A Study of Sharpe’s asymmetric beta model


Term Paper, 2008

23 Pages, Grade: 100%


Excerpt

Index

1. Abstract

2. Introduction

3. Summary statistics

4. Data

5. Methodology

6. Results

7. Conclusions

8. References

9. Appendix A

10. Appendix B

A Study of Sharpe’s asymmetric beta model

1. Abstract

This paper presents the classic-static beta values and beta values estimated by an asymmetric beta model. In asymmetric model we have the possibility to estimate the upside and downside betas, while in the static model we are not able to work it out. We will estimate the static and asymmetric betas of two stocks in France Exchange stock market, Michelin and Tf1. So the data consists of daily returns of France Exchange stock market index CAC-40 and the above two stocks , during the period June 2nd of 2000 to May 17th of 2004. Actually this paper examines the estimation of betas under bull and bear market conditions. Asymmetries are of substantial economic importance for an investor who has symmetric beliefs, so he must switch his beliefs in an asymmetry one, where this is necessary.

2. Introduction

The classic-static beta model is probably not reliable, because it assumes that beta and so the stock or asset’s risk follows the same behavior as in the past, which is an unrealistic assumption (Bilbao et al., 2007). Bai and Perron (2003) found that there are strong evidences that in most, but not in all cases, there are asymmetries in betas, indicating that the risk measures can be different vary depending on market conditions. So the risk measure estimation and forecasting can be usually best feasible and reliable, using the asymmetric beta model and not the static. Also Levy (1974) proposed that beta may differ with market condition. This hypothesis was tested by Fabozzi and Francis (1977) using three different definitions for bull and bear markets, or for upside and downside betas. In the section of methodology we will refer the definitions that we will obtain to estimate the asymmetric beta model. Fabozzi and Francis in their study found, in all the three definitions, that the number of stocks with significant differences in bear and bull market betas is not higher than probability would predict. Clinebell et al. (1993) found that there are significant differences between upside and downside betas for the two of the three bull and bear market definitions used. In other study Woodward and Anderson (2003) found that the transition between market conditions is more abrupt than smooth. Bhardwaj and Brooks (1993), found that beta vary between bull and bear market and also allowing beta to differ between these market conditions, beta has a explanatory power. Of course this study was been made for two sub-periods. Roy (1952) and other economists have recognized that investors care and confront with a different way the downside losses than the upside gains. More specifically agents place greater weights on losses in relation with gains in their utility functions. So the agents who are averse to downside losses they demand a greater compensation, with higher expected returns to convince those holding stocks with high downside risk. Other authors as Campbell et al. (2001), found that market volatility increases in down market conditions. In the opposite Duffee (1995), in his study, found that idiosyncratic volatility decreases in down market. All these different results cause beta to have little asymmetry across downside and upside. So Ang and Chen (2001) found that correlations are immune from different volatility between upside and downside markets, so they suggest that correlations are probably able to capture the asymmetry risk than betas do. Ekholm and Wilhelmsson (2004) used data of weekly returns of S&P-100 index and its companies and found that asymmetric betas are less stable over time than static betas, so they propose and recommend the use of classic beta.

We will take two stocks Michelin and TF1. Michelin is one of the world leaders in manufacturing and marketing of tires. TF1 is the leading general television channel in France. The 80.4% of the operation is concentrated on TV channels in France , while at the end of 2007, owned a generalist channel (TF1) and theme-related channels (11 channels; LCI, Eurosport France, etc.). The group is also active in advertising, television shopping, film and audiovisual co-production and publishing of games, magazines, etc (www.euronext.com). In section 1 we present summary statistics for the two stocks to investigate the basic characteristics of the financial time series as negative skewness and leptokurtosis. In section two and three we present the data structure, the methodology and the models that we will use in our analysis. In section four we present the estimation results and we are doing a comparative analysis between static and asymmetric beta.

3. Summary statistics

In this section we present the summary statistics for the two stocks we examine. First we will show that stocks in their levels are not stationary, while the stock returns are stationary. From figure 1, which is a simple line graph, we can clearly see that stock “Michelin” is not stationary in levels, but is stationary in returns as we can conclude by figure 2. In figures 3 and 4 we present the stock levels and stock returns respectively for “TF1”. Once again in figure 1 we can see that “TF1” is not stationary in level, but returns are I(0).

Figure 1. Stock in level of “Michelin”

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Figure 2. Stock returns of “Michelin”

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Figure 3. Stock in level of “TF1”

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Figure 4. Stock returns of “TF1”

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In figure 5 we confirm that there is leptokurtosis but the skewness is positive. It’s already known that if there is a normal probability distribution, then skewness and kurtosis will be 0 and 3 respectively. So we conclude that there is the leptokurtosis phenomenon. The mean returns are very low but positive. In addition Jarque-Bera statistic is very high, indicating that data don’t follow the normal distribution, as P-value is zero. As for the stock “TF1” and figure 6 we can see that there is negative skewness and high kurtosis so we confirm the leptokurtosis existence. Also the mean returns are very low, but negative, relative to “Michelin” where mean returns are positive. Once again the high value of Jarque-Bera indicates the non-normality of the data.

Figure 5. Summary statistics for stock returns of “Michelin”

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Figure 6. Summary statistics for stock returns of “TF1”

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In figure 7 we present a line graph for the Exchange Stock Market index of France in levels, showing clearly that there is trend and actually a decreasing trend with the pass of time indicating once again that it is not stationary. From the other side, the market returns, which are sketched in figure 8, indicate that the market returns are stationary.

Figure 7. Market index “CAC-40”

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Figure 8. Market Returns “CAC-40”

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In table 1 we confirm that the specific financial time series are not stationary in their levels, but returns are stationary. We applied the Dickey – Fuller and KPSS tests of stationarity and we have the same conclusions. We present only the results of Dickey – Fuller test.

TABLE 1 Unit root test

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From figure 9 and Jarque-Bera statistic we conclude that there is non-normality in market returns. Skewness is almost zero, but kurtosis is greater than 3. Also market returns are negative, but are very close to zero.

Figure 9. Summary statistics for France Exchange Stock market index “CAC-40”

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4. Data

The data used are daily and are referred to the returns of the Exchange Stock Market Index of France, which is the index “CAC-40” and the stock returns of two companies, “Michelin” and “TF1”. The time period we analyze is June 2nd of 2000 until May 17th of 2004. So we analyze a sample of data which are referred in the pre-Euro and the post-Euro era.

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Excerpt out of 23 pages

Details

Title
A Study of Sharpe’s asymmetric beta model
Course
Money and Capital Market Analysis
Grade
100%
Author
Year
2008
Pages
23
Catalog Number
V146638
ISBN (eBook)
9783640622504
ISBN (Book)
9783640622993
File size
567 KB
Language
English
Tags
static and asymmetric betas, bull and bear markets, CAC40
Quote paper
Eleftherios Giovanis (Author), 2008, A Study of Sharpe’s asymmetric beta model, Munich, GRIN Verlag, https://www.grin.com/document/146638

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