Chapter 11: Risk and Return: The Capital Asset Pricing Model (CAPM)
11.1
The expected return of a portfolio is the sum of the weight of each asset times the expected return
of each asset. The total value of the portfolio is:
Total value = $1,200 + 1,900 = $3,100
So, the expected return of this portfolio is:
E(R
P
) = ($1,200/$3,100)(0.11) + ($1,900/$3,100)(0.16) = 0.1406 or 14.06%
11.2
The expected return of a portfolio is the sum of the weight of each asset times the expected return
of each asset. So, the expected return of the portfolio is:
E(R
p
) = 0.50(.11) + 0.30(0.17) + 0.20(0.14) = 0.1340 or 13.40%
11.3
Here we are given the expected return of the portfolio and the expected return of each asset in the
portfolio and are asked to find the weight of each asset. We can use the equation for the expected
return of a portfolio to solve this problem. Since the total weight of a portfolio must equal 1
(100%), the weight of Stock Y must be one minus the weight of Stock X. Mathematically
speaking, this means:
E(R
p
) =0.122 = 0.14 w
X
+ 0.09(1 – w
X
)
We can now solve this equation for the weight of Stock X as:
0.122 = 0.14 w
X
+ 0.09 – 0.09 w
X
0.032 = 0.05 w
X
w
X
= 0.64
So, the dollar amount invested in Stock X is the weight of Stock X times the total portfolio value, or:
Investment in X = 0.64($10,000) = $6,400
And the dollar amount invested in Stock Y is:
Investment in Y = (1 – 0.64)($10,000) = $3,600
11.4
The expected return of an asset is the sum of the probability of each return occurring times the
probability of that return occurring. So, the expected return of each stock asset is:
E(R
A
) = 0.10(0.06) + 0.60(0.07) + 0.30(0.11) = 0.0810 or 8.10%
E(R
B
) = 0.10(–0.2) + 0.60(0.13) + 0.30(0.33) = 0.1570 or 15.70%
To calculate the standard deviation, we first need to calculate the variance. To find the variance, we
find the squared deviations from the expected return. We then multiply each possible squared
deviation by its probability, and then add all of these up. The result is the variance. So, the variance and
standard deviation of each stock are:
Answers to End–of–Chapter Problems
B–
129
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A
2
= 0.10(0.06 – 0.0810)
2
+ 0.60(0.07–0.0810)
2
+ 0.30(0.11 – 0.0810)
2
= 0.00037
σ
A
= (0.00037)
1/2
= 0.0192 or 1.92%
σ
B
2
= 0.10(–0.2 – 0.1570)
2
+ 0.60(0.13–0.1570)
2
+ 0.30(0.33 – 0.1570)
2
= 0.02216
σ
B
= (0.022216)
1/2
= 0.1489 or 14.89%
11.5
The expected return of a portfolio is the sum of the weight of each asset times the expected return
of each asset. So, the expected return of the portfolio is:
E(R
p
) = 0.20(0.08) + 0.70(0.15) + 0.1(0.24) = 0.1450 or 14.50%
If we own this portfolio, we would expect to get a return of 14.50 percent.
11.6
The expected return of an asset is the sum of the probability of each return occurring times the
probability of that return occurring. So, the expected return of the stock is:
E(R
A
) = 0.10(–0.045) + 0.20(0.044) + 0.50(0.12) + 0.20(0.207) = 0.1057 or 10.57%
To calculate the standard deviation, we first need to calculate the variance. To find the variance, we
find the squared deviations from the expected return. We then multiply each possible squared
deviation by its probability, and then add all of these up. The result is the variance. So, the
variance and standard deviation are:
σ
2
= 0.10(–0.045 – 0.1057)
2
+ 0.20(0.044 – 0.1057)
2
+ 0.50(0.12 – 0.1057)
2
+ 0.20(0.207 – 0.1057)
2
=
–0.005187
σ
= (0.005187)
1/2
= 0.0720 or 7.20%
11.7
a.
To find the expected return of the portfolio, we need to find the return of the portfolio in
each state of the economy. This portfolio is a special case since all three assets have the
same weight. To find the expected return in an equally weighted portfolio, we can sum
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 Summer '10
 matazi
 Variance, Capital Asset Pricing Model, Modern portfolio theory

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