). Thus, high oil price volatility can be seen as a factor that creates uncertainty.
Few researches have been conducted using oil price volatility as a predictor for stock returns. Ferderer (1996) showed a link between the oil price volatility and the macroeconomy. But, he uses as a proxy for the macroeconomy the industrial production growth not the stock market returns. Moreover, the monthly oil price volatility is computed by taking the standard deviation (Ferderer, 1996). This method does not take into account the time- varying nature of the volatility which means that these estimators of volatility are not reliable. To solve this problem, I use the multivariate GARCH model which takes into account only information of the previous periods. Huang et al. (2005) also used a GARCH model to forecast the conditional oil price volatility, but they found that small levels of volatility have not a significant impact on economic figures including stock returns.
In this research, the oil price volatility derives from the prices of West Texas Intermediate oil crude. In many relative studies, the producer price index for fuel is used (Huang et al. ,2005). This index depicts the prices of unprocessed crude oil not sold directly to consumers. These prices are not the finals and they lack some important information. Lee, Ni and Ratti (1994) used the prices that US refiners face to obtain the crude oil. But these prices reflect the cost of domestically crude oil which was held down due to price controls (Ferderer, 1996). So, they are biased. The reason to choose the WTI crude lies in the fact that these prices are the ones that quoted in the commodity market, and it is used as underlying commodity of the New York Mercantile Exchange's oil future contracts and incorporates some expectations. The prices are daily spot prices which makes them more accurate.
I conduct a research which assess the effects on US economy. For that reason, I use the US stock market returns. The data which is used to proxy US returns is the S&P 500 Index. The returns are the value-weighted CRSP. Most of the relative studies use this data (Sardorsky,1999). It is easily accessible and is a valid representation of the US stock market Index.
This paper is organized as follows. Section 2 presents all the previous academic work and economic theory which connects oil price volatility to stock market returns. Section 3 discusses all the data that is used in this research. In Section 4 the Descriptive statistics are presented. Section 5 contains the Multivariate Generalized Autoregressive Conditional Heteroscedasticity model (MGARCH) which is used to predict the oil price volatility; in addition, it includes the
empirical results using in-sample and out-of-sample regression analysis. In the last section, I run a Robustness check to support the strength of the proposed model.
2. Literature Review
There are two main academic views. The first one is the EMH (Efficient Market Hypothesis) which advocates that the markets have incorporated all the available information. That means that the stock returns cannot be predicted (Fama, 1970). In other words, investors cannot outperform the market given the available information. On the other hand, the alternative view argues that stock returns can be predicted. They claim that many times markets do not interpret the information correctly. In this frame, this paper claims that oil price volatility is public knowledge, but the markets do not conceive it as a source of uncertainty. In that way, they do not take it into account when forecasting stock returns.
2.1 Predicting stock market returns
Stock markets were considered informational efficient for a considerable period of time. That belief supported the Efficient Market Hypothesis (EMH) where stock returns cannot be predicted since all the available information has been taken into consideration by markets. Market efficiency is concerned with the right allocation of resources in the stock market and whether prices at any time reflect the available information (Fama,1970). This perception led financial economists to argue that no model can outperform the market and consequently lead to higher profitability. Following this notion, differentiations in oil market cannot foresee the movements in stock returns. The reason is that oil prices are available daily, so markets can easily incorporate them in their predictions.
Many academics tried to show that stock returns can be predicted and a trading strategy that produces abnormal returns for the investors can be made. To do that they had to overlap a great obstacle "Why markets do not incorporate all the available information"? The answer lies in the way that markets use the information. The information diffusion hypothesis developed by Hong and Stein (1999) can explain this discrepancy. According to this hypothesis, investors have difficulty in assessing correctly the existing information. In other words, they underestimate the impact of the information on stock values. Another reason has to do with markets' reaction speed. Investors do not react on time. As a result, market needs more time to incorporate the new information. During this time interval and for a small number of periods ahead, some variables can foresee stock returns.
Moreover, by the end of the previous century, academics in finance started to reassess the predictability of aggregate stock returns. Since the 80's, many academic works have proposed some ratios as predictors of stock returns. High valuation ratios like the dividend-price ratio and the earnings-price ratio have been considered an indication that stocks are undervalued and should predict higher future returns (Campbell et al., 2008). It was the academic literature of Fama and French (1988) and Campbell and Shriller (1988) that established the existence of a correlation between those ratios and future stock returns for a much longer horizon. Following their work, I try to predict stock market returns using oil volatility.
To argue that a variable can predict another one is a difficult task in econometrics. Academic literature proposes many different processes to assess the predictive power of a variable. A simple way is to use a regression. A regression analysis using data from a specific period can provide the magnitude of the effect and using a t-test to test whether or not this effect is statistically significant. R2 metric measure the proportion of a variance for the dependent
variable that is explained by an independent. However, this metric has some flaws. For instance, adding an extra explanatory variable increases R2 without the variable provide new
information to the model.
Goyal and Welch (2006) argue that the historical average model, which is the mean of the variable, has a greater predictive power than the simple regression analysis. To test this claim, they use as dependent variable the excess stock returns. Their findings support their argument. Historical average excess stock return forecasts future excess stock returns better than a regression of future excess stock returns on predictors.
Later, Campbel and Thompson (2008) showed that many regressions on predictors can outperform the historical average model when some weak restrictions are imposed. Campbel et al. (2008) study showed that many predictor variables work better than Historical average model in out-of-sample framework. Using the R2 out-of-sample metric, they provided evidence
that even if their explanatory variable is small, it still remains economically significant. This paper follows Campbel and Thompson’s (2008) methodology. Thus, this paper examines also a second hypothesis
Hypothesis 2: Oil price volatility is a better predictor than the Historical average.
2.2 Oil price volatility and stock market returns
The pioneering work of Hamilton (1986) showed that significant increases in the price of oil called “Oil shocks” have been partly responsible for all but one crises in the United States after World War 2. Hamilton pointed out that all crises before 1972 have been proceeded by significant increases in oil prices. He did not imply causation between the two factors but named oil shocks as a "contributing factor." After him, many researchers have used different methods and data to test the relation between oil price increases and many economic variables. More recently, the focus has been shifted on the effect of oil price fluctuations on economic activity. An important variable that is used as proxy for the economic activity is the stock market returns.
The effect of oil price fluctuations on stock market returns is possible to be explained through both micro and macro level channels. In macro level, oil is the main energy source for most of firms. It is considered as part of their production cost. As a consequence, an increase in oil prices drives agents to decrease the utilization of oil. Consequently, the output growth decreases. In this case, we observe negative relation between oil price increases and output growth. This argument has been corroborated by Ferderer (1996), who showed that oil price volatility incorporates important information which is useful to forecast the output growth. He provides significant empirical results that support this premise. The output growth determines the absolute figures of real output. The latter is positive correlated with firm's expected earnings, and thus oil shocks will affect stock prices and consequently aggregate stock market returns. As follows, oil shocks cause negative effects on aggregate stock returns. In other words, an incline in oil prices now lead to a decrease in the aggregate stock returns in the near future.
The academic literature mentioned above argues that there is a significant negative relation between oil price increases and stock market returns but is there the opposite relation when oil prices decrease? Some researchers tried to answer this question, but the results are contradicting. Sardorsky (1999) divided the sample into positive and negative oil price changes. His analysis showed that the positive fluctuations have a more significant impact on stock returns than the negative ones. However, Lee, Ni and Ratti (1994) showed that a decrease in oil prices does not Granger-caused an increase in output growth and rationally neither to stock market returns. This paper tries to fill this gap in literature by using oil price volatility which includes both increases and decreases in oil prices.
In microeconomic level, the economic story behind the relation between oil price volatility and stock market returns can be seen through a management channel. Market participants have always conceived increases in oil prices as an omen for inflation (Sardorsky, 1999). Many academic papers consider oil price volatility as a determinant of uncertainty (Ferderer 1996). Thus, an incline in oil price volatility creates uncertainty in the economy and makes firms reluctant to proceed with investment projects. As firms postpone investments in order to assess whether the oil shocks are permanent or temporarily, they miss a lot of investment opportunities. As a result, oil price volatility lead to value destruction for the firms (Bernanke 1983). The value destruction is pictured in the firms’ stock market value. Their stock prices decline. In that way, higher oil price volatility leads to lower stock market returns.
3. Data
The Stock market data is divided into the CRSP (Center for Research in Security Prices) returns and the Fama and French five factor model, which is used to predict stock returns. The Oil data contains daily prices of WTI oil per barrel from which the monthly oil price volatility has been calculated. All indices are listed in US dollar.
3.1 CRSP data
The CRSP data contains historical data for the returns of S&P 500 Index. It provides the return of the biggest regarding market capitalization firms in the American stock exchange. The returns are aggregated and represent the value-weighted return of the Index. This Index proxy the US stock returns. The data was retrieved from Wharton data page. It is in percentage; the time interval is from January 1986 to December 2016. The returns are calculated for monthly data. The number of observations is 372. The returns were observed at the beginning of each month. The stock returns have been aggregated using the value-weighted average. The advantage of this type of returns is that they include dividends and exhibit less autocorrelation (Driespong and al. 2008).
The data covers a 30-years' time frame in which several economic crises have occurred. Most notable the Black Monday (1987) and the subprime mortgage crisis (2007) when the US
stock returns plunged as we see in Figure 1. Thus, we have to take into consideration these crises because they may affect the results.
Figure 1
The illustration of CRSP returns through the time studied time interval
3.2 Fama and French model
The Fama and French 5 factors come from Fama and French web page. This is the pricing model that I will use to predict the stock returns. The sample contains observations for a term between 1986:1 and 2016:12. The factors are in percentages. The data is monthly with 1860 observations in total.
The five factors are constructed using the six value-weighted portfolios formed on size and book-to-market, the six value-weighted portfolios formed on size and operating profitability and the six value-weighted portfolios formed on size and investment (Fama and French 2014). The SMB (Small Minus Big) factor is the average of the nine small (in terms of market
capitalization) portfolios’ returns minus the nine big portfolios’ return. The second factor is the
HML (high minus low). The value factor which is the average of the two high B/M (book
value over market value) portfolios minus the two portfolios with low B/M value. The third factor takes into account the firms’ profitability. It is called RMW (Robust minus weak), and it is constructed in the same way as the two previous factors. The factor calculates the difference in returns of the robust profitability portfolios and the weak ones. The investment factor is the CMW (Conservative minus Aggressive). It is calculated as the other 3 factors and represents the difference in returns between the two conservative investment portfolios and the two aggressive investment portfolios. Last but not least is the excess return (MktRf) which is the difference between the market return and the risk-free rate (risk premium).
3.3 Oil Data
The proposed predictive variable is the oil price volatility. To obtain this variable, data for the prices of WTI are used. The prices refer to the West Texas Intermediate crude and are daily calculated. They represent the price of a barrel of WTI oil per day between January 1986 and December 2016. They are not seasonally adjusted. The data source is FRED.
The prices are reported for each week-day beginning 2nd of January 1986. The data
contains only the working-days when the commodity markets work. On average, the number of observations is 21 per month or 252 per year. The prices are on U.S dollar.
We observe a permanent rise in oil prices at the beginning of 2000. The prices incline from 25 dollars per barrel to almost 150 dollars. The WTI oil prices were affected by the general rise in oil prices that period. The tension in Middle-East, derived from the war in Iraq, the soaring demand from China and the depreciation of dollar were some of the factors that lead to this rise. We can see that the prices followed a different path from the end of 2008 when the sub-prime crisis heat the US economy and led to the bankruptcy of Lehman Brothers in September 2008. Through the recovery period, the oil prices followed a stable incline path and dropped again at the beginning of 2014 when oil resources discovered in West Texas.
Figure 2
The prices are in dollars. The figure shows the daily fluctuations of oil prices in a frame of 30 years
In this research, I use the daily spot prices to calculate the WTI oil price volatility 𝑂𝑃#,% where m=1,…,12 and t=1986,…,2016.
Where OPt,m is the oil price on month m of the year t.
4. Descriptive Statistics
Table 1 provides the descriptive statistics for the five factors of Fama and French model, the value-weighted returns that are going to be used as dependent variable and the proposed predictive variable, oil price volatility.
The oil price volatility has a mean of 24.83% as reported in column A of Table 1. Its most significant value is 117% and its lowest 0.40%. That shows that the monthly prices are
extremely volatile. The values for the five Fama and French Factors are considerably lower. The difference in returns for the small minus big firms is on average 0.10%. The RMW factor shows a big range from -19.06% to 13.51%. The most prominent standard deviation among the five factors is held by the excess return (4.44). That makes it the most volatile of the five factors.
The monthly stock market return varies from -21.58% to 13.51% and there is quite some variation in returns as can be seen from the second column of Table 1 where the standard deviation is around 4.3%.
Table 1 Descriptive Statistics Sample period 1986:01-2016:12 Mean Standard Deviation Max Min Mkt-RF .6510753 4.448181 12.47 -23.24 SMB .1041129 3.025179 18.75 -15.33 HML .2535753 2.935943 12.9 -11.1 RMW .3456452 2.596413 13.51 -19.06 CMA .2971237 2.035633 9.56 -6.88
Volatility 24.83461 28.8598 117.4385 .4019263 Value-Weighted Returns .0092729 .0434654 .1351564 -.2158164 Observations 372 5. Empirical Method
The goal of this paper is to investigate whether or not the oil price volatility has a predictive power on Stock Returns. The research uses advanced econometrical technics to achieve its purpose. The predictive power is a challenging research, and various steps must be taken to reach reliable results. Firstly, I ran an in-sample regression which was conducted by using data from 1986:1 to 2016:12. This regression tests the magnitude of the effect that the proposed variable has on the dependent variable. It also provides the t-test that shows whether or not this effect is significant. The in-sample regression faces the problem that the time series is highly autocorrelated; a second step is to run an out-of-sample regression and find the R2-out of
sample.
In the first part, the methodology of calculating the oil price volatility is presented.
5.1 Measurement of oil price volatility
The monthly oil price volatility is usually calculated by the monthly standard deviation of the daily spot prices of the crude oil (Ferderer, 1996). This method seems accurate and has three main advantages according to Merton (1980) and French Schwert & Stambaugh (1987). First, the accuracy of the monthly standard deviation increases by sampling stochastic price process more frequently. Second, it is possible that the volatility of the price process varies from one month to the next. Thus, we avoid this danger by using only prices within a specific
month. Finally, there is no price overlapping by using rolling month estimators who share n-1 prices.
However, this process has a main flow which is met regularly in financial studies. Volatility is a forward-looking measure. As we see in Figure 3, the oil price is a time series which exhibits different types of volatility through the years. There are periods of low volatility and periods of high volatility. Since the differences in volatility appear in clusters, the time-series exhibits volatility clustering. The existence of volatility clustering and leptokurtosis (fat tails) lead us to forecast the variance of the daily oil price changes (volatility). In other words, the changing correlations and volatilities over time make the forecast of those variables a basis in an asset pricing model. This approach is based on the notion that if a price made a big move yesterday, it is more likely to make a big move today. So, the estimators are more reliable. The variable that would be derived from the forecast is the conditional volatility. The conditionality derives from the fact that next period's volatility depends on the information from this period (Reider 2009). To compute it, varying variance models are used.
Let's assume that next period's oil prices can be forecasted. The prices follow a deterministic trend; uncertainty about future values does not depend on forecasting horizon (Reider 2009). The oil price is
𝑂𝑃#,%= 𝜇#+ 𝜎#𝜀# where m=1,…,12 and t=1986,…,2016. (1)
Where εt is a sequence of random variables and follows a normal distribution N(0,1). I have
assumed heteroscedasticity which implies that the variance is not constant through time. The residual return is defined OPt,m-µt , as
𝛼#,%= 𝜎# 𝜀# (2)
The model which is normally used in these cases is the Generalized Autoregressive Conditional Heteroscedasticity model GARCH (1,1).
σ2
t,m+1=a0+aiα2t,m+βjσ2t,m where m=1,…,12 and t=1986,…,2016 (3)
Where σ2
t,m is the variance on month m of the year t. The model defines that next period’s
variance consists of last period’s forecast and last period’s squared residuals return. This model is an extension of the simple ARCH model. Its main advantage lies with the fact that GARCH contains a persistence parameter. Thus, the effect of the variable does not decay through time. However, this model assumes that the variance instead of volatility affects returns (Minovic et al. 2008). My model assumes that the volatility moves the variable.
Thus, I use an alternation of the GARCH model. This is the Multivariate Generalized Autoregressive Conditional Heteroscedasticity (MGARCH). This model specifies equations for how the covariance moves over time (Minovic et al. 2008). It also tests whether the variance can impact future returns. On this model, I made use of dynamic conditional correlation estimators. This type of estimators provides two main advantages. They have the flexibility of univariate GARCH but not the complexity of MGARCH (Engle 2012). The conditional correlation is based on information known in the previous period (Engle 2012). The future predictions work in the same way. Thus, the correlation matrix in each period is modeled as a weighted average of its past and recent shocks (Minovic et al. 2008).
In order to predict the future correlation matrixes, I use the oil daily prices. This model provides the correlation matrix for a window of 30 time periods. The reason behind it is that the 30 days gives us the correlation matrix based on the last 30 daily observations so it gives us the correlation matrix a month. The correlation matrix contains the auto-covariance between different t. From the matrix, I extract the diagonal which represents the conditional variance in different t. These are the estimations for the variance in the specified time interval.
The estimations refer to each day of my data set. That create the problem of aggregation. Which is the best way to aggregate variance from daily to monthly frequency? To overcome this problem, I summed the volatilities within each month and then divided them by the number of trading days (21) (Drost et al. 1993). The square root of this figure represents the monthly volatility of oil prices.
5.2 In-Sample regressions
The first hypothesis of this paper assumed that the oil price volatility has a negative effect on stock returns. This statement can be tested by conducting first a simple linear regression. This regression is in-sample, so it contains historical data from 1986:1 to 2016:12. The IS regression uses all the available data. The dependent variable of this regression is the CRSP returns which is used to proxy the US stock returns. The OLS regression can be constructed as
Rt,m+1:m+k=at,m+bi (RMt,m-Rf,t,m)+si SMBt,m+hi HMLt,m+ri RMWt,m+ciCMAt,m+εt,m+1:m+k (4)
where m=1,…,12 and t=1986,…,2016 k=1,…,36 months ahead
Two different models are used to explain the stock returns. The first model takes into account only the Fama and French’s 5 factors (4). In this model, the explanatory variables are
-. 4 -. 2 0 .2 C h a n g e i n o il p ri ce s
01jan1985 01jan1990 01jan1995 01jan2000 01jan2005 01jan2010 01jan2015 Time
those proposed by Fama and French (2014). The model that this paper proposes explain the movements of the stock returns by using an extension of the Fama and French 5 factor model. The new regression is
Rt,m+1:m+k=at,m+bi (RMt,m-Rf,t,m)+si SMBt,m+hi HMLt,m+ri RMWt,m+ciCMAt,m+yi volatilityt,m+εt,m+1:m+k
(5)
where m=1,…,12 and t=1986,…,2016 k=1,…,36 months ahead
In order to show that oil price volatility can explain stock returns, volatility must be statistically significant in the regression analysis and the R2 should be relative high.
However, this type of regression faces some flaws. The data is time series and face the threat of autocorrelation. That can lead to biased results and the coefficients cease to be BLUE. The serial autocorrelation leads also to biased OLS errors. Specifically, OLS estimator underestimates the variance of the parameter. As a result, the t-statistic will be overstated.
To test the existence of autocorrelation, I perform a Durbin-Watson test. The Durbin’s d-statistic is 1.550423. The lower critical value for d is 1.613 which is higher than the DW statistic. That means that there is statistical evidence that the error terms are positively autocorrelated. The serial autocorrelation leads to OLS errors to be unbiased. Specifically, OLS estimator underestimates the variance of the parameter. As a result, the t-statistic will be much too high.
To face this problem, I run Newey West (1987) regression. The new estimator corrects the model for serial autocorrelation, hence obtaining reliable standard errors
Since the Newey West formula subsumes the robust standard errors, it also corrects for heteroscedasticity. The new estimated standard errors are larger than the OLS estimations would be. That leads to smaller t-statistics. In that way, the coefficients will be more difficult to be statistically significant.
5.2.1 In-Sample Regression Results
Table 2 reports the results of the Newey West regression on stock returns. The coefficients and standard errors in parenthesis are presented. The first column presents the result of the Fama and French 5 factors model as described by equation 4. In the FF5 model, all the independent variables are statistically significant except for HML. The t-test showed that three out of the remaining four variables (excess return, SMB and RMW) are significant at 1% confidence level. The CMA variable is significant in 10%confidence level. The R2 is high and
reaches 0.993.
In the second column of Table 2 the results of the proposed model are reported. The model tries to improve the Fama and French 5 factor model by adding the oil price volatility as explanatory variable (5). The results are consistent with the theory and Hypothesis 1. The model shows that the oil price volatility affects negatively the stock return. An increase of 1% in conditional volatility, as calculated using the MGARCH model, will decrease the stock returns by 0.0047%. The R2 of Model 1 has also been increased slightly to 0.9939. The
significance of the proposed variable as predictor and the high R2 are enough evidence to
support the existence of a relation between stock returns and oil price volatility.
Table 2
Newey West regression on Stock Returns Standard errors in parenthesis
FF5 model Model 1 b/se b/se Mkt-RF 0.010128*** 0.010115*** (0.00006) (0.00006) SMB -0.001774*** -0.001752*** (0.00010) (0.00010) HML 0.000211 0.000214
(0.00014) (0.00014) RMW 0.000658*** 0.000671*** (0.00016) (0.00017) CMA 0.000436* 0.000394 (0.00022) (0.00022) Conditional oil volatility - -0.000047*** ( 0.00001) constant 0.002707*** 0.003803*** (0.00041) (0.00044) r2 0.9931 0.9939 df_r 330.000000 329.000000 * p<0.05, ** p<0.01, *** p<0.001 5.3 Out-of-Sample Regression
The in-sample model is not sufficient to prove that oil price volatility can predict the stock returns. Goyal and Welch (2006) state that in-sample correlations conceal a failure of some variables to predict out-of-sample. In other words, the in-sample prediction cannot give reliable results for the predictive power. The out-of-sample diagnostic is a simple way to forecast and diagnose the forecasting ability of predictive regressions (Goyal and Welch 2003).
In contrast with the in-sample regressions, the out-of-sample uses all the then-available information to estimate the regressions’ coefficients and after the regressions are estimated as rolling forecasts to predict one month ahead stock returns. The sample period is divided into two sub-periods: 1986:1 to 2013:12 and 2014:1 to 2016:12. The first sub-sample is used to calculate the coefficients of the regression 5a
Rt,m+1:m+k=at,m+bi (RMt,m-Rf,t,m)+si SMBt,m+hi HMLt,m+ri RMWt,m+ciCMAt,m+volatilityt,m+εt,m+1:m+k
(5a)
where m=1,…,12 and t=1986,…,2013 k=1,…,36 months ahead
The regressors are used to calculate the observation 𝑅.2014,1. I place the data observations for
the time t=2014 and m=1 and I extract the estimated returns for January 2014. The rolling pattern of the forecast means that this estimation is added into the first sub-sample. Then, new coefficients are estimated for the regression 5b.
Rt,m+1:m+k=at,m+bi (RMt,m-Rf,t,m)+si SMBt,m+hi HMLt,m+ri RMWt,m+ciCMAt,m+yi volatilityt,m+εt,m+1:m+k
(5b)
where m=1,…,12 and t=1986,…,2014 k=1,…,36 months ahead
The new regressors used to calculate the estimation for 𝑅.2014,2. The process is continued for
all the k-month ahead returns. The forecast interval (k) is 36 periods(months) which equals 3 years.
A good trader will not use the whole sample to predict the Stock returns. A sub-sample would be used. Thus, the out-of-sample method is useful for practitioners. Normal R2 and
t-test cannot assess the out-of-sample predictability. The out-of-sample method will be evaluated by constructing the R2
oos (Out-of-sample). This diagnostic, which was proposed by Campbell
and Thompson (2008), compares the forecasts of the out-of-sample method with the most basic forecasting model, the Historical mean model. This model assumes that if observations are independent and follow an identical distribution, the best forecast is the mean. The mean is an
unbiased predictor and minimizes the mean square forecasting error (MSFE) regardless the shape of the distribution. The simplicity of the model makes it extremely popular in the forecasting literature. The R2
oos which is constructed as 1 minus the ratio of the forecasting
error over the historical mean forecasting errors. R2
oos is described by the following formula
(Campbell and Thompson 2008)
R2 oos
=1-∑2,9:72,3 (12,345:3478;2,345:347< )
∑2,9:72,3 (;2,345:3478> ;??????5:2 (6)
Where m=1,…,12 , t=2014,…,2016 , k=1,…,36 months ahead.
Table 3
Explanation of the variables that constitute the R2oos metric
Variable Explanation
Rt,m+1:m+k The real stock returns at year t from the next
month to the k months ahead of today
𝑅#,%@A:%@>< The Out-of-sample forecast of the stock returns at
year t for nest period to k periods ahead
𝑅A:#
????? The mean of real stock returns for the period 2014:1 to 2016:12
The critical value of the R2oos is 0. If R2oos>0 means that the variable is a better predictor
than the Historical mean model, otherwise the historical mean model is better so the variable does not have predictive power (Campbell and Thompson 2008).
5.3.1 Out-of- Sample Results In my model, I calculated the R2
oos using as real stock returns the CRSP data. Through the
rolling forecast method, I calculated the Out-of-Sample predictions. The CRSP data was also used to calculate the mean of real stock returns in the time interval 20014:1-2016:12.
Figure 4 reports the time-series.. The out-of-sample forecasts for the sub-sample 2015:1 to 2016:12 fit the movement of the real returns. However, the Out-of- Sample observations are slightly narrower than the real returns. They are not fully capable to capture the outliers of the CRSP observations. Thus, the model can explain and predict the US stock market returns.
Figure 4
The graph pictures the Real stock market returns (Observed Returns) and the out-of-sample forecasts (2015:1 to 2016:12)
The second hypothesis of this research assumes that the proposed model is a better predictor than the historical average. Hence, if the value of R2oos is higher than zero, the second
hypothesis is confirmed.
The results for different k of R2
oos is presented in Figure 5. The higher value of R2oos is met
at period 9 with value 0.9999619. After the 10th in ahead period, R2oos starts to follow a
decreasing pattern. The minimum value is met at the 35th period ahead. The R2oos’s value is
-. 0 5 0 .05 .1 2015m1 2015m7 2016m1 2016m7 2017m1 t
0.999855. For all periods k, the R2
oos is bigger than zero. Thus, the model for all the forecasting
interval predicts the stock market returns better than the Historical Mean model. The value of the diagnostic for the 36th period is 0.9998576 amid the model is capable of predicting the stock
market returns 36 months ahead. In this way, the second hypothesis of the paper is confirmed, and the model including oil price volatility is a better predictor than the historical mean model.
Figure 5
The table reports the R2oos for different number of periods ahead
5.4 Trading Strategy
So far, the paper showed that the oil price volatility is a valid predictor. It is statistically significant in an in-sample regression framework and can provide better forecasts than the mean average model as told by R2oos. However, R2 and R2oos have some flows. The main flow
is that they do not account for risk factor which might be heterogeneous across investors.
0.9998000 0.9998200 0.9998400 0.9998600 0.9998800 0.9999000 0.9999200 0.9999400 0.9999600 0.9999800 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36
Besides, these metrics cannot be directly applied by investors in transactions. In that way, not only the statistical significance but also its economic value for the investors must be assessed. In order to accomplish that a trading strategy must be built.
Following Rapach, Strauss and Zhou (2010), I constructed a trading strategy which computes the average utility for the mean investor on a real-time basis. The strategy replicates the case where a mean investor invests in a market portfolio consisting of a risky asset and a risk-free asset. The risky asset is proxied by the returns that are forecasted by Model 1 in the period 2014:1 to 2016:12. Moreover, the risk-free asset is proxied by using the 1-month treasury bill rate. The US treasury bill is considered the asset with the lowest level of probability of default as agencies rate it as an AAA investment.
I first calculate the monthly portfolio return (Rp) of a mean investor who allocates in a
monthly basis her resources into a portfolio consisting of stocks in US stock markets and the 1-month treasury bill which represents the risk-free asset. The allocation is based on the forecasts of the proposed model which includes the oil price volatility as a predictive variable of the returns. The mean investor decides the proportion of her resources which is going to be invested in the risky asset by the following formula (Campbell and Thompson, 2007)
𝑤C =# AD;2,345:347<
E245:247F< (7)
where 𝑤C represents the weight of the portfolio which is going to be invested in the stock # market and 𝑅#,%@A:%@>< the forecasts for the stock returns over the out-of-sample period. The 𝜎#@A:#@>G variable is the predicted market variance. The literature suggests that the investors estimate the variance using a five-year rolling window of monthly returns (Rapach, Strauss and Zhou ,2010). Finally, γ represents the risk aversion of the mean investor. As literature suggests I assumed γ=2. The weight of the investor’s resources invested in the risk-free asset is the remaining of which is calculated by subtracting 𝑤C from 1 (1-𝑤# C). #
Table 3 pictures the values of the two weight variables for each period ahead. The two variables are ratios, so they sum up together at 1. The negative values of the variables mean that the investor takes a short position on stocks or treasury bill. At k=36, the mean investor puts 10.12% of her money on the risky asset and the rest 89.87% on the treasury bill.
Table 3
The table pictures the weight of investment on risky asset (column 2) and the weight of investment on risk-free asset (column 3) about the predictive periods k
k 𝒘C 𝒕 1-𝒘C𝒕 1 -.2030397 1.20304 2 .1516704 .8483296 3 .03311 .96689 4 .0385681 .9614319 5 .1329492 .8670508 6 .1114591 .8885409 7 -.0820451 1.082045 8 .2224115 .7775885 9 -.0627197 1.06272 10 .0877155 .9122845 11 .176026 .823974 12 -.0227487 1.022749 13 -.1571735 1.157174 14 .2473738 .7526262 15 -.0455761 1.045576 16 .0494658 .9505342 17 .0608796 .9391205 18 -.1106421 1.110642 19 .1097794 .8902206 20 -.3147011 1.314701 21 -.0530871 1.053087 22 .2421761 .7578239 23 .0001139 .9998861 24 -.0437191 1.043719
25 -.168363 1.168363 26 .0096761 .9903239 27 .2694387 .7305613 28 .0240971 .9759029 29 .0749464 .9250536 30 .0109681 .9890319 31 .2139221 .7860779 32 .0203623 .9796377 33 .0022898 .9977102 34 -.0578728 1.057873 35 .2294836 .7705164 36 .1012639 .8987361
Using those weights, I calculate the portfolio returns (Rp). They are constructed as the
weighted-average of the risky asset’s returns and the risk-free asset’s returns. The returns are computed by formula 7
𝑅J = 𝑊L 𝑅# #,%@A:%@>< + M1 − 𝑊L P 𝑅# Q (7)
where 𝑅Q represents the returns of the 1-month treasury bill. From that formula, we extract the returns of the portfolio based on the proposed model including the oil price volatility. The results are pictured in Table 9. In the 36th period of forecasting the returns according to model
1 is 2.9%.
Figure 6
The table contains the returns of the portfolio where the resources have been invested in stock (according to model 1) and the 1-month treasury bill.
The trading strategy provides the returns for the benchmark portfolio when the investor forms forecasts for the US stock returns using the proposed model and the oil price volatility as an explanatory variable. However, the economic significance of the model is linked with the average utility for the mean investor. The utility is proxied by the certainty equivalent rate of return (Rce). That is the rate of return for which the investor is indifferent between the risky
asset and the risk-free asset. The Rce is calculated as formula 8 dictates ( Campbell and
Thompson, 2008)
𝑅RS = 𝑅???? −J DG 𝜎L JG (8)
Where 𝑅???? and 𝜎J L are the mean and the variance of the portfolio returns in the out-of-sample JG period 2014:1-2016:12.
This metric can be explained as an extra fee that the investors are willing to pay in order to have access on the extra information that the predicting model contains (Rapach, Strauss and Zhou ,2010). Following the methodology of Campbell and Thompson (2008) I calculated the Rce factor for the variables of my model. The Rce for Model 1 is 0.0099618. Thus, following
Rapach, Strauss and Zhou (2010), the mean investor is willing to pay 0.99618% of her returns to be provided with the extra information of the proposed model.
0.00% 0.50% 1.00% 1.50% 2.00% 2.50% 3.00% 3.50% 4.00% 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36
5.4.1 Rce and Risk aversion
Campbell and Thompson (2008) come up with an Rce which is highly related to the risk
aversion (γ). In other words, the portion of the returns that the investors are willing to pay to have the extra information which is going to improve their profitability is highly correlated with the amount of risk that they are willing to accept.
The risk aversion of the investor is represented by the variable γ. The variable takes values between 1 and 10, with 1 to be a risk-taker and 10 to be the highest level of a person who avoids risk.
In Figure 5, the values of Rce in relevance with γ are presented. For γ level 1 and 2, the
investor is willing to pay a small fee equal to around 0.001% of his return to take the new information and improve her earnings. However, for risk-aversion equal to 3 or more Rce gets
negative values. In that way, the investor is so feared for the variance of the benchmark portfolio that she always prefers the risk-free asset investment even if its returns are much smaller than the stock returns.
From Rapach, Strauss and Zhou (2010) perspective, the mean investor not only is not willing to pay a fee for the extra information when γ >2 but also request extra returns in order to change her trading model. For γ=10 she requests approximately 3.5% more returns to use the new information in her trading.
Figure 7
The graph shows certainty equivalent return in reference with the how risk avert the mean investor The Rce values are in percentage
6. Robustness Check
In this section, I will extend my Model 1 by adding one more variable and check the in-sample results of the new model. The purpose of this is to investigate whether the alternation a model characteristic (the number of independent variable) leads to different results. The Robustness check involves reporting alternative specifications that test the same hypothesis.
The new added variable is the monthly variance of WTI oil prices. In order to obtain the variance of the oil prices I do not simply calculate the monthly variance from my data. Following the same notion as in calculating the volatility, I also predict this variable. Accurately, I used the MGARCH model (Section 5.1) to calculate the correlation matrix of oil prices. The diagonal of this matrix reports the predictions of the monthly variance of oil prices. I extract this part of the table and obtain the conditional variance of the oil prices. I use this variable as an extra predictor to equation 5.
The regression that is used is the Newey West, so the effect of autocorrelation is taken out and the standard errors remain reliable. The regression still has as dependent variable the CRSP
-4 -3 -2 -1 0 1 C e rt a in ty e q u iva le n t R e tu rn (R ce ) 0 1 2 3 4 5 6 7 8 9 10 Risk aversion (γ)
S&P 500 stock returns and as explanatory variables, the Fama and French 5 factors extended by the oil price volatility and the variance of oil prices.
Table 4 reports the results of the robustness check. The hypothesis that oil price volatility has a negative effect on US stock returns is confirmed. The coefficient which determines the magnitude of this effect has been raised from 0.0047% to 0.0103%. The t-statistic also changed. Volatility in Model 2 (column 3) is significant at 10% confidence level, even though in Model 1 is significant at 1% level. The newly added variable (variance) is not statistically significant in Model 2. That means that the variable is not beneficiary to explain better the Stock Returns. Thus, Model 1 was correct, and the addition of oil price variance does not improve the model.
Table 4
Robustness Check the variance of oil prices has been added to the model
FF5 model Model 1 Model 2
b/se b/se b/se
Mkt-RF 0.010128*** 0.010115*** 0.010115*** (0.00006) (0.00006) (0.00006) SMB -0.001774*** -0.001752*** -0.001762*** (0.00010) (0.00010) (0.00010) HML 0.000211 0.000214 0.000213 (0.00014) (0.00014) (0.00013) RMW 0.000658*** 0.000671*** 0.000659*** (0.00016) (0.00017) (0.00017) CMA 0.000436* 0.000394 0.000394
(0.00022) (0.00022) (0.00021) Conditional Oil price Volatility - 0.000047*** (0.00001) 0.000103* (0.00004) Conditional Oil price Variance 0.000001 (0.00000) constant 0.002707*** 0.003803*** 0.004147*** (0.00041) (0.00044) (0.00046) r2 df_r 330.000000 329.000000 328.000000 * p<0.05, ** p<0.01, *** p<0.001 7. Conclusion
The purpose of this thesis was to assess whether oil price volatility can predict stock market returns. Oil price volatility is a variable that incorporates uncertainty since many market participants consider oil price fluctuation as an omen for inflation. That leads firms to postpone investment projects and lose profit from investment opportunities. In that way, an incline in oil price volatility leads to a decrease in aggregate stock market returns. This notion is supported by the results of this paper. There is a negative, statistically significant relation between volatility and stock market returns.
Moreover, following the methodology of Campbel and Thompson, I tested the predictive power of oil price volatility on stock market returns. The results show that volatility predicts
stock market returns for 36 months ahead. These results can be used by investors in order to form a trading strategy and obtain abnormal returns. I constructed a strategy consisting of a risky asset ans a risk-free asset. The oil price volatility was used to predict the risky asset (stocks). The risk adjusted returns of this portfolio are positive and the investors are willing to pay almost 1% of their returns in order to access the additional information that the oil price volatility offers.Moreover, this research also indicates that oil price variance cannot predict stock market return. The coefficient that describes the effect of this variable on stock returns is insignificant.
This study conducted in US economy using data for the US stock market. It would be interesting to assess the predictive power of oil price volatility on other countries’ stock market returns. In that way, it can be assessed whether high oil price volatility creates uncertainty in different countries and can be used to form a useful trading strategy.
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