Question

PLEASE ANSWER F&G :) THANK YOU!!

4.    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. (This can be done easily with the charting function in Microsoft Excel.)   

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

Sol: (f)

		Stock I
Stock I weight(wi)	Rf (wf)	Bp=wi*Be+wf*Bf	Rp=wi*re+wf*rf
0%	100.00%	1	6.00%
25%	75.00%	1.25	10.75%
75%	25.00%	1.75	20.25%
100%	0.00%	2	25.00%
125%	0%	2.5	31.25%
150%	0%	3	37.50%

		Stock J
Stock J weight(wi)	Rf (wf)	Bp=wi*Be+wf*Bf	Rp=wi*re+wf*rf
0%	100.00%	1	6.00%
25%	75.00%	1.175	9.50%
75%	25.00%	1.525	16.50%
100%	0.00%	1.7	20.00%
125%	0%	2.125	25.00%
150%	0%	2.55	30.00%

The Expected return for Stock I is higher than the expected return of Stock J hence Stock I for same amount of risk is higher hence it is a better investment.

b)Yes in case of mutual funds stocks inferior to other persists depends on the sector you choose.Lets suppose a stock is performing lower than other stock in terms of return an investor is expecting but is diversifying the overall portfolio risk to a larger extent. Since these returns were subjected to market risks any issues in the sector having higher return stocks deviates other sector stocks can balance it an their net effect would be zero or positive. Hence an inferior stocks can exist in a well organized market.