Question

Your company offers a retirement plan administered by Forever Investments. The plan allows you to invest in a variety of mutual funds, including Forever’s Growth fund (FG for short), Forever’s Value fund (FV), and Forever SnP 500 Index Fund (FSI). FSI is an ‘index’ fund that simply tries to match the performance of the S&P 500 index. Suppose you have data about each fund’s monthly returns during the last 20 years.

Explain briefly (max a paragraph, with 3 sentences) how you could evaluate whether the funds performed well on a risk-adjusted basis. You can use S&P 500 index as a benchmark for all three funds. No calculation needed.

Answer 1

First, lets understand what risk-adjusted return is. Risk-adjusted return is the return earned over and above the returns generated by a risk-free asset like a government bond, which is termed as the benchmark. The excess returns are evaluated in the light of the “extra risk” which an investor takes upon investing in a risky asset like mutual funds.

Such evaluation of a fund on a risk adjusted basis over a benchmark can be done with the help of Sharpe ratio. Sharpe ratio is calculated using the following formula:

Sharpe Ratio = (Average fund returns − Riskfree Rate) / Standard Deviation of fund returns

In the given question, the benchmark will be S&P 500 index and hence risk free rate will be the return in relative to the S&P 500 index. S&P 500 index can be used as a benchmark for equity related funds as it is a better gauge for large U.S. listed companies ( this index moves basis the 500 of the largest U.S. listed companies).

The risk inherent in an investment is determined using the standard deviation. Thus, one can evaluate risk adjusted return using the Sharpe ratio as above.

In the question, Forever SnP 500 Index Fund (FSI) matches the S&P 500 index. Hence the Sharpe ratio will be the lowest and hence the risk adjusted return for this index will be lower.

Performance of other 2 funds (Forever’s Growth fund (FG for short), Forever’s Value fund (FV)) can be evaluated using the sharpe ratio as above. A higher Sharpe ratio shows better return yielding capacity of a fund for every additional unit of risk taken by it. It becomes a justification for the underlying volatility of the fund. Thus, whichever fund has highest sharpe ratio, that fund would have generated the best risk adjusted return.