The Sharpe ratio is the best-known risk-adjusted statistic. You calculate an investment’s Sharpe ratio by taking the average period return, subtracting the risk-free rate, and dividing it by the standard deviation for the period.
This calculation generates a number we can use to compare investments. Note that for meaningful comparisons, all comparative investment statistics must be calculated over the same time period.
Example: Let’s compare two investments, Fund A and Fund B. Fund A has a return of 10% and standard deviation of 8%, while Fund B has a return of 20% and standard deviation of 16%. If the risk-free rate is 4%, Fund A has a Sharpe ratio of 0.75, and Fund B has a Sharpe ratio of 1.0.
Comparing the Sharpe ratios, Fund B would have been the better investment because:
- If we invested $1,000,000 in Fund A, with a 10% return, we would have $1,100,000 after 1 year.
- If we invested $500,000 in Fund B, with a 20% return, and $500,000 in a bank account with a 4% return, we would have $1,120,000 after 1 year. This is called de-leveraging.
According to Sharpe, a higher standard deviation is not bad, provided it is accompanied by a proportionally higher return. Note that there is no such thing as a good or bad absolute number for a comparative investment statistic, only its relative relationship to other peers. Also note that in real world investing, investors do not, in fact, de-leverage.
Investors who are required to select and monitor investment managers should develop a basic understanding of investment statistics. Quantitative tools can provide you with good insight that you can use in your qualitative interviews with managers and when monitoring your investments.