Question

You know the following information about the possible return offered by the two stocks, Stock X and Stock Y next year .

scenerio| Probability Return(x) Return Y

recession| 40% -5% -6%

normal | 60%. 10%. 14%

a. Calculate the expected return and variances for stock X, Stock Y

b from risk return point of view , which stock , X or Y is better investment , why?

c what is the correlation coefficient between returns on stock X and stock Y?

d. Calculate the expected returns and standard deviation for a portfolio consisting of 40% stock X and 60% of stock Y

E. IF i investment 80% of my money in this portfolio (40% in stock X and 60% in stock Y) and 20% of money in T-bills which offers a rate of return of 2%. What is the expected return and standard deviation of my investment portfolio ?

Answer 1

a. Expected Return of Stock X =Probability of Recession*Return of Stock X in recession +Probability of Normal*Return of Stock X in normal =40%*-5%+60%*10% =4%
Expected Return of Stock Y =Probability of Recession*Return of Stock Y in recession +Probability of Normal*Return of Stock Y in normal =40%*-6%+60%*14% =6%
Standard Deviation of X =(40%*(-5%-4%)^2+60%*(10%-4%)^2)^0.5 =7.3485% or 7.35%
Standard Deviation of Y =(40%*(-6%-6%)^2+60%*(14%-6%)^2)^0.5 =9.7980% or 9.80%

b. Risk Return ratio of Stock X =standard Deviation/Expected Return =7.3485%/4% =1.84
Risk Return ratio of Stock Y =standard Deviation/Expected Return =9.7980%/6% =1.63
Lower the risk return ratio better is the stock. Stock Y is better.

c. Covariance  of Portfolio =Probability of Recession*(Return of X in Recession-Expected Return of X)*(Return of Y in Recession-Expected Return of Y)+Probability of Normal*(Return of X in Normal -Expected Return of X)*(Return of Y in normal -Expected Return of Y) =40%*(-5%-4%)*(-6%-6%)+60%*(10%-4%)*(14%-6%)=0.0072
Correlation coefficient =Covariance  of Portfolio/(Standard Deviation of X*Standard Deviation of Y) =0.0072/(7.3485%*0.7980%) =1

d. Expected Return in recession =Weight of Stock X*Return of X+weight of Stock Y*Return of Stock Y
=40%*-5%+60%*-6% =-5.60%
Expected Return in Normal =Weight of Stock X*Return of X+weight of Stock Y*Return of Stock Y
=40%*10%+60%*14% =12.40%
Expected Return of Portfolio =40%*-5.60%+60%*12.40% =5.20%
Standard Deviation of Portfolio =(40%*(-5.60%-5.20%)^2+60%*12.40%-5.20%)^2)^0.5 =2.70656% or 2.71%

e. Expected if invested in both portfolio and risk free asset =Weight of Portfolio*Expected Return of Portfolio+Weight of Risk free rate*Expected Return*Risk free rate =80%*5.20%+20%*2% =4.56%

Standard Deviation of Risk free asset =0%
Correlation between portfolio and risk fee asset =0
Standard Deviation of Portfolio and risk free asset =((Weight of Portfolio*Standard Deviation of Portfolio)^2+
(Weight of Portfolio*Standard Deviation of Risk free rate)^2)^0.5 =((80%*2.70656%)^2)^0.5 =2.17%