Consider the following information about stocks I and II. Assume both stocks are
ID: 2811363 • Letter: C
Question
Consider the following information about stocks I and II. Assume both stocks are correctly priced. The market risk premium is 7.5 percent, and the risk-free rate is 4 percent.
Rate of return if state occurs
State of the economy
Probability of state of the economy
Stock I
Stock II
Recession
0.15
0.11
-0.25
Normal
0.55
0.18
0.11
Irrational exuberance
0.30
0.08
0.31
a) Compute the systematic risk and total risk for each of the two stocks.
b) From the perspective of a risk-averse, well-diversified investor, which stock is riskier? Explain.
Rate of return if state occurs
State of the economy
Probability of state of the economy
Stock I
Stock II
Recession
0.15
0.11
-0.25
Normal
0.55
0.18
0.11
Irrational exuberance
0.30
0.08
0.31
Explanation / Answer
stock 1
state of economy
probability
return
probability*return
( return-averagereturn)
square of (return-average return)
probability* square of (return-average return)
Recession
0.15
11
1.65
-2.95
8.7025
1.305375
Normal
0.55
18
9.9
4.05
16.4025
9.021375
irrational exuberance
0.3
8
2.4
-5.95
35.4025
10.62075
average return
13.95
variance
sum of probability*(square of return-average return)
20.9475
total risk = standard deviation = square root of variance
4.576844
stock 2
state of economy
probability
return
probability*return
( return-averagereturn)
square of (return-average return)
probability* square of (return-average return)
Recession
0.15
-25
-3.75
-36.6
1339.56
200.934
Normal
0.55
11
6.05
-0.6
0.36
0.198
irrational exuberance
0.3
31
9.3
19.4
376.36
112.908
average return
11.6
variance
sum of probability*(square of return-average return)
314.04
total risk = standard deviation = square root of variance
17.72117
Systematic risk stock -1
required rate of return = risk free rate+(market risk premium)*beta
13.95 = 4+(7.5)*beta
7.5 beta = 9.95
beta = 9.95/7.5
1.32666667
systematic risk stock-2
required rate of return = risk free rate+(market risk premium)*beta
11.6 = 4+(7.5)*beta
7.5 beta = 7.6
beta = 7.6/7.5
1.01333333
From the risk averse well diversified investor stock A is a better option as its return is higher and total risk is low
stock 1
coefficient of variance
standard deviation/average stock
33%
stock 2
153%
stock 1
state of economy
probability
return
probability*return
( return-averagereturn)
square of (return-average return)
probability* square of (return-average return)
Recession
0.15
11
1.65
-2.95
8.7025
1.305375
Normal
0.55
18
9.9
4.05
16.4025
9.021375
irrational exuberance
0.3
8
2.4
-5.95
35.4025
10.62075
average return
13.95
variance
sum of probability*(square of return-average return)
20.9475
total risk = standard deviation = square root of variance
4.576844
stock 2
state of economy
probability
return
probability*return
( return-averagereturn)
square of (return-average return)
probability* square of (return-average return)
Recession
0.15
-25
-3.75
-36.6
1339.56
200.934
Normal
0.55
11
6.05
-0.6
0.36
0.198
irrational exuberance
0.3
31
9.3
19.4
376.36
112.908
average return
11.6
variance
sum of probability*(square of return-average return)
314.04
total risk = standard deviation = square root of variance
17.72117
Systematic risk stock -1
required rate of return = risk free rate+(market risk premium)*beta
13.95 = 4+(7.5)*beta
7.5 beta = 9.95
beta = 9.95/7.5
1.32666667
systematic risk stock-2
required rate of return = risk free rate+(market risk premium)*beta
11.6 = 4+(7.5)*beta
7.5 beta = 7.6
beta = 7.6/7.5
1.01333333
From the risk averse well diversified investor stock A is a better option as its return is higher and total risk is low
stock 1
coefficient of variance
standard deviation/average stock
33%
stock 2
153%
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