Education

# Calculating Sharpe Ratio in Forex

The Sharpe Ratio is one of the most popular investment evaluation techniques. The Sharpe Ratio is a commonly used formula throughout the investment world and has been for decades. The Sharpe Ratio is used to compare the return on investment compared to the amount of risk that was taken to achieve the profit. Typically you will hear about the Sharpe Ratio in the context of evaluating the performance of a fund or portfolio. It can also be beneficial to use the Sharpe Ratio in forex, and that is something we will explore in this article.

## How Sharpe Ratio Helps Forex Traders

It’s not easy to compare two forex trading strategies, primarily due to the numerous variables that could be involved. For example;

• What currency pairs are being traded?
• How many different pairs are being traded at the same time?
• How long are positions being held for?
• Are multiple positions being held concurrently
• How many trades are placed in a day
• How big are the positions
• What is the risk to reward ratio

You might be wondering why it matters how or what the strategy is trading so long as it’s profitable. Of course, profit is important. However, the return on investment is not the only metric that determines the appeal of a forex strategy. In fact, a highly profitable trading strategy may only be achieving impressive gains because incredibly risky decisions are being made. By applying the Sharpe Ratio to a forex strategy, you’re able to see a ratio of how much risk was taken to generate the profit.

Considering that forex trading is notoriously risky due to the application of leverage combined with the volatility of the market, comparing the risk trading strategies is a vital skill to possess.

## How Does the Sharpe Ratio Work?

Generally, the Sharpe Ratio is applied to the performance of a portfolio that may contain different instruments and asset classes where trades have variable order sizes and entry & exit points and exits. It can also be used to evaluate an individual trade or subset of transactions. For example, if you have been trading EUR/USD and USD/JPY and want to compare the risk to reward ratio of each currency pair, that can be easily achieved.

To calculate the Sharpe Ratio, you need to collect a few details, there are;

• The return on investment
• The risk-free rate of return
• The standard deviation

In this article, we will walk through an example of calculating the Sharpe Ratio of a forex strategy from the 1st of September 2019 to the 30th of September 2020. The trading account in this example is denominated in US dollars and was funded with \$10,000. At the end of the 12 months, the account balance was \$13,440.91.

## The Return on Investment

The return on investment is quite simply how much money you made on an investment over a certain period. To calculate the RoI of your account, all you need to do is take your account balance today (\$13,440.91) which is considered the current value of your investment and subtract it from your account balance on the first day of the 12-month period (\$10,000) which is regarded as the cost of the investment. Then you divide the number by the cost of investment.

13,440.91 – 10,000 = 3,440.91

3,440.91 ÷ 10,000 = 0.344091

0.344091 ⨉ 100 = 34.4%

Your return on investment will be 34.4%

## The Risk-Free Rate of Return

The risk-free rate of return is actually quite confusing as it has no correlation to your trading strategy. The risk-free rate of return tries to remove any upside that could have been achieved had you alternatively put your money in an investment that has no downside. Essentially, the risk-free rate of return is the return on investment of an asset that is as close to risk-free as possible.

There is no fixed definition for what source should be used to get the risk-free rate of return value. As a general rule, if you’re investing in US stocks, you may use US Treasury Bonds, if you’re investing in UK stocks, then you could use gilts, or if you’re investing in European stocks, then you could use Eurobonds (denominated in Euros).

As a Forex trader, it can be tricky to decide which risk-free rate of return correlates to your trading strategy, particularly if you’re trading different currency pairs and even precious metals and energy products. The most straightforward value that could be used is a US Treasury bond yield that correlates to the period you’re analysing with the Sharpe Ratio.

As we will continue with our example of using the Sharpe Ratio to assess the performance of a forex strategy over 12 months, and our trading account balance is denominated in USD, we could use 12-month US Treasury Bonds. The average yield rate between the 3rd of September 2019 and the 30th of September 2020 was 0.81%.

The risk-free return rate of return we will use in the Sharpe Ratio is 0.81%.

## The Standard Deviation

As the Sharpe Ratio is designed to show how much risk is being taken to achieve our returns, the Standard Deviation component of the formula introduces the volatility measurement, and naturally, volatility implies risk.

You may have the term Standard Deviation. If you have, that’s because it’s a pretty standard technical analysis indicator for measuring price volatility by showing how far prices have moved from the moving average price. Standard Deviation is a common mathematical principle that is not just applicable to assessing price volatility.

Calculating the Standard Deviation of your trading account is very similar to a typical candlestick chart with a Standard Deviation applied on top of it shows how far prices spread out from the moving average price.

Every time you open and close a trade inside your account, the balance goes up and down according to profit and loss. Standard Deviation of a trading strategy also considers the weight of each trade, i.e. how large was it.

Standard Deviation is not very manageable to calculate and will undoubtedly require some assistance from an Excel spreadsheet. As you can imagine, one-year of trading history will have a lot of data to be processed to get the final figure.

To proceed with the example, we can conclude the Standard Deviation of this trading strategy is 40%.

## Calculating The Sharpe Ratio

Now we’ve collected all the necessary parameters for the equation; we can now calculate the Sharpe Ratio of the trading strategy.

To break down the formula:

S(x) = Sharpe Ratio

x = Investment

Rx = Return on Investment

Rf = Risk-free Rate

StdDev (x) = Standard Deviation of rx

34.4% – 0.81% = 33.59%

33.59% ÷ 40% = 0.83975

The trading strategy we just analysed has a Sharpe Ratio of 0.84.

## What is a Good Sharpe Ratio?

Generally speaking, the higher the Sharpe Ratio, the better. But that isn’t always the case. A good Sharpe Ratio can be quite subjective. Consider the risk-free rate of return component of the calculation. In our example, we used the 12-month US Treasury Bonds, if we applied the Sharpe Ratio to this asset, it would be zero.

A negative Sharpe Ratio is not a good thing at all as it highlights that you could have made more money just by sticking it into whatever asset was used as the risk-free rate of return. You want an investment that carries a level of risk to perform better than fixed income products.

## How to Use Sharpe Ratio in Forex

The Sharpe Ratio of a forex strategy is not a determining factor on its own. The Sharpe Ratio can be especially helpful when it comes to comparing different methods and techniques but should not be used to make conclusions without any other supporting metrics.

Having a profitable trading strategy with low volatility is a great target to try and meet, but it should not rule your life. The Sharpe Ratio is one of many other evaluation techniques that attempt to sum up performance in a single number. It also depends on how the risk-free rate of return is calculated. As of October 2020, Bond-Yields are incredibly low, which automatically increases the Sharpe Ratio without any improvement to the performance of the strategy or reduction of risk.

Check the table below with a few examples of strategies and their Sharpe Ratio according to a risk-free rate of return of 1%. Strategy #1 generates half as much return as Strategy #2, but it has less than half the risk. Yet the Sharpe Ratio is lower, indicating that Strategy #1 isn’t as good as Strategy #2 which therefore proves that Sharpe Ratios are open to interpretation.

## A Few Words About William Sharpe

William Forsyth Sharpe created the Sharpe Ratio in 1966. The most recent revision he made to the ratio was completed in 1994 and has remained as it is since then. Sharpe is an American economist who made numerous significant contributions to the financial services industry. He won the 1990 Nobel Prize in Economic Sciences alongside Merton Miller and Harry Markowitz for developing models that assist with evaluating investment products. Besides creating the Sharpe Ratio, Sharpe was involved in the development of the capital asset pricing model (CAPM), binomial method for the valuation of options and many other notable contributions. In March 2018, Sharpes’ company Financial Engines was acquired for \$3 billion, and he is now retired.