Question

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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

First lets look at the following table:

	Stock I	Stock J	Risk Free asset
Expected return	25%	20%	6%
Beta	2	1.7	0
Sharpe Ratio	0.095	0.082352941
Weights	Portfolio returns for Stock I + Riskfree Asset	Portfolio returns for Stock J + Riskfree Asset	Portfolio betas for Stock I + Riskfree Asset	Portfolio betas for Stock I + Riskfree Asset
0%	6.00%	6.00%	0.00	0.00
25%	10.75%	9.50%	0.50	0.43
75%	20.25%	16.50%	1.50	1.28
100%	25.00%	20.00%	2.00	1.70
125%	29.75%	23.50%	2.50	2.13
150%	34.50%	27.00%	3.00	2.55

• Formula for portfolio return =
• Formula for portfolio beta=
• 
• Beta of risk free asset = 0 as there is no risk
• 

Answers:

Part a) for different value of weights, we have calculated portfolio returns in the above table

Part b) reward to risk ratio is the sharpe ratio of 0.095 it is a measure of the risk adjusted return that is how much return does the stock provide as compared to the amount of risk it entails when compared to a riskfree asset. We can say that for each unit of beta it provides 9.5% of return

Part c) for different value of weights, we have calculated portfolio returns in the above table

Part d) reward to risk ratio is the sharpe ratio of 0.082352941 it is a measure of the risk adjusted return that is how much return does the stock provide as compared to the amount of risk it entails when compared to a riskfree asset. We can say that for each unit of beta it provides 8.23% of return rounded to 2 decimal places

Part e)

Part f) as we can see from the above graph, stock J is always below stock I and this is so because it has a lower sharpe ratio which is a measure of the risk adjusted return. Therefore we can clearly say that stock J provides lower return for the amount of risk it entails as compared to stock I. This is the reason why stock J is inferior to stock I