# Sharpe ratio

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Developed in 1966 by Nobel Laureate William Sharpe, the ratio is used to measure and compare the level of risk in a portfolio. The higher the Sharpe ratio, the better a portfolio has performed relative to the risk taken.

As an example, if two portfolio managers, A and B, have enjoyed successive returns of 20% in the last three years, but A has a Sharpe ratio of 1.07 and B has a Sharpe ratio of 0.79, then A took on less risk than B to achieve the same return.

The Sharpe ratio tells us whether a portfolio’s returns are due to smart investment decisions or a result of excess risk.

### The formula for the Sharpe ratio

The ratio was developed by Nobel laureate William F. Sharpe in 1966. It is calculated by:

• Subtracting the risk-free interest rate – for instance, the one given by the 10-year US Treasury bond – from the rate of return of a portfolio;
• Dividing the result by the standard deviation of the portfolio returns (the standard deviation measures the volatility of the portfolio).

The formula is the following:

Rp – Rf / σ

Where:

Rp = expected portfolio returns

Rf = risk-free interest rate

σ = standard deviation of the portfolio

### A simple explanation of the Sharpe ratio

Now, do not panic! This looks complex, but it has quite simple implications.

In practical terms, the Sharpe ratio asks first how much the rate of return of your portfolio is. To do this, it calculates:

Rp – Rf

This measures the difference between the return of your portfolio – usually on an annual basis – and the interest rate you would get by simply buying a 3-month US Treasury bill.

The Sharpe ratio shows two things: first, if your strategy is making more money than the risk-free interest rate; second, it relates your profits to the amount of risk you are taking. In other words, the Sharpe ratio tells you whether you are a smart trader or simply a risk-taker.

In other words, this part of the formula shows you if your trading or investment strategy is actually making money, or if you would be better off by forgetting about it and buying Treasury bills instead.

Now, let us say that your strategy is making more money than the interest rate you would get on a US treasury bill. At this point, the Sharpe ratio asks the second question: are you making more money because of your skills or because you are simply risking more than other investors?

To answer this question, the Sharpe ratio divides the first part of the fraction (Rp – Rf ) by the so-called standard deviation (σp).

### What is the standard deviation?

In finance, this is often identified with the Greek letter known as ‘sigma’ and it is used to assess the volatility of an investment.

Calculating volatility through the standard deviation can be daunting and it should not concern us here. The important thing about this measure is that it tells us how much the return of your portfolio rises or falls compared to its mean return in a given period of time.

To put it differently, if returns are so volatile that they move up and down considerably, this means that your portfolio is exposed to a higher risk because its performance is subject to quick changes in both favourable and unfavourable directions.

### How to use the Sharpe ratio effectively

Sharpe ratios work best when taking into account at least three years of a portfolio’s performance. Keep in mind that standard deviation measures the volatility of a fund’s return in absolute terms, not relative to an index. Given no other information, it’s impossible to tell whether a Sharpe ratio of 1.07 is good or bad.

Only when you compare one portfolio’s Sharpe ratio with that of another portfolio do you get a feel for its risk-adjusted return. When used in conjunction with other measures, the Sharpe ratio can help investors develop a strategy that matches both their return needs and risk tolerance.

## Sortino ratio

A variation of the Sharpe ratio is the Sortino ratio, which removes the effects of upward price movements on the standard deviation to measure only the return against downward price volatility.