The following four questions data refer to the two investments characterized in

Question

The following four questions data refer to the two investments characterized in the table below. Portfolio C is a portfolio that is 50% investment in A and 50% investment in B. The returns on A and B have zero correlation. All returns are total annual returns.

Asset A

Asset B

Mean return

.12

.18

Standard deviation of return

.20

.40

Beta

1.5

2.0

SPX return

.10

.10

Riskless return

.02

.02

1)What is the standard deviation of C?

2)What is the beta of C?

3)According to the Sharpe ratio, which of investment A or B performed better over this period?

4)According to (Jensen’s) alpha, which of investment A or B performed better over this period?

5)Suppose you have zero coupon bond with a par value of $1000 and 6 years to maturity. What is it price if its yield is 8%?

6)Approximately what is its price if interest rates rise by 1%?

7)Exactly what is its price if interest rates rise by 1%?

8)Assume you have a preferred stock that pays an annual dividend of $8 beginning in exactly 5 years. What is its price if its yield is 6%?

9)Suppose Neal Inc. has issued a convertible bond at its par value of $1000. The bond pays an annual coupon of 3% while the yield on Neal’s other bonds is 6%. What is the value of this bond’s option to convert?

Asset A

Asset B

Mean return

.12

.18

Standard deviation of return

.20

.40

Beta

1.5

2.0

SPX return

.10

.10

Riskless return

.02

.02

Explanation / Answer

Part 1

Variance = (WA)^2*(STDA)^2 + (WB)^2*(STDB)^2 + + 2*(WA)*(WB)*(STDA)*(STDB)*[Correlation(RA, RB)
]    =+(0.5*0.5*0.2)+(0.5*0.5*0.4)+2*(0.5*0.5*0.2*0.4)=.19 Standard deviation of portfolio C = sqrt(Variance) =sqrt(.19)=43.6%

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