$($a$)$ Assume that stock market returns do not resemble a single$-$index structure. An investment fund analyzes $3,000$ stocks in order to construct a mean$-$variance efficient portfolio constrained by $3,000$ investments. They will need to calculate $($N$)\_3000\_\_\_$ expected returns, $($N$)\_\_\_3000\_\_\_\_\_\_\_\_$ variances of returns and $\_\_\_\_\_\_\_\_$ covariances.

Covariances

$($b$)($b$)$Assume that stock market returns do follow a single$-$index structure. An investment fund analyzes $3,000$ stocks in order to construct a mean$-$variance efficient portfolio constrained by $3,000$ investments. They will need to calculate $($N$)\_\_\_\_\_\_\_\_$ estimates of expected returns and $($N$)\_\_\_\_\_\_\_\_$ estimates of sensitivity coefficients to the market factor $($betas$).$