Add a new stock, stock 4, to the model in Example 7.9. Assume that the estimated mean and standard deviation of return for stock 4 are 0.125 and 0.175, respectively. Also, assume the correlations between stock 4 and the original three stocks are 0.3, 0.5, and 0.8. Run Solver on the modified model, where the required expected portfolio return is again 0.12. Is stock in the optimal portfolio? Then run SolverTable as in the example. Is stock 4 in any of the optimal portfolios on the efficient frontier?
EXAMPLE 7.9 PORTFOLIO SELECTION AT PERLMAN & BROTHERS
Perlman & Brothers, an investment company, intends to invest a given amount of money in three stocks. From past data, the means and standard deviations of annual returns have been estimated as shown in Table 7.7. The correlations among the annual returns on the stocks are listed in Table 7.8. The company wants to find a minimum-variance portfolio that yields an expected annual return of at least 0.12.
Objective To use NLP to find the portfolio of the three stocks that minimizes the risk, measured by portfolio variance, subject to achieving an expected return of at least 0.12.
WHERE DO THE NUMBERS COME FROM? Financial analysts typically estimate the required means, standard deviations, and correlations for stock returns from historical data, as discussed at the beginning of this section. However, you should be aware that there is no guarantee that these estimates, based on historical return data, are relevant for future returns. If analysts have new information about the stocks, they should incorporate this new information into their estimates.