Question

The beta of four stocks-----​G, ​H, I, and J----are 0.47​, 0.71​, 1.19​, and 1.55​, respectively and the beta of portfolio 1 is 0.98​, the beta of portfolio 2 is 0.82​, and the beta of portfolio 3 is 1.13. What are the expected returns of each of the four individual assets and the three portfolios if the current SML is plotted with an intercept of 3.0​% ​(risk-free rate) and a market premium of 9.5​% ​(slope of the​ line)? What is the expected return of stock​ G?

Answer 1

As per CAPM model, the expected return can be calculated by the following equation:

Expected return = Risk free rate + Beta * ( Market return - Risk free rate)

Here, Market premium = Market return - Risk free rate

In our question, market premium is given, so we will further reduce the above equation to below:

Expected return = Risk free rate + beta * Market premium

Now we will calculate the expected return of stocks by putting their betas in the above equation as per below:

Expected return of stock G:

Risk free rate = 3%, Beta = 0.47, risk premium = 9.5%

Expected return = Risk free rate + beta * Market premium

Expected return = 3% + 0.47 (9.5%)

Expected return = 3% + 4.465% = 7.765%

Expected return of stock H:

Risk free rate = 3%, Beta = 0.71, risk premium = 9.5%

Expected return = Risk free rate + beta * Market premium

Expected return = 3% + 0.71 (9.5%)

Expected return = 3% + 6.745% = 9.745%

Expected return of stock I:

Risk free rate = 3%, Beta = 1.19, risk premium = 9.5%

Expected return = Risk free rate + beta * Market premium

Expected return = 3% + 1.19 (9.5%)

Expected return = 3% + 11.305% = 14.305%

Expected return of stock J:

Risk free rate = 3%, Beta = 1.55, risk premium = 9.5%

Expected return = Risk free rate + beta * Market premium

Expected return = 3% + 1.55 (9.5%)

Expected return = 3% + 14.725% = 17.725%

Now we will calculate the expected return of portfolio by putting their betas in the above equation as per below:

Expected return of portfolio 1:

Risk free rate = 3%, Beta = 0.98, risk premium = 9.5%

Expected return = Risk free rate + beta * Market premium

Expected return = 3% + 0.98 (9.5%)

Expected return = 3% + 9.31% = 12.31%

Expected return of portfolio 2:

Risk free rate = 3%, Beta = 0.82, risk premium = 9.5%

Expected return = Risk free rate + beta * Market premium

Expected return = 3% + 0.82 (9.5%)

Expected return = 3% + 7.79% = 10.79%

Expected return of portfolio 3:

Risk free rate = 3%, Beta = 1.13, risk premium = 9.5%

Expected return = Risk free rate + beta * Market premium

Expected return = 3% + 1.13 (9.5%)

Expected return = 3% + 10.735% = 13.735%