MIDDLE EAST TECHNICAL UNIVERSITY
SPRING 2010
DEPARTMENT OF BUSINESS ADMINISTRATION
BA 5802 – FINANCIAL MANAGEMENT
Dr. Danışoğlu
Problem Set #1
Due on Wednesday, March 31, 2010
1.
Stocks offer an expected rate of return of 18%, with a standard deviation of 22%. Gold offers an
expected return of 10% with a standard deviation of 30%.
a.
In light of the apparent inferiority of gold with respect to both mean return and volatility, would
anyone hold gold? If so, demonstrate graphically why one would do so.
Even though it seems that gold is dominated by stocks, gold might still be an attractive asset to hold
as a
part
of a portfolio. If the correlation between gold and stocks is sufficiently low, gold will be held
as a component in a portfolio, specifically, the optimal tangency portfolio.
Standard Deviation(%)
0.00
5.00
10.00
15.00
20.00
25.00
0
10
20
30
40
Gold
Stocks
Optimal CAL
P
b.
Given the data above, reanswer part (a) with the additional assumption that the correlation
coefficient between gold and stocks equals 1.0. Draw a graph illustrating why one would or would
not hold gold in one’s portfolio. Could this set of assumptions for expected returns, standard
deviations, and correlation coefficients represent an equilibrium for the financial markets?
If the correlation between gold and stocks equals +1, then no one would hold gold. The optimal
portfolio would be comprised of bills and stocks only. Since the set of risk/return combinations of
stocks and gold would plot as a straight line with a negative slope (see the following graph), these
combinations would be dominated by the stock portfolio. Of course, this situation could not persist. If
no one desired gold, its price would fall and its expected rate of return would increase until it became
sufficiently attractive to include in a portfolio.
Efficient
frontier
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View Full DocumentStandard Deviation(%)
0
5
10
15
20
25
0.00
10.00
20.00
30.00
40.00
Gold
Stocks
r
f
18
2.
Assume that the following two investment classes are available in the market:
Asset
E(r
i
)
σ
i
Debt
0.08
0.12
Equity
0.13
0.20
Determine
the portfolio standard deviation and expected return if you invest the following weights
in the two investment classes and when r
D,E
= +1.00, or r
D,E
= +0.50, or r
D,E
= 0.00, or r
D,E
= −0.50,
or r
D,E
= −1.00:
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 Spring '12
 Danısoglu
 Finance, Management, Standard Deviation, Corr

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