Question

Stocks A and B have the following probability distributions of expected future returns: Probability (119) (34 ) 0.1 0.5 02 0.1 a. Calculate the expected rate of return, for Stock B (TA1440%.) Do not round intermediate calculations. Round your answer to two decimal places. 16 % b. Calculate the standard deviation of expected returns, or for Stock AO = 19.89%.) Do not round intermediate calculations. Round your answer to two decimal Now calculate the coefficient of variation for Stock B. Do not round Intermediate calculations, Round your answer to two decimal places. Is it possible that most investors might regard Stock B as being less risky than Stock A? 1. Stock B is more highly correlated with the market than A, then it might have a lower beta than Stock A, and hence be less risky in a portfolio sense. IT. IF Stock Bis more highly correlated with the market than A, then it might have the same beta as Stock A, and hence be just as risky in a portfolio sense. III. 1 Stock B is less highly correlated with the market than A then it might have a lower beta than Stock A, and hence be less risky in a portfolio sense TV. IF Stock B is less highly correlated with the market than A, then it might have a higher beta than Stock A, and hence be more risky in a portfolio sense V. If Stock B is more highly correlated with the market than A, then it might have a higher beta than Stock A, and hence be less risky in a portfolio sense. c. Assume the risk-free rate is 2.5%. What are the Sharpe ratios for Stocks A and B? Do not round Intermediate calculations. Round your answers to four decimal places. Stock A: Stock : Are these calculations consistent with the information obtained from the coefficient of variation calculations in Part > 1. In a stand-alone risk sense A is more risky than B. If Stock risky in a portfolio sense is less highly correlated with the market than A, then it might have a lower beta than Stock A

Answer 1

a) Expected Return of B =0.1*-34%+0.1*0%+0.5*18%+0.2*30%+0.1*44% =16%

b) Standard Deviation of A =(0.1*(-11%-14.40%)^2+0.1*(3%-14.40%)^2+0.5*(15%-14.40%)^2+0.2*(20%-14.40%)^2+0.1*(37%-14.40% )^2)^0.5 =11.6207% or 11.62%

Coefficient of Variation = Standard Deviation of B/Expected Return of B =19.88%/16% = 1.24

Option III is correct option.Lower the beta lower is the risk in portfolio sense.

c) Sharpe ratio of A =(Expected Return-Risk Free Rate)/Standard Deviation =(14.40%-2.5%)/11.6207%=1.0240
Sharpe ratio of B =(Expected Return-Risk Free Rate)/Standard Deviation =(16%-2.5%)/19.88%=0.6791

Option IV is correct Option