You should estimate numerous variances/covariances to find an optimal portfolio of 200 stocks. However, you can use the single index model to reduce the scope of your problem. What is the difference in the numbers of (necessary & unique) estimates between the original (full) Markowitz model and the single index model for the var/cov matrix of a 200-stock universe? (1) 7 11,024; (2) 19,499; (3) 19,699; (4) 30,624; (5) 30,874; (6) 44,249; (7) 44,549; (8) 60,374; 99) 60,724