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Homework answers / question archive / QUESTION 5 The table below contains output from a CAPM regression based on weekly data of returns in decimal form for the 2-year period that you have owned this stock
QUESTION 5 The table below contains output from a CAPM regression based on weekly data of returns in decimal form for the 2-year period that you have owned this stock. That is, a return data equal to 0.01 equals 1% return. R-squared of the regression: 0.85 Coeff. t-statistics Intercept 0.001 8.92 Regression coefficient of the independent variable 0.10 12.54 A friend of you is of the opinion that there must be something wrong with the regression since the very high R-squared indicates that most of the risk of this stock is systematic risk and therefore the beta coefficient cannot be as low as estimated. Furthermore, your friend says that the alpha of the regression is large and significant, which would not be the case if the CAPM is the correct model of asset returns. He therefore recommends that you use another asset-pricing model that better captures the variation in stock returns. Provide detailed comments on the correctness of your friend's arguments. (10p)
CAPM i.e. Capital Assets Pricing Model is a model for estimating the expected return of an asset based on its market risk. It is a single index model i.e. it believes that the only variable impacting the expected returns of any assets is its comovement with the market i.e. its market risk which is represented by the Beta. Thus, as per CAPM equation:
Expected Return on Equity = Risk Free Rate + Beta of Stock * Market Risk Premium
Thus, as per CAPM model, there is only and only one reason why market is giving extra return i.e. inherent market risk. If there is any other significant variable which is also explaining the extra variable then we can say that CAPM is not the correct model which can explain the return of that asset. Thus, based on above discussion, the arguement made by friend can be analysed as follows:
1. A very high and significant Alpha of the Stock makes the CAPM model not valid in this stock. This statement is correct as we can see that alpha of weekly returns is 0.1% which is very high and significant also at the same time as we can notice from t - statistic which should be less than 3 if the alpha is not significant. Thus, we can say that this alpha is huge as this is weekly alpha if compounded to annually it would be much bigger and at the same time significant also which raises the concern of validity of CAPM as a model to explaining the returns.
Annual Alpha = (1 + Weekly Alpha)52
Annual Alpha = (1 + 0.1%)52
Annual Alpha = 5.33
Thus, as we can see that Alpha when calculated for annum is as high as 5.33% which is very huge extra return not explained by the CAPM model.
But there is one caveat there. Returns used should be excess weekly returns for both the stocks and market. In case, it is raw returns then some of the alpha is just due to that error. But still alpha makes the CAPM model's validity suspicious.
2. Low Beta and High R2: R2 represents the explanation of the total risk of the stock by the CAPM model. Simply put, it is the segregation of the market and unique risk. Here, market risk is 85% (Value of R2) of the total risk of the stock.
While Beta represents the market risk of the stock i.e. if market moves by 1% by how much is the stock expected to move. A lower beta means lower market risk while a higher number represents higher market risk.
Thus, Beta and R2 are different and it is very much possible for a stock to have the low beta and high R2at the same time. This would be because of the overall lower total risk. If a stock is very less volatile i.e. operating in a defensive industry i.e. Stable industry, operating with less leverage and a really stable company, i.e. a rare gem whose value doesn't change much with the market movements. Although it is very difficult to find, but it can be possible. Thus, based on theoratical side, we can say that this arguement is not correct but to be practical, this arguement is also correct.
Thus, we are truely satisified that there is something wrong with the regression model. There might be some other variables which should be there in the model to get accurate assesment of the model. High R2 can be just because of the collinearity of the variables.