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Efficient Portfolio
The weighted average expected return under the new scenario will be 14%. This is calculated as follows:
The standard deviation of returns under the new scenario is 24.5. We calculate the difference between each potential return and the mean. Thus,
(44-14) = 30; (14-14) = 0, and (14+16) = 30.
Each is squared, and then the squares are added together. So 302 = 900. This means that the sum of squares is 900 + 0 + 900 = 1800. This is divided by the number of data points, as follows:
This is the variance. To obtain the standard deviation we take the square root of 600 as follows:
The expected return is .333(12)+(.333)(4)+(.333)(-5.5) = 3.5
The standard deviation therefore is 12.38.
With half in T-bills the expected return is 3.75%. The standard deviation is therefore 6.015. The expected return improves because you reduce the downside risk with the T-bills. This also reduces the variability of the portfolio as well.
Problem
The expected return of this portfolio is as follows:
(.5)(15)+(.4)(10)+(.1)(6) = 12.1%
Problem 2: Coppa should recommend to Stephenson Fund D. The first criterion is that the fund needs to maintain or enhance the expected return, which is currently 13.8%. The first criteria, therefore, rules out Fund B. The other three funds, however, are still contenders at this point.
The second criterion is that the fund should reduce volatility. There are two elements to portfolio volatility. The first is the volatility of the fund and the second is the correlation with the current portfolio. The lowest volatility, as measured by standard deviation, of the three remaining funds is with Fund D. This fund is also the only one of the three remaining funds to have a standard deviation lower than the current portfolio.
However, that does not immediately rule out the other funds. It is also recommended to consider the correlation with the current portfolio. The less correlated the new fund is with the current portfolio, the more the new fund will reduce overall portfolio volatility. Fund D. is also the fund with the lowest correlation to the current portfolio. Because of this, the relatively low standard deviation, and the expected annual return above that of the current portfolio, Coppa should recommend that Stephenson purchase Fund D.
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