Forex Trading Statistics: Understanding Sharpe ratio and Sortino Ratio

Sharpe ratio and Sortino ratios are perhaps the two most commonly cited terms when it comes to trading statistics. For the absolute beginner to trading, these ratios may seem like an alien concept. However, the further you grow as a trader, the more frequent, you come across these terms.

If you feel confused or intimidated by these terms, then worry not. This article explains the Sharpe ratio and Sortino ratio in simple terms. By the end of this article, you will learn what these two ratios are and where they are used.

These ratios are important especially if you are on the lookout for a copy trading system or an automated trading strategy. Understanding these ratios and learning how to interpret them will help traders potentially sieve through the numerous trading systems and copy trading accounts that are available.

It is also prudent for the forex investor, especially if they want to invest money into another trading account by usual a social copy trading system for example. Many traders tend to shy away from learning about these factors or ratios. However, although it may seem intimidating at first, these ratios are relatively easy to comprehend.

You can also apply these concepts to building your own excel sheet and assess your own trading performance. Of course, this is applicable only if you are serious about building a long-term career in forex trading. Going into details such as estimating the Sharpe ratio or the Sortino ratios will give you more insights into your trading strategy.

So without further ado, let’s deep dive into what the Sharpe ratio and Sortino ratio mean. Learn how you can use these key ratios to estimate the various performance levels of trading accounts and automated trading strategies.

What are Sharpe and Sortino Ratios?

The Sharpe ratio and the Sortino ratio are two risk ratios used to measure the effectiveness of a trading strategy. Broadly speaking, these two ratios measure the effectiveness of a portfolio that can comprise stocks or other assets.

From a forex trading perspective, when looking at these two ratios, one will be able to gauge whether the trading system or strategy provides good enough returns when adjusted for the risk it takes. In the investing world, one of the key aspects is risk and return.

Any investment is expected to give a certain return, for the risk it takes.

When choosing to invest in a fund, or in a trading strategy from a forex perspective, investors look at whether the returns justify the risk taken. This is basically what Sharpe and Sortino ratios tend to answer.

Sharpe ratio and Sortino ratio answer the question of whether the returns are justified by the risk taken by a trading strategy, also known as a risk-adjusted return.

In other words, these two ratios combined answer the question of at what cost are the returns being made. Is the strategy using a high risk? And more importantly, are the returns justified for the risk taken.

Whether you are looking to invest in a forex fund management company, or looking to copy trades from another trader, or even purchase an automated trading strategy, Sharpe and Sortino ratios are key ratios to keep an eye on.

There are many types of ratios, but commonly, we can drill them down into four main types:

• Sharpe Ratio
• Sortino Ratio
• Treynor Ratio
• Calmar Ratio

Definition of the Sharpe ratio

The Sharpe ratio is the most popular among the four ratios mentioned earlier. The Sharpe ratio measures the excess return (on top of the risk-free rate), compared to its volatility. The Sharpe ratio was developed by William F. Sharpe, a Nobel laureate.

Although William F. Sharpe is widely attributed for the Sharpe ratio, his biggest contribution was to the creation of the CAPM or the Capital Asset Pricing Model. The formula for the Sharpe ratio is:

• The expected Portfolio return is nothing but the returns from your trading system or the portfolio
• The risk-free rate of return can be the risk-free rate that you earn (government securities)
• The standard deviation of the excess portfolio returns is the standard deviation of the returns above the risk free rate

How to calculate Sharpe ratio?

Sharpe ratio can be calculated in Excel, or you can also use scripting languages such as Python too. The first step is to get a summary of your trades. You can export the trading history from your MT4 trading platform.

The next step is to group these trades into periods. It is best to use a yearly time period. In doing this, you can get the “portfolio returns” on a yearly basis. The next column to the Expected portfolio return is the risk-free return as well.

This risk free rate can be any prevailing rate of your choice. For example, depending on where you live, you may get a certain interest rate for a fixed-term deposit. This can also serve as the risk free rate. By and large, investors use the Fed funds rate or treasuries to calculate the risk free rate.

Finally, we need to get the standard deviation of the excess portfolio returns. This is derived by subtracting the risk-free rate of return from the expected, or the portfolio returns. We then use a standard deviation of this excess portfolio return to derive the third variable.

The last step before deriving the Sharpe ratio is to take the averages. The screenshot from the excel calculation is seen below.

The above table, shows that the Sharpe ratio is 0.29. Then comes the next question as to what this means? Broadly speaking, a higher the Sharpe ratio, the better it is for the portfolio. The table below gives details on the different levels of Sharpe ratios and how to interpret the ratio itself.

Should you only consider the Sharpe ratio?

However, considering just the Sharpe ratio alone can be very misleading. In fact, academicians have concluded that Sharpe ratio itself has certain limitations. This mainly comes form the fact that the formula uses the Standard deviation.

Thus, if a portfolio is trading in assets that are more volatile, it can lead to a higher standard deviation. A higher standard deviation in turn can lead to a lower Sharpe ratio. Thus, learning about this fact, the question is how to consider the Sharpe ratio when assessing the performance of a trading system.

Let’s take an example.

The chart below shows an example of one of the Top forex trading systems. You can see that the Sharpe ratio is 0.15, which despite being a good trading system, fare poorly in terms of risk adjusted returns.

But as we know, Sharpe ratio in isolation does not really give you many details. Let’s now look at the top five trading systems from MyFxbook.

Trading System	Sharpe Ratio	Absolute Gain
#1	0.15	575.44%
#2	0.09	2503.55%
#3	0.13	1266.79%
#4	1.42	979.25%
#5	0.11	256.55%

We also plot the Absolute gain for comparison on how each of these trading systems is performing. Among the top 5, you can see that the fourth trading system has the highest Sharpe ratio, which is 1.42. Compare this with the trading system that ranked #1, and you will see that the Sharpe ratio here is just 0.15.

Thus, using Sharpe ratio, you can determine which of the two trading strategies are offering a higher risk-adjusted return.

What is the Sortino ratio and how to calculate it?

The Sortino ratio is yet another risk-adjusted return measure. The main difference is that Sortino ratio measures the return for each unit of downside risk. This is the main differentiating factor in the Sharpe ratio.

Similar to Sharpe ratio, a higher Sortino ratio is needed in order to ascertain whether the portfolio is yielding a good risk-adjusted return. The Sortino ratio was developed by Frank A. Sortino. It replaces the standard deviation of returns with the downside deviation.

The formula for Sortino ratio is:

• The average realized return is the average of returns over a period of time
• The expected rate of return is also known as the risk-free rate
• The downside risk deviation is the square root of the average of negative returns squared

With the above formula, we can now derive the Sortino ratio for the same example we used to get the Sharpe ratio.

Here, we have additional columns called negative returns which are squared and then averaged.  We then take the square root of the resulting number which can then be used to calculate the Sortino ratio.

Similar to the table outlined for the Sharpe ratio, the Sortino ratio also has its meanings.

Interpreting the Sharpe ratio and the Sortino ratio on a forex trading account

Now that we are able to derive the Sharpe ratio and the Sortino ratio, the obvious question that comes to mind is the relationship between these two ratios. From our above example, for the same portfolio returns, we see that the Sharpe ratio is lower than the Sortino ratio.

What this infers is that there is higher upside volatility (which is why the Sharpe ratio is lower) for the portfolio in question. This is evident from the fact that if you look at the returns closely, we have higher returns to the upside, namely 0.23 and 0.35 compared to the downside returns.

Although both measures of risk-adjusted returns spit out two different ratios, using this data one can easily understand the volatility of the returns and their skewness. But since we are using the Sortino ratio (as well as the Sharpe ratio) to compare portfolios within the forex asset class, ideally, the Sortino ratios should be well aligned especially if the two portfolios are trading the same instruments.

While there are different schools of thought as to which of these two are better, it is recommended that potential investors assess both these figures, due to the obvious differences. As we illustrated in the previous example of looking at various trading system performances, the risk-adjusted ratios can act as a guiding light in picking the correct trading system.

Of course, besides the Sharpe ratio and Sortino ratios, traders should also account for other trading statistics to get a full picture of the performance of the trading system in question. The Sharpe and Sortino ratios don’t necessarily have been to be used to assess a potential trading system.

Using the Sharpe ratio and Sortino ratio - Conclusion

One can also apply the formula outlined in this article to their own trading systems as well. This will give you a good idea of whether your trading is generating returns well adjusted for the risk taken or not.

As there are more and more automated trading platforms and the rise of social trading, it can be easy for traders to simply look at the headline returns and make a decision to use that strategy. However, when considering the risk-adjusted ratios, one can get a better picture.

This information will be helpful especially to understand if the fees charged by the trading system or the trading manager are justified or not. Besides the Sharpe ratio and the Sortino ratio, other key ratios to keep in mind include the drawdown, the trading history (usually at least a few years), and the returns on a yearly basis.

Using this data can help you assess how a trading system was faring during the different periods. One can further infer more data by understanding how the markets were faring during the periods of analysis to deduce whether the trading system is more suited for volatile markets or for trending markets.

As you may already know by now, the Sharpe ratio essentially penalizes your trading system when there is higher volatile. At the same time, it accounts for both positive and negative deviations. This is where the Sortino ratio comes into the picture as it accounts for the downside deviation or the negative deviation alone.