Case Study:
Listed below are the annual rates of return on the stocks for companies A, B, C, …, G for each year 1975-2004.
(1) Determine the efficient frontier using portfolios generated from combining just these seven risky assets. Graph the results.
In listing the results in tabular form, show the weights for each level of sigma that you chose to look at in addition to the expected returns and the standard deviation of the portfolio. You should show at least twenty different portfolios.
(2) Identify the minimum variance portfolio.
(3) If the risk-free rate of return is 7%, what is the "market portfolio?" Do the same for 2%. Explain, briefly, the significance of the market portfolio in this context.
(4) Using the risk-free rate of return of 7%, if an investor preferred to invest 40% of his/her assets in the risk-free asset and 60% in the market portfolio, what would be their expected return on the portfolio? The standard deviation? What would be the asset weights for the portfolio as a whole?
(5) Could an investor get an expected return on his/her investments using the risk-free asset that is higher than the expected return on any one of the stocks? If so, explain how this could be done.
|
A |
B |
C |
D |
E |
F |
G |
| 1975 |
4.75% |
9.75% |
-7.19% |
4.26% |
59.92% |
7.04% |
-41.82% |
| 1976 |
-49.87% |
80.84% |
-30.53% |
-49.34% |
42.29% |
5.00% |
-69.17% |
| 1977 |
-11.88% |
15.81% |
-32.62% |
121.90% |
-55.65% |
-9.31% |
160.90% |
| 1978 |
-12.63% |
-38.80% |
-90.00% |
10.75% |
-92.20% |
49.73% |
117.45% |
| 1979 |
46.07% |
-12.44% |
29.93% |
75.11% |
-68.45% |
-0.79% |
3.45% |
| 1980 |
13.54% |
40.77% |
-32.79% |
6.35% |
18.73% |
-41.96% |
-16.29% |
| 1981 |
21.08% |
-38.15% |
-89.74% |
11.27% |
20.76% |
-8.45% |
18.38% |
| 1982 |
21.43% |
58.58% |
45.13% |
81.30% |
-42.87% |
-4.89% |
113.78% |
| 1983 |
-30.43% |
4.83% |
59.84% |
8.79% |
-35.81% |
-3.92% |
34.60% |
| 1984 |
-30.52% |
-36.41% |
-57.87% |
-6.10% |
116.41% |
-4.78% |
-34.97% |
| 1985 |
6.58% |
31.75% |
-65.74% |
76.85% |
29.57% |
9.67% |
-36.34% |
| 1986 |
-22.68% |
2.33% |
-74.52% |
-68.95% |
101.96% |
34.67% |
-5.32% |
| 1987 |
49.36% |
-90.00% |
-20.34% |
53.09% |
-27.14% |
21.62% |
-90.00% |
| 1988 |
-3.38% |
0.92% |
99.71% |
-16.08% |
89.08% |
0.14% |
-93.21% |
| 1989 |
9.97% |
4.77% |
-25.77% |
75.19% |
-33.13% |
13.89% |
45.77% |
| 1990 |
23.43% |
11.42% |
-62.67% |
-7.51% |
30.74% |
10.64% |
-12.27% |
| 1991 |
-16.68% |
59.74% |
105.87% |
34.23% |
-89.47% |
40.31% |
127.32% |
| 1992 |
32.06% |
-18.08% |
64.62% |
23.40% |
94.94% |
-9.38% |
-68.73% |
| 1993 |
75.82% |
12.18% |
81.48% |
-1.65% |
-59.41% |
6.59% |
92.31% |
| 1994 |
-19.42% |
-1.83% |
10.17% |
-6.63% |
-75.51% |
9.66% |
-64.22% |
| 1995 |
-48.13% |
-5.04% |
-28.89% |
-90.00% |
144.20% |
-5.00% |
14.47% |
| 1996 |
-20.53% |
71.49% |
-53.93% |
40.01% |
18.95% |
14.97% |
-10.41% |
| 1997 |
-49.89% |
-7.72% |
-25.06% |
-19.21% |
-18.24% |
-15.10% |
-4.04% |
| 1998 |
61.02% |
-10.38% |
-81.45% |
44.88% |
-73.94% |
-0.62% |
79.37% |
| 1999 |
85.58% |
5.17% |
194.44% |
-13.28% |
8.18% |
8.66% |
17.85% |
| 2000 |
43.06% |
4.92% |
43.41% |
100.09% |
-78.12% |
45.34% |
11.67% |
| 2001 |
36.02% |
0.50% |
48.34% |
67.53% |
-59.73% |
14.32% |
63.98% |
| 2002 |
-20.40% |
-42.88% |
83.35% |
36.92% |
36.72% |
-3.07% |
-61.51% |
| 2003 |
15.72% |
26.32% |
-14.65% |
76.22% |
-30.91% |
15.74% |
107.33% |
| 2004 |
82.67% |
-7.77% |
42.49% |
46.47% |
-87.72% |
-1.17% |
76.63% |