Consider the following annualized information about risk and return measures of two portfolios. The S&P500 Index portfolio may be viewed as the market portfolio for purposes of applying the Single index model.

Portfolio	Average Return	Standard Deviation	Beta
Money Market	2%	0%	0.0
Portfolio AA	10%	16%	0.6
Portfolio BB	15%	25%	1.2
S&P500 Index	14%	20%	1.0

(a) Compare the Sharpe Ratio for AA and BB against the market Sharpe Ratio. If the single-index model holds which, would you expect to have the larger Sharpe Ratio?

(b) Under the assumptions of the single-index model what is the idiosyncratic standard deviation of AA’s and BB’ returns?

(c) Given that the single-index model holds exactly, what is AA’s and BB’s alphas?

(d) Find the correlation between AA’s and BB’s returns and the S&P500 Index return.