Question

The risk-free interest rate is 4.0%. The market risk premium or MRP is 6%. The market index has a standard deviation of 20%. Habanero common stock has a standard deviation of 40% and a correlation coefficient of 0.40 with the market portfolio. Calculate the equity Beta and the required return for Habanero’s stock.

Answer 1

Given:

Risk-free interest rate = 4%.
The market risk premium or MRP =  6%
Standard deviation of Market index = 20%.
Standard deviation of stock = 40%
Correlation coefficient of stock & market = 0.40

Step 1 : Calculate Covariance of stock & market

where, r(s,m) = correlation coefficient of stock & market
= Standard deviation of stock
= Standard deviation of Market index

Cov(s,m) = 0.40 * 0.40 * 0.20

Cov(s,m) = 0.032

Step 2 : Calculate Beta of stock

Where, Cov(s,m) = Covariance of stock & market
= Standard deviation of Market index

= 0.032 / 0.20^2

= 0.032 / 0.04

= 0.8

Equity Beta = 0.8

Step 3 : Calculate required return of stock

Rs = Rf - (Rm-Rf)*
where Rf = Risk-free interest rate
Rm - Rf = market risk premium
= beta of stock

Rs = 4% + 6% * 0.8

Rs = 4% + 4.8 %

Rs = 8.8%

Required return for Habanero’s stock = 8.8%