Question

1. A stock has n HPR of 15%. The stock's beta is 0.76. The risk-free rate is 2% and the market risk premium is 6.98%.  Would you buy it or short it? If so, how much will you gain? Answer as a percent. Show work.

2.  

Given the data below, what is the risk premium on the stock?

Beta: 0.89

Market risk premium: 5

Risk-free rate: 1.5%

Answer as a percent. Show work.

Answer 1

Answer 1) According to the CAPM, the required rate of return is calculated as:

Cost of equity (Ke) = Rf + Beta * (Rm - Rf)

Rf = Risk free rate = 2%

Rm - Rf = Market risk premium = 6.98%

Beta = 0.76

Hence, cost of equity (Ke) = 2% + 0.76*6.98%

= 2% + 5.3048%

= 7.3048%

The Holding period return (HPR) for the stock = 15%

Since, the Holding period return (HPR) for the stock is greater than the cost of equity, thus, the stock is currently overvalued.

Let Stock price be 100

Required return as per the CAPM model taking into account the systematic risk = 7.3048%

Thus, the stock price should be 100*(1+7.3048%) = 107.3048

But as per the holding period return of 15%, the stock price is 100*(1+15%)

= 100*1.15 = 115

Thus, the stock is overvalued and hence, should be sold. Thus, the recommendation is 'Short' the stock.

Profit earned = (115-107.3048)/107.3048 = 7.17%

Answer 2) Beta: 0.89

Market risk premium (Rm -Rf) : 5%

Risk-free rate: 1.5%

According to the CAPM, the required rate of return is calculated as:

Cost of equity (Ke) = Rf + Beta * (Rm - Rf)

Risk Premium on the stock = Ke - Rf

= Beta*(Rm - Rf)

= 0.89*(5%) = 4.45%