The Sharpe Ratio Explained (With Examples)

Last Updated on March 6, 2021 by Oddmund Groette

The Sharpe Ratio is a popular and widely used parameter for comparing the return and its risk. The name is given from its inventor, William Sharpe, who developed the ratio during the 1960s. Sharpe later won the Nobel Prize in economics in 1990 for his contributions to the financial industry.

The Sharpe Ratio measures the excess return compared to the risk-free rate per unit of risk. Risk is measured in terms of volatility. The ratio is used for any asset and its return, but mainly for funds that try to smooth the returns, for example, hedge funds and traders. It’s used less for traditional mutual funds.

This article covers what the ratio is, how it’s calculated, and how it’s used.

A hedge fund’s Sharpe Ratio

Let’s first explain the simple logic behind the Sharpe Ratio. We use a practical example from one of Europe’s oldest and largest asset managers: The Swedish Brummer & Partners. They have been 25 years in the business and manages about 10 billion USD spread among about ten different hedge funds across all asset classes. Below is the latest chart for December 2020, which shows how their Multi-Strategy has performed since 2002:

Brummer & Partner’s return. Source: Website.

The red line is the Multi-Strategy, a fund that allocates capital to about 10 different funds to diversify and smooth returns, while the grey line is the MSCI World Index. They both have about the same return, but Multi-Strategy has smaller drawdowns. Because of this, the Sharpe Ratio is much higher: 1.11 vs. 0.39. The difference should give a pretty good idea of what the Sharpe Ratio is all about:

If your strategy is volatile, you need to be compensated in the form of higher returns. When you evaluate an investment, professional managers look at the returns and the associated risks. It doesn’t make sense to earn a little more if you face the possibility of a higher drawdown. All things equal, investors prefer the smoothest returns.

Nevertheless, risk is very much a personal preference. If you are young, you can take greater risk in your portfolio because you have more time until retirement, while someone closer to retirement might be more conservative to avoid a significant drop just before he or she starts withdrawing money. The balance is difficult, and no mathematical number has ever predicted the future accurately.

Behavioral risk

Some readers might ask if it matters what the Sharpe Ratio is as long as the total return is the same. That’s a good question, and you are not alone. Even Warren Buffett has said numerous times that volatility is a poor measurement for risk.

However, the math tells us that a 50% drawdown needs a 100% return to get back to break even. Likewise, if you’re a long-term investor, a huge drawback puts a spanner in the works for your compounding.

We know that many traders and investors make behavioral mistakes. They sell during a panic, for example. The idea is that less volatility in the returns makes investors less likely to make irrational decisions. Moreover, a higher Sharpe Ratio means you can potentially increase the leverage.

How is the Sharpe Ratio calculated?

The Sharpe Ratio’s main idea is that investors should be compensated for the additional risk they undertake above the risk-free rate. In most cases, the risk-free rate is the 90 day Treasury Bills, which is regarded as the safest on the planet. If you own other assets than short-term Treasuries, you need to be compensated.

The formula can be broken down, in plain English, to this: The difference between the return of the portfolio and the risk-free return, divided by the standard deviation of the portfolio’s return:

(return on the investment/portfolio – the risk-free rate) / standard deviation of the investment returns

Let’s make a practical example: If your portfolio has returned 10%, the risk-free rate is 1%, and the standard deviation is 12%, the Sharpe Ratio would be 0.75 – a pretty good number over many years.

What is a good and bad Sharpe Ratio?

Money managers aim for a high Sharpe Ratio – a high as possible. The Sharpe Ratio’s main determinants are the return over the risk-free return, and the smoother the returns are (small variations in the returns). If your portfolio makes 0.5% per month like clockwork, for example, the ratio is high.

We can argue the ratio should be above one, which means the returns are greater than the risk. Excellent traders have a higher Sharpe Ratio, but many traders “blow-up” after a while (see more about Nassim Taleb below). We believe a number above 0.75 is acceptable over many years.

In practice, very few funds manage a ratio above 1, like Brummer & Partner in the example above. Anything above 1.5 is extraordinary. Opposite, a Sharpe Ratio below 0.5 could be improved.
If the Sharpe Ratio is negative, the return is worse than the risk-free rate and you would be better off in Treasuries.

What is the Sharpe Ratio of The Medallion Fund?

Jim Simons’ Medallion Fund is regarded as the most successful ever. What is their Sharpe Ratio? The fund is secretive and most investors are the fund’s employees. However, we quote from this website:

For a closer look at Medallion’s performance numbers, we reference Ziemba’s Scenarios for Risk Management and Global Investment Strategies. Astonishingly, out of the 148 months that elapsed between January 1993 and April 2005, Medallion only had 17 monthly losses. Out of 49 quarters in the same time period, Medallion only posted three quarterly losses. Additionally, it has seen a yearly Sharpe ratio of 1.68. In twelve plus years of trading, Rentec’s Medallion Fund has never had a down year.

The Sharpe Ratios of our strategies

Many of the strategies on this webpage have a high Sharpe Ratio, for example, this one:

The Sharpe Ratio is 2.98:

The calculation is done automatically by Amibroker and we are not sure what the default rate of the interest-free rate is.

Diversification increases the Sharpe ratio

The main reason for Brummer & Partners’ smooth equity return, is the diversification among uncorrelated funds. Brummer only accepts new management teams if the fund adds diversification to the existing teams/funds. Likewise, this should be the goal of your portfolio of strategies as well:

Nassim Nicholas Taleb on the Sharpe Ratio:

Taleb has written on Twitter that high Sharpe ratios are predictive of huge blowups. The more stable the return, the more likely the blowup. Volatile funds lose money; but not as much as nonvolatile ones. Long-Term Capital Management had smooth returns for many years – until they blew up and the FED stepped in to avoid repercussions throughout the financial system.

Taleb has a point. Be vary when you see stable and smooth returns. Even The Medallion Fund was close to disaster in 2007 when the market turned against them. Taleb says smooth returns don’t predict future Sharpe Ratios very well. (For those who don’t know Taleb: he’s famous for his Black Swan theory where he says infrequent black swans have truly huge consequences.) For example, Taleb argues the Bell curve (which shows the normal distribution) doesn’t apply to investment returns because most of the returns are closer to the average than the Bell curve suggests. He argues this is close to a sure sign that the risk of a Black Swan event is about to happen.

Taleb is no fan of Saudi-Arabia and uses that as an example of his ideas. For example, Italy has changed the political administration multiple times, while Saudi-Arabia has only had one ruling family in power for decades, which means Italy is the riskiest of the two. But this is the wrong way to look at it. If something does happen in Saudi-Arabia, it will have much greater consequences.

Of course, exposure to tail risk is difficult to assess, and Taleb offers little advice on dealing with it, except to argue that volatility is a poor way of measuring risk.

The limitations of the Sharpe Ratio

With the comments from Taleb in mind, the Sharpe Ratio has many limitations. Any measurement of standard deviations assumes the return to follow the Bell curve, ie. follow a normal distribution. This is, of course, not how it works in the real world. Violent spikes up and down come surprisingly and distort many algorithms. History never repeats itself 100%.

No matter how high your Sharpe Ratio is, be prepared for adverse movement in your portfolio by always having a safety margin. Never lower your guard.

 

Disclosure: We own units in Brummer & Partner’s Multistrategy. We are not financial advisors. Please do your own due diligence and investment research or consult a financial professional. All articles are our opinion – they are not suggestions to buy or sell any securities.