Kelli Blakely is a portfolio manager for the Miranda Fund, a core large$-$cap equity fund. The benchmark for performance measurement purposes is the S&P $500.$ Although the Miranda portfolio generally mirrors the asset class and sector weightings of the S&P$,$ Blakely is allowed a significant amount of leeway in managing the fund.

Blakely was able to produce exceptional returns last year $($as outlined in the table below$)$ through her market timing and security selection skills. At the outset of the year, she became extremely concerned that the combination of a weak economy and geopolitical uncertainties would negatively impact the market. Taking a bold step, she changed her market allocation. For the entire year her asset class exposures averaged $50\%$ in stocks and $50\%$ in cash. The S&P$$s allocation between stocks and cash during the period was a constant $97\%$ and $3\%,$ respectively. The risk$-$free rate of return was $2\%.$

One$-$Year Trailing Returns

Miranda Fund S&P $500$

Return $10\mathrm{.}2\%22\mathrm{.}5\%$

Standard deviation $37\%44\%$

Beta $1\mathrm{.}101\mathrm{.}00$

Required:

a$.$ What are the Sharpe ratios for the Miranda Fund and the S&P $500?($Do not round intermediate calculations. Negative amount should be indicated by a minus sign. Round your answers to $4$ decimal places.$)$

c$.$ What is the Treynor$$s measure for the Miranda Fund and the S&P $500?($Do not round intermediate calculations. Negative amount should be indicated by a minus sign. Round your answers to $4$ decimal places.$)$