What is Sharpe Ratio

The Sharpe Ratio Interpretation

The Sharpe Ratio is a frequently used ratio that is used to measure a portfolio or fund’s out performance for every unit of risk that has been taken.

The excess return, or out performance, of an investment is the return that was achieved minus the return that could have been obtained by a risk-free return. It is hope that this figure is positive, since a negative would indicate that the investment returned less than could have been obtained by staying safely invested in a risk-free asset.

The standard deviation (denote by the s) of the investment is also used in calculating the Sharpe Ratio. That is normally calculated from the monthly returns over fairly short periods. It is important when using the Sharpe Ratio to ensure you are comparing like-with-like, both in terms of the time period used and how the returns are calculated.

Sharpe Ratio Equation

what is the sharpe ratio equation

The Sharpe Ratio formula is therefore:

S = (M-F) / s

where:

  • M – is the Market Return that was achieved.
  • F – is the risk-free rate of return over the same period.
  • s – is the standard deviation.

 

Example of the Sharpe Ratio calculation

If an investment returns 12% on an annualized basis, with the risk-free return being 4% and the standard deviation of the investment was 10%, then the Sharpe Ratio is simply

S = (12 – 4) / 10 = 0.8

 

How to Interpret the Sharpe Ratio

The higher the value of a portfolio Sharpe Ratio, the better the portfolio has performed on a risk-adjusted basis.

The calculation can be seen to be quite simple, but fortunately, there are many resources on the internet where it is possible to find the Sharpe Ratio of mutual funds already calculated and done so consistently, so the figures can be used as part of an investment appraisal process.

 

Further, Examples of the Sharpe Ratio

Suppose there are two fund managers ‘A’ and ‘B’ that have achieved annualized returns on their portfolio of 9% and 11% respectively. Superficially, it may seem that fund manager B has been the most successful.

However, if you additionally found out that the standard deviation of fund manager A’s portfolio was 6% and for fund manager B it was 10%, with the risk-free rate of return of 3%. This would mean:

  • Fund manager A had a Sharpe Ratio of (9 – 3) / 6 = 1.0
  • Fund manager B had a Sharpe Ratio of (11 – 3) / 10 = 0.8

Therefore, although fund manager B achieved a higher annualized return than fund manager A, on a risk adjusted basis, fund manager A had a higher Sharpe Ratio. This shows that they therefore achieved the better risk adjusted returns.

 

Advantages and disadvantages to the Sharpe Ratio

One of the strengths of the Sharpe Ratio is that it is easy to calculate and use in comparisons. It does have limitations in that it is not sufficient, by itself, to enable investors to make sensible investment decisions.

Further to the example above, consider the case of fund manager C, who achieved annualized returns of 15% on his portfolio with a standard deviation of 12%, over the same period as fund managers A and B, where the risk-free rate of return was 3%

Here fund manager C had a Sharpe Ratio of (15 – 3) / 12 = 1.

This is an identical Sharpe Ratio to that of fund manager A. So on a risk adjusted basis fund manager A and C are equal. Fund manager C had higher returns, but these came at the cost of higher volatility and risk.

The Sharpe Ratio, in itself, will not help investors choose between these two portfolio managers. That can only come from the investor considering their attitude to risk and their need to achieve a higher return to fund their investment goals, whether it is to pay college fees or fund retirement. That can only be done on an individual basis by each investor.

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