CHAPTER 13
RISK, RETURN, AND THE SECURITY
MARKET LINE
Solutions to Questions and Problems
NOTE: All end of chapter problems were solved using a spreadsheet. Many problems require
multiple
steps. Due to space and readability constraints, when these intermediate steps are included in
this
solutions manual, rounding may appear to have occurred. However, the final answer for each
problem is
found without rounding during any step in the problem.
Basic
1.
The portfolio weight of an asset is total investment in that asset divided by the total portfolio
value.
First, we will find the portfolio value, which is:
Total value = 100($40) + 130($22) = $6,860
The portfolio weight for each stock is:
Weight
A
= 100($40)/$6,860 = .5831
Weight
B
= 130($22)/$6,860 = .4169
2.
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 = $2,300 + 3,400 = $5,700
So, the expected return of this portfolio is:
E(R
p
) = ($2,300/$5,700)(0.11) + ($3,400/$5,700)(0.16) = .1398 or 13.98%
3.
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
) = .50(.10) + .30(.16) + .20(.12) = .1220 or 12.20%
CHAPTER 13 B233
4.
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
) = .122 = .15w
X
+ .10(1 – w
X
)
We can now solve this equation for the weight of Stock X as:
.122 = .15w
X
+ .10 – .10w
X
.022 = .05w
X
w
X
= 0.44
So, the dollar amount invested in Stock X is the weight of Stock X times the total portfolio value,
or:
Investment in X = 0.44($10,000) = $4,400
And the dollar amount invested in Stock Y is:
Investment in Y = (1 – 0.44)($10,000) = $5,600
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5.
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 asset is:
E(R) = .3(–.09) + .7(.33) = .2040 or 20.40%
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 asset is:
E(R) = .25(–.05) + .40(.12) + .35(.25) = .1230 or 12.30%
7.
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
) = .15(.06) + .60(.07) + .25(.11) = .0785 or 7.85%
E(R
B
) = .15(–.2) + .60(.13) + .25(.33) = .1305 or 13.05%
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, then add all of these up. The result is the variance. So, the variance
and
standard deviation of each stock is:
σ
A
2
=.15(.06 – .0785)
2
+ .60(.07 – .0785)
2
+ .25(.11 – .0785)
2
= .00034
σ
A
= (.00034)
1/2
= .0185 or 1.85%
B234 SOLUTIONS
σ
B
2
=.15(–.2 – .1305)
2
+ .60(.13 – .1305)
2
+ .25(.33 – .1305)
2
= .02633
σ
B
= (.02633)
1/2
= .1623 or 16.23%
8.
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 Spring '08
 CARNEY
 Weighted average cost of capital, YTM

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