At the end of current year, investor wants to make donation of 20,000 to charity but does not want year end market value of her portoflioto fall below 600,000. if the shortfall level is equal to RF and return from all protfolio considered are normally distributed, will the portfolio that minimizes the probability of failing to achieve the investor’s objective most likely have the the Ans is: Highest safety-first ratio (YES), Highest Sharpe ratio (YES) From the curriculum explain, The portfolio with the highest sharpe ratio minimizes the probability that portfolio return will be less that RF (given normality). In this problem, the shortfall level is equal to the RF and thus the highest safety-first ratio protfolio will be the same as the highest sharpe ratio portfolio My question is : 1) don’t know why shortfall level = RF will have high safety-first ratio 2) why there have relationship to normal distribution Can anyone (expert) help to resolve my problem? Thanks yours
The normal distribution tells us that standard deviation levels are consistent, which allows for the Sharpe and SF ratio formula’s to have the same input in the denominator, and hence be comparable. Look at the formula’s for SF risk and Sharpe Ratio. They are essentially the same, with the only difference being that in the SF Risk formula the Risk Free Asset return is replaced with the safety first return value. In this question, since the Riskfree rate and the Shortfall Return level are the same, both returns will be same. Certainly not the expert analysis you were hoping for, but I hope it helps…
Thanks for Nahsuar explaination. May i asked one question further, why it can achieve Highest safety-first ratio (YES), or Highest Sharpe ratio (YES) ? Can you further explain ? Many Many thanks
“will the portfolio that minimizes the probability of failing to achieve the investor’s objective most likely have the…” If you notice they do not talk about the highest absolute return, which would be R§ - R(f). They ask about probabilities, which take into account the standard deviation of the return as well. Keeping that in mind, the portfolio that has the lowest rate of failing has the highest probability of not failing. Combine that with the effect of standard deviation, and you have the portfolio that will MOST LIKELY have the highest sharpe ratio. The key lies in probabilities.
nahsuar, Many Many thanks