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CHAPTER 10 CASE 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
3. We can use the equations for the expected return of the portfolio, and the portfolio standard deviation,
that is:
E(RP) = XEE(RE) + XDE(RD)
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%
6.93%
9.9600%
10%
7.45%
9.6380%
20%
7.97%
9.9520%
30%
8.50%
10.8468%
40%
9.02%
12.1952%
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:
XE = .2013
XD = .7987
So, the expected return and standard deviation of this portfolio are:
5. To find the weights of each asset in the minimum variance portfolio, we begin with the equation for
the variance of the portfolio. Using S to represent the large company fund and B to represent the bond
fund, the variance of a portfolio of two assets equals:
2
P
= X
2
S
2
S
+ X
2
B
2
B
+ 2XSXBS,B
XS = (
B
– SBS,B)/(
S
+
B
– 2SBS,B)
Using this expression, we find the weight of the stock fund, must be:
XS = [.09962 – (.2443)(.0996)(.15)]/[.24432 + .09962 – 2(.2443)(.0996)(.15)]
XS = .1006
This implies the weight of the bond fund is:
P
= (.10062)(.24432) + (.89942)(.09962) + 2(.1006)(.8994)(.2443)(.0996)(.15)
2
P
= .009289
And the standard deviation is:
= .0092891/2
6. We can find the Sharpe optimal portfolio by using Solver. To use Solver, we input the Sharpe ratio
in a cell. The Sharpe ratio is:
Sharpe ratio =
P
f
σ
R E(R)−
so, we find the weight of equity in the Sharpe optimal portfolio is 28.35 percent.
This question can also be solved directly. The goal is to maximize the Sharpe ratio, so we can use the
expression for the Sharpe ratio, set the derivative equal to zero, and solve for the weight of equity (or
debt). Doing so, the resulting expression for the weight of equity in the Sharpe optimal portfolio is:
XE =
2
22
[.1215 .032].0996 [.0693 .0320](.2443)(.0996)(.15)
[.1215 .0320].0964 [.1215 .032].2443 [.1215 .0320 .0693 .0320](.2443)(.0996)(.15)
− − −
− + − − − + −
and the weight of debt is:
CHAPTER 10 CASE C-5
So, the expected return and standard deviation of the Sharpe optimal portfolio is:
E(R) = .2835(.1215) + .7165(.0693)
E(R) = .0841, or 8.41%
The Sharpe optimal portfolio is the best risky portfolio for all investors because it delivers a greater
reward-to-risk ratio than any other portfolio. If a line is drawn from the risk-free rate to the Sharpe
optimal portfolio, it shows the best combination of portfolios available to any investor. Investors can
