The Basics of Sharpe Ratio

The Sharpie Ratio is the “reward-to-variability ratio” written by Professor William F. Sharpe. It has proven to be one of the most effective and advanced risk/return estimation tools in finance that measures risk-adjusted performance. Through applying this ratio it is feasible to estimate if portfolio's returns are due to smart investment decisions or an outcome of excess risk. This becomes extremely useful for estimation of one’s strategy and fine-tuning of Your investment decisions.

The Sharpe Ratio

William F. Sharpe

In 1966 Stanford professor and Nobel laureate William F. Sharpe wrote about the “reward-to-variability ratio” which after some time became known as "The Sharpe Ratio". Since then, it has been one of the most advanced risk/return estimation tools in finance.

In 1990 Professor Sharpe won a Nobel Memorial Prize in Economic Sciences for his work on the Capital Asset Pricing Model (CAPM) which promoted the truthfulness of the ratio.

Sharpe developed the ratio to measure the risk-adjusted performance. The Sharpe ratio is a ratio of return versus risk. Appling this ratio makes it possible to conduct a comparative analysis of coequal portfolios on the basis of risk-return ratio and choose the optimal one i.e. the portfolio where higher returns do not come along with excessive risk.

To understand how the ratio works it's important to explain its formula:

Sharpe Ratio = (Rx - Rf) / StdDev

where:

Rx = the expected return on the investor's portfolio
Rf = the risk-free rate of return
StdDev = the portfolio's standard deviation, a measure of risk.

For example, let us assume that next year you expect your stock portfolio return to be 15%. If the returns on risk-free Treasury notes are, say, 3%, and your portfolio carries a 0.08 standard deviation, then you can easily calculate the Sharpe ratio for your portfolio according to the above-mentioned formula:

(0.15 - 0.03)/0.08 = 1.5

Note, that if portfolio A brings about, say, 20% return with a Sharpe ratio of 1.30 and portfolio B also brings a 20% return with the Sharpe ratio of 1.00, then surely A is the better portfolio because it achieves the same return with less risk.

Return (Rx)

The returns can be measured daily, weekly, monthly or annually, as much time as they are normally distributed, since the returns can always be annualized. In this case the main weakness of the ratio is that not all asset returns are normally distributed.

Risk-Free Rate of Return (Rf )

The risk-free rate of return shows whether you are compensated for the additional risk that you carry when investing in a risky asset. Though risk free security has the least volatility, there is a view that the given risk-free security should match the duration of the investment it is being compared against.

Standard Deviation (StdDev)

After calculating the excess return by subtracting the return of the risky asset from the risk-free rate of return, it is necessary to divide the result by the standard deviation of the risky asset. Standard deviation represents the statistical measurement of dispersion about an average, which shows how widely portfolio’s returns varied over a specific period of time. The standard deviation of historical performance is used by investors to predict the range of returns that seems to be most likely for a given investment. The predicted range of performance is wide and implies greater volatility in case investment has a high standard deviation.

The higher the Standard Deviation is the better investment will be expected from a risk/return perspective. However, if the standard deviation is not large, leverage may not have an impact on the ratio. No problem occurs when doubling the return and standard deviation. Only in case of excessively high standard deviation some problems may occur.

Thus, the basic concept of the Sharpe Ratio is to see how much additional return you get for the additional volatility of holding the risky asset over a risk-free asset - the higher the ratio, the better it is.

  • Higher Sharpe ratio signifies more return per unit of risk.
  • Lower Sharpe ratio is a sign of more risk carried by the investor to gain additional returns.

Through showing which portfolio carries the highest risk the Sharpe ratio levels the playing field.