A portfolio manager summarizes the input from the macro and micro forecasters in the following table:

Micro Forecasts

Asset Expected Return $(\%)$ Beta Residual Standard Deviation $(\%)$

Stock A $201\mathrm{.}564$

Stock B $182\mathrm{.}277$

Stock C $171\mathrm{.}166$

Stock D $121\mathrm{.}061$

Macro Forecasts

Asset Expected Return $(\%)$ Standard Deviation $(\%)$

T$-$bills $80$

Passive equity portfolio $1533$

Required:

Calculate the following for a portfolio manager who is not allowed to short sell securities$.$ If allowed to short sell securities$,$ the manager's Sharpe ratio is $0\mathrm{.}2762.$

What is the cost of the restriction in terms of Sharpe$$s measure?

What is the utility loss to the investor $($A $=1\mathrm{.}4)$ given his new complete portfolio?