In the last post, I wrote about the different methods in comparing performance of funds. I have assumed the investor is indifferent to risk. The only question the investor had asked himself was “Who will give me the best expected returns?”
What if the investor asks “Who will give me the best expected return for a given risk?” That is an entirely different question. Mathematically, it looks like this:
Where is the expected return on the investment,
is the risk free rate and
is the volatility of the investment. Note: The above is better understood when you have the basic idea of the CAPM down. You can either google it, or wait for me to write about it which I plan in the future. The above formula is known as the Sharpe Ratio. The theory is that investors want to maximize the above equation.
The Sharpe ratio can tells us which fund had a better performance. We can also compute the sharpe ratio of the market (we can pick the S$P500 for instance). The sharpe ration of the market is the bench mark to beat. If the sharpe ration of the fund was lower than the sharpe ratio of the market, the fund did poorly.
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