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CHAPTER 11 C-1
CHAPTER 11
A JOB AT EAST COAST YACHTS,
PART 2
1. There should be little, if any, money allocated to the company stock. The principle of diversification
indicates that an individual should hold a diversified portfolio. Investing heavily in company stock
does not create a diversified portfolio. This is especially true since income also comes from the
company. If times get bad for the company, employees face layoffs, or reduced work hours. So, not
only does the investment perform poorly, but income may be reduced as well. We only have to look
stock. At most, 5 to 10 percent of the portfolio should be allocated to company stock.
2. This is not the portfolio with the least risk. By adding stocks, a riskier asset, the overall risk of the
3. For the risk-free rate, we will use the 10-year average risk-free rate we calculated in Chapter 10. We
can use the equations for the expected return of the portfolio, and the portfolio standard deviation, that
is:
Using these equations and equity portfolio weights from zero to 100 percent at intervals of 10 percent,
we get the following portfolio expected returns and standard deviations:
Weight of stock fund
Portfolio E(R)
Portfolio standard
deviation
0%
8.15%
10.34%
10%
8.44%
10.08%
20%
8.74%
10.54%
30%
9.03%
11.63%
40%
9.32%
13.19%
50%
9.62%
15.08%
60%
9.91%
17.19%
70%
10.20%
19.45%
80%
10.49%
21.81%
90%
10.79%
24.24%
100%
11.08%
26.73%
4. Now we can use Solver to maximize this expression by changing the weight of the equity input cell.
The constraint is that the standard deviation of the portfolio is equal to the standard deviation of the
bond fund. Using Solver, the weight of the large cap stock fund and bond fund in this portfolio is:
5. To find the weights of each asset in the minimum variance portfolio, we begin with the equation for
2
P
= X
2
S
2
S
+ X
2
B
2
B
+ 2XSXBS,B
0%
2%
4%
6%
8%
10%
12%
0% 5% 10% 15% 20% 25% 30%
Portfolio expected return
Portfolio standard deviation
CHAPTER 11 C-3
Since the weights of the assets must sum to one, we can write the variance of the portfolio as:
2
P
= X
2
S
2
S
+ (1 – XS)2
2
B
+ 2XS(1 – XS)SBS,B
dσp2/dXS = 2XS
2
S
– 2(1 – XS)σB2 + 2σSσB S,B – 4XSσSσBS,B = 0
Solve for XS to get:
XS = (
2
B
– SBS,B)/(
2
S
+
2
B
– 2SBS,B)
Using this expression, we find the weight of the stock fund, must be:
XS = [.10342 – (.2673)(.1034)(.16)]/[.26732 + .10342 – 2(.2673)(.1034)(.16)]
XS = .0855
This implies the weight of the bond fund is:
The variance of the portfolio is:
2
P
= X
2
S
2
S
+ X
2
B
2
B
+ 2XSXBS,B
2
And the standard deviation is:
= .0101551/2
With these returns and variances, the minimum variance portfolio is important because no investor
would ever hold a portfolio with a greater weight in bonds. If an investor increases the weight of bonds
in the portfolio, the risk of the portfolio increases and the expected return decreases. The result is
illustrated in Question 4.
in a cell. The Sharpe ratio is:
Sharpe ratio =
σ
R E(R) f
−
Substituting the equations for the expected return of the portfolio and the standard deviation of the
portfolio, we get:
Sharpe ratio =
2/1
DE,DEEE
2
D
2
E
2
E
2
E
fDEEE
)ρσ)σ(12 σ) (1 σ(
R ))E(R (1 )E(R
XXXX
XX
−+−+
−−+
Now we can use Solver to maximize this expression by changing the weight of equity input cell. Doing
so, we find the weight of equity in the Sharpe optimal portfolio is 15.29 percent.
XE =
.16)3)(.1034)(.036](.267 .0815 .036 [.1108 .036].2673 [.0815 .036].1034 [.1108
.16)3)(.1034)(.036](.267 [.0815 .036].1034 [.1108
22
2
−+−−−+−
−−−
CHAPTER 11 C-5
Sharpe ratio =
.1033
.036 .0865 −
optimal portfolio, it shows the best combination of portfolios available to any investor. Investors can
change the level of risk by altering the percentage of their investment in the risk-free asset and the
Sharpe optimal portfolio. This line is the Security Market Line.
