A Sensitivity Analysis between Common Risk Factors and Exchange Traded Funds

Transcription

1 A Sensitivity Analysis between Common Risk Factors and Exchange Traded Funds Tahura Pervin Dept. of Humanities and Social Sciences, Dhaka University of Engineering & Technology (DUET), Gazipur, Bangladesh ABSTRACT This paper investigates the applicability of the Augmented Fama and French (FF) three-factor model to size and Book-to-Market (BM) characterized-sorted portfolios including two other macro risk factors; crude oil price and VIX (VOLATILITY S&P 500) from the Exchange Traded Funds over a recent daily data set from July 01, 2007 to December 31, The new results are derived from Ordinary Least Square (OLS) methods, 2 Stage Least Sqaure (2SLS) and the Generalized Method of Moments (GMM). There is evidence that the risk premium is positively and the value effects are negatively related to the ETF returns whereas the other factors are not statistically significant. The 2SLS and GMM approach suggest that it is difficult to find a general relationship between ETFs returns and macro risk factors. 1. INTRODUCTION The investors who want to invest in stock exchange should decide carefully to maximize the profits. There are many financial instruments by which one could decide to do so. Exchange traded funds (ETF) is one of them. An exchange traded fund (ETF) is an investment fund, traded like a stock in the stock market representing a basket of underlying stocks that can reflect one specified or portfolio (gold ETF) index. Most ETFs track an index, like S&P 500 or MSCI EFRI. After the introduction of ETF in 1993 in US, it become most attractive investment instruments because of their low costs, tax efficiency, and flexibility of trading. The SPDR S&P 500, symbol SPY, was the first ETF in It tracks the S&P 500 index. In 2004, there were 150 ETFs; by the end of the February 2011, the number of ETFs rose to over 1000 (for details, see SPDR). To make more profits, the investors have to consider all important factors related to the ETF that effect to return from her investment in the future. Considering these important factors needs a lot of information for assessment, stipulation and offering suitable prices in stock trading. That s why, modeling is very essential device to evaluate stock prices and help the investors to make their plans and decide in investment correctly and efficiently. As we see that ETFs are rapid growing and popular financial instruments, in this paper, we are interested to assess the FTF s returns by estimating a model for returns on ETFs with reference to common risk factors. We examine empirically the relationships between the ETF returns and macro risk factors. The organization of the rest of the paper is as follows: Section 2 explains the literature review, section 3 explains the methodology, section 4 refers the data and its sources, section 5 explains the result analysis and finally section 6 concludes the study. 2. LITERATURE REVIEW The Capital Asset Pricing Model (CAPM) is the most widely recognized explanation of stock prices and expected return. The CAPM probably builds on the model of portfolio theory base on the mean-variance optimization proposed by Harry Markowitz in 1959 and was developed and improved continuously across the time. It was started with [1-3]. The CAPM shows the relationship between the average return of a stock and market risk factor E( Ri ) Rf i E( Rm ) Rf ui, where ER ( i ) the expected is return of any security i, R f is the risk free rate, ER ( m) is the expected return of the market portfolio, is the sensitivity of the asset returns to i market returns E( R ) R is excess return of the market m f portfolio and u i is the residual term of any security i. The CAPM requires a large number of assumptions, including those initially suggested by Harry Markowitz when he developed the mean-variance optimization. The Arbitrage Pricing Theory (APT) introduced in [4] is an alternative to the CAPM and requires less assumption than the CAPM does [5]. The APT allows for many risk factors in addition to the excess returns of market portfolio. (1) 30

2 During the 1980 s several studies had identified additional common risk factors to the excess returns of market portfolio. Variables that have no special criteria in asset pricing theory were shown to have a loyal power for the explanation of cross section of stock returns (these variables are referred to as anomalies in [6-7]. In [8], it is found that low earnings-price ratios (E/P) stocks can help to explain higher returns of the stocks while high E/P stocks can help to explain lower returns. In [9], it is shown that stocks with abnormally low long term returns (average returns in three years) experience abnormally high long term future returns (average returns in the next three years) and vice versa. In [10], it is found that a positive relationship between the average return and the ratio of a firm s book value to market equity (BE/ME). In [11], it is found strong positive relationship between average stock returns and BE/ME and cash flow/price ratio (C/P). These findings go beyond standard CAPM or APT. In [12], it is found that average stock returns in the US market shows little statistical relation to the sensitivity (β) of the original CAPM model. Instead they find that the market β, firm size (ME), (E/P), financial leverage and BE/ME explain jointly average returns of the stock traded in the New York Stock Exchange (NYSE), American Stock Exchange (AMEX), and National Association of Securities Dealers Automated Quotations (NASDAQ). In particular, they find that the ME and BE/ME can capture the cross sectional variation in average stock returns. Given the literature there is little prior study as to whether size and value premiums are related in ETFs. Markov regime-switching framework on selected investment instruments consist of the nine sector exchange traded funds (ETFs) is used in [13]. They evaluate the in-sample and out-of-sample. They find that the former generally outperforms the latter. I further provide empirical evidence on a different data set and a more recent time period than in the past study to explain the common risk factors related to the investment in ETF s. In this paper, I want to examine the relationships between the ETF returns and the macro risk factors of the FF models including the crude oil price and VIX with the help of instrumental variable approach, applying the 2Stage Least Square (2SLS) and Generalized Methods of Moments (GMM). 3. RESEARCH METHODOLOGY The fundamental idea of the CAPM model is defined in [6], that returns depend on the risk and thus lead them to create the three-factor model in which they included a multidimensional risk, i.e. in addition to the market risk, they introduced two other dimensions of risk: the risk of investing in small companies and the risk of investing in the companies in which the market equity is low compared to the book equity. The Fama-French Three Factor Model is as follows: E( Ri ) Rf i E( Rm ) Rf ie( SMB) ie( HML) ui, (2) 31 where SMB (Small Minus Big) is the difference between the returns on the portfolios of small stocks and the portfolios of big stocks which is the measure of risk associated with investing in small companies and HML (High Minus Low) is the difference between the returns on the portfolios of high BE/ME stocks and the returns on the portfolios of low BE/ME stocks which is the measure of risk associated with investing in the undervalued companies. And the augmented FF model can be written as: E( Rt ) 0 1 E( Rm ) Rf 2SMB 3HML 4Ot V u ( 3) 5 t t, where O t is the crude oil price and Vt is weighted blend of implied volatility estimates for options on S&P 500. The appropriate testing of Augmented Fama and French Model with set of data for ETF s in the NASDAQ and I use the standard multivariate regression method. Thus the equation (3) can be written as: R X U, (4) where R is N 1, X is N k, is k 1 and U is N 1 matrix. After estimating the equation 4, we check whether the coefficient of the risk factors are statistically significant or not by using the p value statistic. We suspect that there might have an endogenous relationships in all five explanatory variables. Then we will use the log of crude oil price and log of VIX as instrument variables respectively to estimate the 2 Stage Least Square (2SLS) and Generalized Method of Moment (GMM). GMM is a very powerful and general estimation method, which encompasses practically all the parametric estimation techniques used in econometrics. 4. DATA SOURCES SPDR funds are shares of a family of ETFs which is managed by State Street Global Advisors (SSgA). Informally, they are also known as Spyders or Spiders. SPDR is a trademark of Standard and Poor's Financial Services LLC, a subsidiary of McGraw-Hill Companies, Inc. (Wikipedia). The name is an acronym for the first member of the family, Standard & Poor s Depository Receipts (NYSE:SPY), the biggest ETF in US. We consider the NYSE: SPY as the representative of the ETFs in this study. Daily price indices on SPY from July 1, 2007 to December 31, 2010 are retrieved from SPDR website. The SPDR ETF return is the log-difference of ETF s prices. MKT, SMB, HML are retrieved from the Fema & French data Library. Crude oil price are retrieved from US Energy and Information Administration, VIX are retrieved from yahoo finance website for the same period of time. 5. MODEL ESTIMATION AND RESULTS ANALYSIS 5.1 Descriptive Statistics The descriptive statistics of the returns of ETF, SMB, HML and the risk premium, crude oil price and VIX can be

3 summarized by Table-1. The mean return of SPY is where the variation is from to The correlation matrix of the five macro factors is given in Table-2. The risk premium and SMB highest correlation (0.5305). The VIX and crude oil price have lowest correlation ( ). These highest and lowest correlations further suggest that the investment in a well diversified portfolio based on different macro risk factors can substantially reduce the investment risk. Table-1: Descriptive Statistics Variable No. of Observation Mean Standard Deviation Min. Max. Skewness Ex. Kurtosis SPY Rm-Rf SMB HML O t Vt Table-2: Correlation Matrix Rm-Rf SMB HML VIX Oil Rm-Rf SMB HML VIX Oil 5.2 Estimation and Result Analysis The results in Table-3 are obtained from the OLS estimation of the augmented FF models which show that both the market risk factor (risk premium) and the HML factor are significantly related to the SPY returns and these are statistically significant. The risk premium is positively related to the SPY returns which is similar to the CAPM [1] and Fama French Three factor Model estimated in the cross stock returns and HML is negatively related to the SPY returns. The size effects, crude oil price and VIX are not statistically significant to the ETF returns. We suspect that there might have endogenous problems caused by these five factors in the augmented FF model. That s why we introduce the log of the daily crude oil price and log of daily price index of VIX as instrument for these two variables and lag of order 1 for the risk premium, SMB, HML. Then we run the 2 Stage Least Square (2SLS) model to estimate the ETF returns on the instruments. The results are given in Table-4. In the 2SLS model, following the conventional F-statistic approach for testing that whether the instrument are weak or not, the F-statistic is which is lower than 10 which mean that these instruments are weak. But if we consider only one instrument variable, suspecting there is an endogenous problems caused by only one variable, following the conventional approach then we see the instrument variable for each explanatory variable is not a weak instrument. Hausman test statistic also suggests that there is an evidence of endogeniety. But the coefficients are not statistically significant. Then we run Generalized Methods of Moments (GMM) to check the relationships. Table-5 shows the results for GMM estimation procedures of ETF returns by using the Augmented FF three factor model. The Wald statistic suggests that the model is exactly identified. None coefficient from the Augmented FF three factor model are statistically significant. 32

4 Table-3: OLS, using observations Coefficient Std. Error t-ratio p-value α α < * α α * α e e α e e R squared Adjusted R-squared * 1% level of significance Table-4: TSLS, using observations (n = 889) Instrumented: V1 V2 V3 VIX Instruments: const LV1 LV2 LV3 V4 V5 Coefficient Std. Error z p-value α α α α α α R-squared Adjusted R-squared F(5, 883) P-value(F) Table 5: 1-step GMM, using observations (n = 889) Instrumented: V1 V2 V3 VIX OIL Instruments: const LV1 LV2 LV3 LVIX V5 Coefficient Std. Error z p-value α α α α α e α e GMM criterion: Q = e-029 (TQ = 6.26e-026) 33

5 6. CONCLUSION This study incorporates two macro risk factors; VIX Volatility S & P 500 and Crude oil in the Fame French three factor model for explaining the ETF returns. From the basic OLS approach, there is a significant relationship between the ETFs returns and risk premium and value effect. The risk premium is positively related to the ETFs return which is almost similar to the original FF three factor model and the value effect of the market is negatively related to the ETF returns. Suspecting there is endogenous problem in the Augmented FF model, applying the 2SLS and GMM model suggest that the style and macro risk factors are not significantly related to the ETF returns. The results from IV techniques (2SLS, GMM) imply that it is not possible to make a general statement about the relationships between the ETF returns and macro risk factors. REFERENCES [1] W. F. Sharpe, Capital Asset Prices: A theory of market equilibrium under condition of risk, Journal of Finance, Vol. 19, pp , [2] J. Lintner, Security prices, risk and maximal gains from diversification. Journal of Finance, Vol. 20, pp , [3] J. Mossin, Equilibrium in a capital asset market, Econometrica 34, pp , [4] S. Ross, The arbitrage pricing theory of capital asset pricing, Journal of Economic Theory, Vol. 13, pp , [5] W. F. Sharple, G. J. Alexander, V. B. Jeffery, D. J. Flower, and D. L. Domain, Investment, Third Canadian Edition, Princeton Hall Canada, [6] E. F. Fama, and K. R. French, Common risk factors in the returns on stocks and bonds, Journal of Financial Economics, Vol.33, pp. 3 56, [7] E. F. Fama, and K. R. French, Multifactor explanations of asset pricing anomalies, Journal of Finance, Vol. 51, pp , [8] S. Basu, The relationship between earnings yield, market value, and return for NYSE common stocks, Journal of Financial Economics, Vol. 12, pp , [9] W. DeBondt and R. H. Thaler, Does the stock market overreact? Journal of Finance, Vol. 40, pp , [10] B. K. Rosenberg, B. K. Reid, and R. Lanstein, Persuasive evidence of market inefficiency, Journal of Portfolio Management, Vol. 11, pp. 9-17, [11] J. Lakonishok, A. Shleifer, and R. W. Vishny, Contrarian investment, extrapolation, and risk, Journal of Finance, Vol. 49, pp , [12] E. F. Fama and K. R. French, The cross-section of expected stock returns, Journal of Finance, Vol.47, pp , [13] M. Ying, X. Kuan, and Z. Yonggan, A portfolio optimization model with regime-switching risk factors for select sector exchange traded funds, Working Paper, Department of Economics and School of Business Administration, Dalhousie University, Appendix: Correlation coefficients, using the observations % critical value (two-tailed) = for n = 890 V1 V2 V3 VIX Oil V V V VIX Oil 34

6 Model 1: OLS, using observations Coefficient Std. Error t-ratio p-value const V < * V V * VIX e e Oil e e * 1% level of significance Mean dependent var S.D. dependent var Sum squared resid S.E. of regression R-squared Adjusted R-squared F(5, 884) P-value(F) 4.0e-197 Log-likelihood Akaike criterion Schwarz criterion Hannan-Quinn Model 2: TSLS, using observations (n = 889) Instrumented: V1 V2 V3 VIX Instruments: const LV1 LV2 LV3 V4 V5 const V V V VIX Oil Mean dependent var S.D. dependent var Sum squared resid S.E. of regression R-squared Adjusted R-squared F(5, 883) P-value(F) Log-likelihood Akaike criterion Schwarz criterion Hannan-Quinn Hausman test - Null hypothesis: OLS estimates are consistent Asymptotic test statistic: Chi-square(4) = with p-value = e-016 Weak instrument test - Cragg-Donald minimum eigenvalue =

7 Model 3: 1-step GMM, using observations (n = 889) Instrumented: V1 V2 V3 VIX OIL Instruments: const LV1 LV2 LV3 LVIX V5 Coefficient Std. Error z p-value const V V V VIX e OIL e Mean dependent var , S.D. dependent var GMM criterion: Q = e-029 (TQ = 6.26e-026) 36