Answer:
Step-by-step explanation:
a. To optimize the portfolio using the 68 stocks, the organization would need the following estimates:
1. Estimates of expected returns: The organization would need an estimate of the expected return for each of the 68 stocks.
2. Estimates of variances: The organization would need an estimate of the variance for each of the 68 stocks, which measures the volatility or risk associated with each stock individually.
3. Estimates of covariances: The organization would need estimates of the covariances between all pairs of the 68 stocks. Covariance measures the relationship between the returns of two stocks and is used to assess the diversification benefits in the portfolio.
Total estimates needed:
- For expected returns: 68 estimates
- For variances: 68 estimates
- For covariances: The number of estimates can be calculated using the formula n*(n-1)/2, where n is the number of stocks. In this case, n = 68. So, the total number of estimates of covariances would be 68*(68-1)/2 = 2,278 estimates.
b. If one could safely assume that stock market returns closely resemble a single-index structure, only one estimate would be needed. The single-index structure assumes that the returns of individual stocks can be explained by the overall market return. In this case, the organization would only need an estimate of the market return to optimize the portfolio.