问一道题：NO.PZ2018062001000010

问题如下：

Tim has an investment portfolio of $500,000 at the beginning of 2016. At the end of that year, Tim wants to withdraw $15,000 for daily expenses but maintain the original value of the portfolio. Assume that return of the portfolio is 5% and normally distributed, risk-free rate is 2%  and standard deviation of the return is 16%. The Sharpe ratio and Safety-first ratio are:

选项：

Sharpe ratio: 12.5%, Safety-first ratio:18.75%

Sharpe ratio: 18.75%, Safety-first ratio: 31.25%

Sharpe ratio: 18.75%, Safety-first ratio: 12.5%

解释：

C is correct.

Sharpe ratio =(R_p-R_f)/ σ=(5%-2%)/16%=18.75%.

15,000/500,000=3%. For any return lower than 3%, Tim has to withdraw from the orginial value of the portfolio. Therefore,

 Safety-first ratio= (R_p-R_L)/ σ=(5%-3%)/16%=12.5%