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Solution to Problem Set 5
ECN 134
Finance Economics
Prof. Farshid Mojaver
Part A: Optimal Risky Portfolio
1.
a.
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.
b.
If the correlation between gold and stocks equals +1, then no one would hold
gold.
The optimal CAL 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.
2.
The probability distribution is:
Probability
Rate of Return
0.7
100%
0.3
−50%
Mean = [0.7
×
100] + [0.3
×
(

50)] = 55%
Variance = [0.7
×
(100

55)
2
] + [0.3
×
(

50

55)
2
] = 4725
Standard deviation = 4725
1/2
= 68.74%
3.
σ
P
= 30 = y
σ = 4 0
y
⇒
y = 0.75
E(r
P
) = 12 + 0.75(30

12) = 25.5%
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Since we do not have any information about expected returns, we focus exclusively
on reducing variability.
Stocks A and C have equal standard deviations, but the
correlation of Stock B with Stock C (0.10) is less than that of Stock A with Stock B
(0.90).
Therefore, a portfolio comprised of Stocks B and C will have lower total
risk than a portfolio comprised of Stocks A and B.
5.
Rearranging the table (converting rows to columns), and computing serial correlation
results in the following table:
Nominal Rates
Small
company
stocks
Large
company
stocks
Longterm
government
bonds
Intermedterm
government
bonds
Treasury
bills
Inflation
1920s
3.72
18.36
3.98
3.77
3.56
1.00
1930s
7.28
1.25
4.60
3.91
0.30
2.04
1940s
20.63
9.11
3.59
1.70
0.37
5.36
1950s
19.01
19.41
0.25
1.11
1.87
2.22
1960s
13.72
7.84
1.14
3.41
3.89
2.52
1970s
8.75
5.90
6.63
6.11
6.29
7.36
1980s
12.46
17.60
11.50
12.01
9.00
5.10
1990s
13.84
18.20
8.60
7.74
5.02
2.93
Serial Correlation
0.46
0.22
0.60
0.59
0.63
0.23
For example: to compute serial correlation in decade nominal returns for large
company stocks, we set up the following two columns in an Excel spreadsheet.
Then, use the Excel function “CORREL” to calculate the correlation for the data.
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This note was uploaded on 11/02/2009 for the course ECON 134 taught by Professor Mojaver during the Summer '08 term at UC Davis.
 Summer '08
 MOJAVER
 Economics

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