# CAPM regression

This needs to be done in Excel.

The CAPM states that the excess return on a stock is proportional to the excess return on the market. This implies:

X stock = beta*(X market)

Where X is the excess return = return- (return on risk free asset). One criticism of the CAPM regression we ran in class is that it excludes relevant variables. Some have argued that "surprise" factors impact excess return on stocks. You will explore this issue.

Choose two companies from the CAPM example we did in class. (CAPM - From Class.xls)

(1) Redo the CAPM regression

(2) The attached filed APM.xls contains data on POIL, FRBIND and CPI which are: price of oil, Federal Reserve Board Index of industrial production and Consumer price Index. Calculate the growth rate of these variables. For example:

Growth rate of CPI at t = (CPI at t-CPI at t-1)/CPI at t

Now calculate the "surprise" in these variables for each year. The surprise is calculated as growth rate minus sample mean

(3) Perform a regression of X stock on a constant, X market, and the three surprise variables.

(4) Analyze your results.

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#### Solution Preview

(1) Redo the CAPM regression

<br>we pick up Coned and Delta for this question. As shown in the attached table, we have Xconed and Xciti and the regressions respectively. Because these two stocks both have significantly high t-value of the slope estimate.

<br>Then:

<br>Xdelta = 0.48*Xmkt , and

<br>Xciti = 0.67*Xmkt

<br>

<br>(2) The attached filed APM.xls contains data on POIL, FRBIND and CPI, which are: price of oil, Federal Reserve Board Index of industrial production and Consumer price Index. Calculate the growth rate of these variables. For example:

<br>Growth rate of CPI at t = (CPI at t-CPI at t-1)/CPI at t

<br>Now calculate the "surprise" in these variables for each year. The surprise is calculated as growth ...

#### Solution Summary

Regression Analysis-CAPM-is achieved step by step.

Significance of R Square Statistics in CAPM

Capital Asset Pricing Model (CAPM) is used to calculate the required return from a stock. To calculate the required return from ABC stock, a regression was run between the S&P Index daily retun over risk free rate and ABC daily returns over risk free rate on the historical data for 500 days. The R square value of the regression is 20%. What does this value represent. What does a low value of R square mean. Could you find some possible reasons for low R sqaure. Since the R square value is only 20%, can we conclude CAPM is not a good model to calculate the required rate of return.

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