CAPM Solved Questions with Worksheet

Q1. A stock is part of the Euronext Paris. An analyst downloads monthly returns of the stock and the index for past 2 years and performs regression analysis. The equation is given below.

X= is the regressor or predictor variable (index) and y is the response variable (stock).

y = β0 + β1 X +ε

a. What’s is beta of the stock?
b. Which variable would you use to understand the systematic risk and unsystematic risk?

Q2. You have two assets i.e. two securities A and B. Last two years data for the two stocks are given below. A portfolio has 40% of component A and 60% of component B.

a. What is the expected return and standard deviation of the portfolio?
b. Ignoring risk free return, which security is more efficient?
c. If risk free rate is 3%, what is the risk adjusted return of the two securities.
d. What will be weightage of the securities for the most efficient portfolio i.e. highest expected return/ portfolio standard deviation.

Answers 

1. a. β1; b. ε β1​X represents systematic risk, and $ϵ$ represents unsystematic risk. 
2. a. 15.74%, 10.40%; b. Better expected return for unit of risk c. If risk free rate is 3%, what is the risk adjusted return of the two securities (0.28, 0.45).  Use Sharpe Ratio for this, d. A 0.39, B 0.61