Question

Problem Set #2 – Regression Model

The capital asset pricing model (CAPM) provides an alternative measure of risk to the standard deviation of an asset and/or a portfolio of assets. Generally, the rate of return on any investment is measured relative to its opportunity cost, which is the return on a risk-free asset. The resulting difference is called the risk premium, since it is the reward or punishment for making a risky investment.

The CAPM suggests that the risk premium on security j is proportional to the risk premium on the market portfolio. That is, rj – r_f = β_j (r_m – r_f).

where: r_j and r_f are the returns to security j and the risk-free rate, respectively
            r_m is the return on the market portfolio
            β_j is the j^th security's "Beta" value.

Use the Excel dataset capm posted on Canvas to answer the following questions:

a) Convert the Excel dataset into a Stata dataset.

b) Calculate and report the descriptive statistics for each of the firms in the model.

c) Construct a scatterplot for each firm compared to the market.

d) Calculate the correlation coefficient between each firm and the market.

e) Estimate a regression model for each firm to predict its Beta.

f) Write the estimated model in equation form for each firm.

g) Report and interpret the value of r² and r²_adj for each model.

h) Report and interpret the coefficients on β₀ and β₁ for each model.

i) For the Microsoft stock, plot the fitted regression line (with confidence intervals) with the scatterplot in the same graph.

i) Finance theory suggests that the coefficient on β₀ =0 for every stock. Are the results consistent with Finance theory? Why or Why not?

j) Estimate the model for each stock under the assumption that β₀ =0. Do the estimates change very much statistically?

k) Are the coefficients individually significant at the .01 level of significance? How do you know?

l) What do you conclude about the value of Beta compared to the market for each firm? How do you know?

m) Rank the stocks from high to low using each measure of risk.

n) Which stock represents the risker investment under each measure of risk? Why?

o) Which measure of risk do you prefer? Why?

Answer 1

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