Consider the expression of the single$-$factor model:

ri$=$rf$+$ iF$+"$i;

where rf denotes the risk$-$free rate, F the factor return, and $"$i is an idisoyncratic shock

with mean zero. The assumptions underlying the arbitrage pricing theory hold.

$($a$)$Find an expression for the components of total risk.

$($b$)$Also derive an expression of the covariance between any pair of securities i; j in this framework.