The Risk Adjusted Return of the Portfolio S&P 500 and the Proposed Actions
The risk adjusted return or the return from S&P 500 can be considered as the market return because it contains a large number of stock; thus all types of market risks are reflected in it.
According to the summary statistics, the return on S&P 500 had been 12.4% with a standard deviation of 20.4%.
By using the raw beta of all the companies that are potential stocks to be included in the portfolio, and the risk free rate on one year T-Bond along with the market return; the expected rate of return for all the companies can be calculated using the CAPM model.
Selection of Stocks for the Fund Monticello
By theory of portfolio and risk measurement, a positive alpha of 1.0 means that the fund has outperformed its benchmark index by 1%. Correspondingly, a similar negative alpha will indicate an underperformance of 1%.
By calculating the alpha of the individual stocks using the calculated return through CAPM and the anticipated annual return since 2004-2007; it is evident that Mylan Labs and Placer Dome have exceeded the expectations whereas, Micron Technologies had highly underperformed.
Stocks that have highest alpha values should be selected to be included in the portfolio. From the selected stocks, Mylan Labs and Placer Dome will be selected for the portfolio. However, it is very important to find the optimal proportion between the stocks to maximize the return at a given level of risk.
The efficient frontier line between the expected return and beta will help the fund team in determining this proportion. The point at which the SML expected return is equal to the maximized portfolio return and the alpha value is zero will be the optimal level; where the return will be highest at the lowest risk level.
With this calculation, it can be seen that the 50-50 proportion is not valid. However, 35.00% and 65.00% proportion between Placer Dome and Mylan Labs is the optimal level where stock portfolio return will be 10.17% at a risk level (beta) of 0.80 that is acceptable for the fund.
Appendix
|
Risk free rate |
1.23% |
|
|
Beta for individual stocks |
||
|
Boise Cascade |
1.14 |
|
|
Boston Beer |
0.46 |
|
|
Micron Technologies |
2.19 |
|
|
Mylan Labs |
0.26 |
|
|
New York Times |
0.72 |
|
|
Placer Dome |
0.25 |
|
|
Market return |
||
|
S&P 500 index |
12.40% |
|
|
Standard Deviation |
20.4%. |
|
|
Estimated Return through CAPM |
||
|
Boise Cascade |
13.96% |
|
|
Boston Beer |
6.37% |
|
|
Micron Technologies |
25.69% |
|
|
Mylan Labs |
4.13% |
|
|
New York Times |
9.27% |
|
|
Placer Dome |
4.02% |
|
|
αi= E(ri) –RA_E(ri) |
||
|
Boise Cascade |
-3.16% |
|
|
Boston Beer |
1.83% |
|
|
Micron Technologies |
-12.69% |
|
|
Mylan Labs |
6.77% |
|
|
New York Times |
-0.27% |
|
|
Placer Dome |
4.78% |
|
Optimal Level of Proportion, Risk And Return Tradeoff
|
Proportion |
|||||
|
Beta |
SML Exp. Return |
Maximized portfolio return |
Placer Dome |
Mylan Labs |
Portfolio Alpha |
|
0.30 |
4.6% |
10.69% |
10.00% |
90.00% |
6.1% |
|
0.40 |
5.7% |
10.59% |
15.00% |
85.00% |
4.9% |
|
0.50 |
6.8% |
10.48% |
20.00% |
80.00% |
3.7% |
|
0.60 |
7.9% |
10.38% |
25.0% |
75.00% |
2.4% |
|
0.70 |
9.0% |
10.27% |
30.00% |
70.00% |
1.2% |
|
0.80 |
10.2% |
10.17% |
35.00% |
65.00% |
0.0% |
|
0.90 |
11.3% |
10.06% |
40.00% |
60.00% |
-1.2% |
|
1.00 |
12.4% |
9.85% |
50.00% |
50.00% |
-2.6% |
|
1.10 |
13.5% |
9.75% |
55.00% |
45.00% |
-3.8% |
|
1.20 |
14.6% |
9.64% |
60.00% |
40.00% |
-5.0% |
|
1.30 |
15.8% |
9.54% |
65.00% |
35.00% |
-6.2% |
|
1.40 |
16.9% |
9.43% |
70.00% |
30.00% |
-7.4% |
..................................
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