1. Use the following table to answer parts A and B. The risk-free rate is 4%, th
ID: 2801986 • Letter: 1
Question
1. Use the following table to answer parts A and B. The risk-free rate is 4%, the return on the market index is forecast at 14% with a standard deviation of 9%.
A) Use CAPM to calculate the expected/fair return and the alpha for each stock.
B) Would you recommend either of these stocks to an investor with a well-diversified portfolio? Explain.
2. Assume you buy a $1,000 face value bond with 7 years until maturity, a coupon rate of 5% paid semiannually, and a yield to maturity of 8%.
A) What is the price of this bond?
B) Assume that the yield to maturity falls to 7% after one year, and the investor decides to sell the bond. What would be the holding period return for the investor?
Mercury Inc. Electric Co. Forecast return 20% 13% Standard deviation 18% 6% Beta 2.5 0.8Explanation / Answer
.A) Risk free rate=Rf=4%
Return of the market index=Rm=14%
Mercury Inc.
Beta=2.5
Expected or fair return of Mercury Inc. Rs=Rf+Beta*(Rm-Rf)=4+2.5*(14-4)=29%
Alpha of Mercury Inc.:
Return of stock=Rs+Alpha
20=29+Alpha
Alpha =20-29=-9%
Electric Co..
Beta=0.8
Expected or fair return of Electric Co. Rs=Rf+Beta*(Rm-Rf)=4+0.8*(14-4)=12%
Alpha of Electric Co.:
Return of stock=Rs+Alpha
13%=12%+Alpha
Alpha =13-12=1%
B).
Mercury Inc
Electric co.
Market Index
Forecast return
20
13
14
Standard deviation(Risk)
18
6
9
Return/Risk ratio
1.11
2.17
1.56
A well diversified folio will have market return and risk. The return /risk ratio of a well diversified folio will be=1.56
The stock of Electric Co. will have a higher return/risk ratio at 2.17
Hence, investment in Electric Co, is recommended
.2.
.A. Price of the bond =Present Value of cash flow discounted at annually 8% or semiannually4%=0.04(yield to maturity)
Present value (PV) of cash flow=(Cash flow)/((1+0.04)^N)
N=Period of cash flow
Semi annual coupon payment=(5% of 1000)/2=$25
Cash flow and PV of cash flows are given below:
N
A
B=A/(1.04^N)
Semiannual
Cash
PV of cash flow
Period
flow
1
$25
24.03846154
2
$25
23.11390533
3
$25
22.22490897
4
$25
21.37010478
5
$25
20.54817767
6
$25
19.75786314
7
$25
18.99794533
8
$25
18.26725513
9
$25
17.56466839
10
$25
16.88910422
11
$25
16.23952329
12
$25
15.61492624
13
$25
15.01435215
14
$1,025
591.9119599
Total
$ 841.55
Price of bond=$841.55
.B) Price of bond after one year= PV after one year at (7/2)=3.5 % semi annual discount
Cash flow and PV of cash flow after one year is given below:
N
A
B=A/(1.035^N)
Semiannual
Cash
PV of cash flow
Period
flow
1
$25
24.15458937
2
$25
23.33776751
3
$25
22.54856764
4
$25
21.78605569
5
$25
21.04932917
6
$25
20.33751611
7
$25
19.64977402
8
$25
18.98528891
9
$25
18.3432743
10
$25
17.72297034
11
$25
17.12364284
12
$1,025
678.3278807
Total
$ 903.37
Price of the bond after one year=$903.37
Holding Period Return=(903.37/841.55)-1=0.0735
Holding Period Return in percent=7.35%
Mercury Inc
Electric co.
Market Index
Forecast return
20
13
14
Standard deviation(Risk)
18
6
9
Return/Risk ratio
1.11
2.17
1.56
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