Question

4) The stock of Ralph's Restaurants has a standard deviation of 70% and has a correlation with the market of 0.40. The expected return for the market is 13% and it has a standard deviation of 20%. Currently the risk-free rate of return is 5%. 4a. What is the beta for Ralph's Restaurants? 4b. What is the required return for Ralph's Restaurants? 4c. What is the expected return for Ralph's restaurants in equilibrium?

Answer 1

1. Beta of security = {Covariance of (Stock, Market)}/(std deviation of mkt)^2

2. Covariance of (Stock, Market) = Correlation( Stock,Market) * Std deviation of stoc* Std deviation of market.

3. As per above formuleas Covariance of (Ralpha, Market) = 0.4*0.7* 0.2 = 0.056

And from 1 and 3 and given info in the question, Beta of Ralpha = 0.056/ (0.2)^2 = 1.4

a) Beta of Ralpha= 1.4

b) Required return of ralpha = Rf + B(Rm- Rf) = 0.05+ 1.4(0.13-0.05) = 0.162 = 16.2%

c) In Equilibrium, Required Return is same as Expected Return, Hence Expected Return on Ralpha in Equilibrium is 16.2%