Question

Joaquim recently learned about a fund that boasted a 25% return in its marketing materials. Eagerly, he invested $100,000 without doing any research into the fund. A year later, he had $125,000 in the bank. However, he was not pleased with the high return once he learned about the Sharpe Ratio. What is the most likely reason why?

• He learned that the portfolio's volatility was 5%, so he could have lost $5,000. Taking on this level of risk may not justify the return.  

• He learned that the portfolio's volatility was 50%, so he could have lost $100,000. Taking on this level of risk may not justify the return. 

• He learned that the portfolio's volatility was 50%, so he could have made or lost $50,000. Taking on this level of risk may not justity the return 

• He learned that the portfolio's volatility was 5%, so he could have made $100,000. Taking on this level of risk justifies the return.

Answer 1

Answer: 3^rd option

Share ratio = (Rate of return – risk-free rate) / rate of volatility (or, standard deviation)

Taking other variables constant, risk and return on a portfolio depends of its volatility. If volatility is high, such as 50%, the risk on portfolio would be high; in such case he can expect more returns, since excess return is the reward of higher risk.

If volatility counts, the return would have been (100,000 × 50% =) $50,000. He could have received in the bank (100,000 + 50,000 =) $150,000 after 1 year; but he actually received $125,000 (based on the 25% rate); therefore, he may not be pleased because of losing returns of (150,000 – 125,000 =) $25,000.

Answer 2

 He learned that the portfolio's volatility was 50%, so he could have made or lost $50,000.