Sharpe ratio: What it is and what it is for

The Sharpe ratio is a mathematical formula based on the idea that excess returns over a period of time can mean more volatility and risk than investing skill. That is, it compares the profitability of an investment with its risk. Let's see what the Sharpe ratio is, what it is for and how to calculate it.

What is the Sharpe ratio

The Sharpe ratio compares the profitability of an investment with its risk. It is a mathematical formula for the idea that excess returns over a period of time can mean more volatility and risk than investing skill.. Economist William F. Sharpe proposed the Sharpe ratio in 1966 as a consequence of his work on the capital asset pricing model (CAPM), calling it reward/variability ratio. Sharpe won the Nobel Prize in Economics for his work on the CAPM in 1990. The numerator of the Sharpe ratio is the difference over time between realized, or expected, profitability and a reference value, such as the risk-free rate of return or the profitability of a specific investment category. Its denominator is standard deviation of profitability over the same period of time, a measure of volatility and risk.

What is the Sharpe ratio for?

The Sharpe ratio is one of the most used methods to measure risk-adjusted relative return. Compares a fund's historical or expected performance relative to an investment benchmark with the historical or expected variability of that performance. In more general terms, represents the risk premium of an investment compared to a safe asset such as a bond. When compared to the profitability of a sector or investment strategy, the Sharpe ratio provides us with a measure of return adjusted to non-attributable risk. It is useful in determining the extent to which excess historical returns are accompanied by excess volatility. While excess returns are measured against an investment benchmark, the standard deviation formula measures volatility based on the variance of the return with respect to its mean. The higher the Sharpe ratio of a portfolio, the better its risk-adjusted return.. A negative Sharpe ratio means that the risk-free or benchmark interest rate is higher than the historical or expected return of the portfolio, or that the portfolio's return is expected to be negative.

How the Sharpe ratio is calculated

The value of the Sharpe ratio It is obtained from the variability of the profitability of a series of time intervals that add up to the total of the performance sample considered.. The total return differential of the numerator against a reference index (Rp – Rf) is calculated as the average of the return differentials in each of the incremental time periods that make up the total. For example, the numerator of a 10-year Sharpe ratio could be the average of a fund's 120 monthly return spreads versus an industry benchmark. In this example, the denominator of the Sharpe ratio will be the standard deviation of these monthly returns, calculated as follows:

• We take the variance of the average profitability in each of the incremental periods, square it and add the squares of all the incremental periods.
• We divide the sum by the number of incremental periods.
• We take the square root of the coefficient.

Example of using the Sharpe ratio

The Sharpe ratio is sometimes used to evaluate how adding an investment could affect the risk-adjusted return of the portfolio. Let's take an example. An investor is considering adding an ETF allocation to a portfolio that has generated a return of 18% over the last year. The Current risk free rate is 3%, and the annualized standard deviation of the monthly portfolio return is 12%, which gives a One-year Sharpe ratio of 1,25. The investor believes that adding an investment to the portfolio could affect the risk-adjusted return. Therefore, the investor can interpret that adding an ETF to the portfolio will reduce the expected profitability to 15% for next year, but also hopes that the Portfolio volatility drops to 8% as a result. The risk-free rate is expected to remain the same over the next year. Using the same formula with the estimated future figures, the investor will discover that The portfolio would have a projected Sharpe ratio of 1,5. Sharpe ratios greater than 1 are usually considered good, since they offer excess profitability in relation to volatility. Yes, investors They usually compare the Sharpe ratio of a portfolio or fund with those of its peers or market sector. For example, a portfolio with A Sharpe ratio of 1 could be considered poor if most of your rivals have ratios greater than 1,2. A good Sharpe ratio in one context may be more or less good in another.