You have been provided the following data on the securities of three firms and t
ID: 2620334 • Letter: Y
Question
You have been provided the following data on the securities of three firms and the market:
Security
E[Rj]
sj
rjM
bj
Firm A
0.13
.12
?
.90
Firm B
0.16
?
0.40
1.10
Firm C
0.25
0.24
0.75
?
Market
0.15
0.10
1
1
Risk-free
0.05
0
0
0
Assume the CAPM holds true.
Fill in the missing values in the table.
0.9 = (rjM)(0.12) / 0.10
ri,m= .75
bj = (rjM)(sj) / sm
= .4 (sj) / .10
sj) = .275
bj= (rjM)(sj) / sm
= (0.75)(0.24) / 0.10= 1.8
What is your investment recommendation on each asset? Buy or sell?
E(r) = fr + b[EMR – rf]
Firm A: 0.05 + 0.9(0.15 – 0.05) = 0.14
Firm B: 0.05 + 1.1(0.15 – 0.05)= .16
Firm C: 0.05 + 1.8(0.15 – 0.05) = 0.23
Firm A is the only underpriced stock so I would buy firm A.
Suppose that you are currently holding a portfolio consisting of Firm B only. If you increase your portfolio weight on Firm B by 0.2 (or 20%) and borrow the needed money at the risk-free rate, what will be the new standard deviation of your portfolio?
Security
E[Rj]
sj
rjM
bj
Firm A
0.13
.12
?
.90
Firm B
0.16
?
0.40
1.10
Firm C
0.25
0.24
0.75
?
Market
0.15
0.10
1
1
Risk-free
0.05
0
0
0
Explanation / Answer
Beta = Corr(Security, Market) * STDEV(Security) / STDEV(Market)
Firm A: Corr = 0.90*0.10/0.12 = 0.75
Firm B: STDEV(Security) = 1.10*0.10/0.4 = 0.275
Firm C: Beta = 0.75*0.24/0.10 = 1.80
Compute required return using CAPM
Firm A: 0.05 + 0.9*(0.15 - 0.05) = 0.14
Higher required return makes price low.
Based on risk involved, price of firm-A is lower but speculator expects higher price.
Rule: buy low, sell high.
As A is underpriced, buy security of firm-A.
When you leverage your portfolio, both risk and return will increase.
Weight of portfolio B = 1.2, weight on risk-free asset = -0.2
Standard Deviation of risk-free asset = 0
Standard Deviation of portfolio = 0.275*1.2 = 0.33
Return on portfolio = 1.2*0.16 + (-0.2)*0.05 = 0.182
Secirity E(R) STDEV Corr Beta Required Return Firm A 0.130 0.120 0.750 0.900 0.140 Underprice; Buy Firm B 0.160 0.275 0.400 1.100 0.160 Fairly Priced Firm C 0.250 0.240 0.750 1.800 0.230 Overprice; Sell Market 0.150 0.100 1.000 1.000 Risk-Free 0.050 0.000 0.000 0.000Related Questions
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