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

Answer 4)

We have been given:

	Expected Return	Beta
Stock 1 (I)	25%	2
Risk Free Asset (T)	6%	0

a) Expected return of portfolio = (Weight of Stock I * Return of Stock I) + (Weight of Risk Free Asset T * Return of Risk free asset T)

Similarly, Beta of the portfolio will be the weighted average of beat of individual assets.

Beta of portfolio = (Weight of Stock I * Beta of Stock I) + (Weight of Risk Free Asset T * Beta of Risk free asset T)

Using this, We can construct following table:

Weight of I	Weight of T	Expected Return of portfolio	Beta of Portfolio
0%	100%	6.00%	0.00
25%	75%	10.75%	0.50
75%	25%	20.25%	1.50
100%	0%	25.00%	2.00
125%	-25%	29.75%	2.50
150%	-50%	34.50%	3.00

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b) Reward to risk Ratio = ( Expected Return - Risk Free return ) / beta

Putting values:

Reward to risk Ratio = ( 25% - 6%) / 2 = 9.5%

Now, using SML we need to calculate the market risk premium.

If Reward to risk ratio for Stock I < Market risk premium, then

the stock is under-valued in the market.

Else

Stock is over-valued

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c)

	Expected Return	Beta
Risk Free Asset (T)	6%	0
Stock 2 (J)	20%	1.7

Expected return of portfolio = (Weight of Stock J * Return of Stock J) + (Weight of Risk Free Asset T * Return of Risk free asset T)

Similarly, Beta of the portfolio will be the weighted average of beat of individual assets.

Beta of portfolio = (Weight of Stock J * Beta of Stock J) + (Weight of Risk Free Asset T * Beta of Risk free asset T)

Using this, We can construct following table:

Weight of J	Weight of T	Expected Return of portfolio	Beta of Portfolio
0%	100%	6.00%	0.00
25%	75%	9.50%	0.43
75%	25%	16.50%	1.28
100%	0%	20.00%	1.70
125%	-25%	23.50%	2.13
150%	-50%	27.00%	2.55

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d)

Reward to risk Ratio = ( Expected Return - Risk Free return ) / beta

Putting values:

Reward to risk Ratio = ( 20% - 6%) / 1.7 = 8.235%

Now, using SML we need to calculate the market risk premium.

If Reward to risk ratio for Stock I < Market risk premium, then

the stock is under-valued in the market.

Else

Stock is over-valued