Question

Could someone please provide the answers to f) & g) of the below question?

Suppose we have one risky asset Stock I and a risk-free asset. Stock I has an expected return of 25% and a beta of 2. The risk-free asset’s return is 6%.

a. Calculate the expected returns and betas on portfolios with x% invested in Stock I and the rest invested in the risk-free asset, where x% = 0%, 25%, 75%, 100%, 125%, and 150%.

b. What reward-to-risk ratio does Stock I offer? How do you interpret this ratio?

c. Suppose we have a second risky asset, Stock J. Stock J has an expected return of 20% and a beta of 1.7. Calculate the expected returns and betas on portfolios with x% invested in Stock J and the rest invested in the risk-free asset, where x% = 0%, 25%, 75%, 100%, 125%, and 150%.

d. What reward-to-risk ratio does Stock J offer? How do you interpret this ratio?

e. Plot the portfolio betas against the portfolio expected returns for Stock I on a graph, and link all the points together with a line. Then plot the portfolio betas against the portfolio expected returns for Stock J on the same graph, and link all these points together with another line.

f. Use the graph in part (e) above, together with your answers to parts (b) and (d) above to explain why Stock J is an inferior investment to Stock I.

g. Can a situation in which one stock is inferior to another stock persist in a well organized, active market? Why or why not?

Answer 1

a) calculate the expected return of portfoio:

1) 0% in stock x and 100% in risk free asset

return= 6% beta is zero

2)25% in stock i

=0.25*0.25( 25% of the expected return of 25%)

=6.25+ 4.5( 0.75% *6)

=10.75 beta is 1.5

3) 0.75*0.25= 18.75 + 1.5

=20.25

4) 25% ( 100% allocation to stock i) beta is 2

5) 125% *25 -(25%6)

=31.25 - 1.5

=29.75 beta is 2.5

6)37.5 - 0.5*6

=37.5-3

=34.5 beta is 3

b) reward to risk ratio: (return on the stock i-risk free rate)/beta of the stcok

= (25-6)/2

=9.5

it means for very on eunit of risk the perosn investing in stock i will get 9.5 % times of return.

c 1) 0% invested in stock j

= return on the prtfolio will be equal to the risk free rate= 6% beta is 0

2) 25% invested in stock j and 75% to the risk free asset:=11 beta is 4.25

3) 75 percent invested in stock j and 25 % in risk free asset

=15+ 1.5=16.5 beta is 1,275

4) 20% return and 1.7 beta

5) 25 -1.5 =23.5 beta is 2.125

6) 30-3% over allocation to stock j so we are selling the risk free asset by 50% beta is 2.55

=27% and beta is 2.55

d) the reward to risk ratio is 11.176 (25-6)/1.7

which is higher than stock i

g) yes it can exists.

because in active markets we are continuosly looking for stocks which are undervalued so that we can buy them at at a lower price amd later sell them at a higher price and book profits.

traders are constanly on the look out to generating alphas on their trade.