The expected return of an asset is the sum of the probability of each state occu
ID: 2654526 • Letter: T
Question
The expected return of an asset is the sum of the probability of each state occurring times the rate of return if that state occurs.
a. Expected return (Show work):
1. E(RA) =
2. E(RB) =
b. What is the expected market risk premium? Hint: We can use the expected returns we calculated to find the slope of the Security Market Line. (We could also solve this problem using CAPM.) The slope of the security market line (SML) equals the expected market risk premium. (Show work):
Expected Market Risk Premium =
29. SML Suppose you observe the following situation: Return if State Occurs State of Economy Bust Normal Boom Probability of State Stock A Stock B .10 65 .25 09 .35 10 .21 Calculate the expected return on each stock Assuming the capital asset pricing model holds and stock A's beta is greater than stock B's beta by .25, what is the expected market risk premium? a. b.Explanation / Answer
Answer
Answer (a)
Stock A
State of Economy
Probability
Return
Prob * Return
Stock A
A
B
A*B
Bust
0.1
-0.12
-0.012
Normal
0.65
0.09
0.0585
Boom
0.25
0.35
0.0875
1
Expected return
0.134
Stock B
State of Economy
Probability
Return
Prob * Return
Stock B
A
B
A*B
Bust
0.1
-0.05
-0.005
Normal
0.65
0.1
0.065
Boom
0.25
0.21
0.0525
1
Expected return
0.1125
Answer (b)
Capital Asset pricing model holds, So Expected return of stock and required return of stock as per CAPM model will be same.
Risk free rate = Rf
Market return = Rm
Beta = B
Beta of stock A = Ba = x+0.25
Beta of stock B = Bb = x
Market risk premium = Rm –Rf = ?
Required return for stock = Rf + B ( Rm –Rf)
So,
Required/expected return for stock A = Rf + Ba ( Rm –Rf)
0.134 = Rf + (x+0.25)(Rm – Rf) .............................................................(1)
Required/expected return for stock B = Rf + Bb ( Rm –Rf)
0.1125 = Rf + (x)(Rm – Rf) ....................................................................(2)
Equation (1) minus Equation (2)
0.0215 = (x+0.25)(Rm – Rf) - (x)(Rm – Rf)
0.0215 = (x)(Rm – Rf) + (0.25)(Rm – Rf) - (x)(Rm – Rf)
0.0215 = (0.25)(Rm – Rf)
(Rm – Rf) = 0.086
So (Rm – Rf) = 8.60%
Answer : So Market risk premium is 8.60%
State of Economy
Probability
Return
Prob * Return
Stock A
A
B
A*B
Bust
0.1
-0.12
-0.012
Normal
0.65
0.09
0.0585
Boom
0.25
0.35
0.0875
1
Expected return
0.134
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