Question

Consider the following information:

Consider the following table, which gives a security analyst's expected return on two stocks for two particular market returns:

Market Return		Aggressive Stock		Defensive Stock
6	%	2.8	%	4.6	%
15		28		10

a. What are the betas of the two stocks? (Round your answers to 2 decimal places.)

b. What is the expected rate of return on each stock if the market return is equally likely to be 6% or 15%? (Round your answers to 2 decimal places.)


c. If the T-bill rate is 7%, and the market return is equally likely to be 6% or 15%, what are the alphas of the two stocks? (Negative values should be indicated by a minus sign. Do not round intermediate calculations. Round your answers to 2 decimal places.)

a. Calculate the Sharpe ratios for the market portfolio and portfolio A. (Round your answers to 2 decimal places.)

b. If the simple CAPM is valid, is the above situation possible?

• Yes

• No

Answer 1

a. Beta of aggressive Stock =Change in return of Stock/Change in market return =(28%-2.8%)/(15%-6%) =2.8
Beta of defensive Stock =Change in return of Stock/Change in market return =(10%-4.6%)/(15%-6%) =0.6

.b. Expected Return of aggressive of Stock =(2.8%+28%)/2 =15.4%
Expected Return of defensive of Stock =(4.6+10%)/2 =7.3%

c.Average Market Return =(6%+15%)/2 =10.5%  
Required Rate using CAPM =Risk free Rate+Beta*(Average Market Return-Risk free rate) =7%+2.8*(10.5%-7%) =16.8%
Alpha =Expected Return- Required Rate=15.4%-16.8% =-1.40%

Required Rate using CAPM =Risk free Rate+Beta*(Average Market Return-Risk free rate) =7%+0.6*(10.5%-7%) =9.1%%
Alpha =Expected Return- Required Rate=7.3%-9.1% =-1.80%