Capital asset pricing model (CAPM) is a widely accepted, though controversial, theory of asset pricing in the capital market. According to CAPM, the expected return of any asset in the capital market is a linear function of the expected return on the whole market and the expected return of the risk-free rate. Mathematically, the model is stated as per Equation 1:E(Re) = E(RFR) + β *E(Rm – RFR) (1) Where E(Re) is the expected rate of return on a specific asset, E(RFR) is the expected risk-free rate, β is the sensitivity of the stock return with respect to the overall market return, and E(Rm – RFR) is the expected capital market risk premium.Empirical verification of CAPM is done by running a regression model of historical returns of stocks against historical returns of the overall market.In this assignment, your professor will assign you the stock of a publicly-traded company to conduct the following:
- Download the stock’s last 10 years’ monthly price history from yahoo finance or other sources.
- Select a broad stock market index, such as the S&P 500 Index or the Russell 3000 Index, etc., and download its last 10 years of monthly price history.
- Use the adjusted closing prices of the stock and the index and calculate the monthly rate of return of each.
- Consider the stock’s monthly return as the dependent variable and the index’s monthly return as the independent variable and run the following regression model:
Re = α + β*Rm + ε (2)Where Re is the realized monthly rate of return of your stock, Rm is the realized monthly rate of return on the overall capital market, and ε is the error term.
- After estimating the regression coefficients of equation (2) through the ordinary least square (OLS) method, conduct a test of hypothesis and determine if the estimates of α and β are statistically significant at the 5% level and report their t statistics and p values.
- Determine if the F value for the correlation coefficient is statistically significant at the 5% level.
- What is your interpretation of the R-square value? Explain to what extent your regression estimates can predict the future return of your stock against your index’s movements.
- What is the estimate of RFR?
- Calculate the value of the error term for each year and construct the histogram of the error terms.
- Using the Explore feature in SPSS (in Excel: Data Analysis, Regression, Normal Probability Plots), conduct a test for normality of the error terms and exhibit the normality plot.
- Does the result of the test for normality of the error terms affect the validity of your regression model? Explain.
- Present an APA-formatted write-up of your finding in one paragraph.