# How to Calculate Sharpe Ratio and Sortino Ratio Correctly on Day Trading Strategies

By Lawrence

## What is Sharpe Ratio?

To make it short, Sharpe Ratio is a measure of an investment compared to a risk-free asset adjusted for its risk. It was created by William Sharpe back in 1966 before many of us were born. It tells you the expected return of your investment (or trading strategy) per unit of increased risk.

Hence, a negative Sharpe Ratio is obviously not desirable. Positive Sharpe Ratio greater than one is what many fund managers trying to maintain with their asset allocation in order to keep their clients happy. Sharpe Ratio of 2 or more is considered as good comparing to majority of the fund performance out there. With a Sharpe Ratio of 3 or more makes you a star in the financial industry.

The calculation of Sharpe Ratio is based on the periodic changes of the asset value and the statistical variation of this periodic change. For most people, you would collect the daily net value of your investment (or the accumulated profit / loss of your trading strategy) to compute the answer. It is a simple process hence the value is computed in all trading platforms with backtesting capability.

Sortino Ratio focuses on the deviations of negative returns to better measure the ability of an asset or strategy to recover from drawdowns.

## What’s Wrong With the Standard Calculation of Sharpe Ratio When Applied to a Day Trading Strategy?

The underlying reason of using daily net value of an asset to measure the day to day changes is that the price of the next trading day depends on the price from the previous one. In other words, the risk comes from overnight. The daily, weekly or even monthly net changes is a measure of the risk taken from one period to the next. But this is not true for a day trading strategy that you are backtesting or deploying because there is no overnight risk.

Let’s look at an example here as a comparison. Say a fund manager added a stock to his portfolio. The changes in price of the stock implies more than just a change in the number. If over the years, the stock price increased 100%, the underlying company may have also increased its revenue by say 50% with profit margin improved by 30%. Hence measuring the change in stock price by percentage, lack of other alternative, is a reasonable way to measure the performance of the entity as a whole.

However, it is a completely different story when you are looking at a day trading strategy with, say, a fixed initial capital, to trade a fixed number of contracts. It is the basic form of all strategies. The accumulated net profit / loss from the previous trading day is independent from the performance of the very next trading day. The monthly performance measured as a percentage of the accumulated net value from previous month has no meaning at all as the algorithm is not using all the capitals available at the time to trade.

The same performance of 10% increase in the first year of backtesting can become 1% or less in the 20th year of backtesting (if you have a decent trading strategy) even though you are committing the same risk off the same initial capital to generate that return in the 20th year.

The classic Sharpe Ratio and all its variations break down on day trading strategies as the underlying assumption is not valid.

Of course, you can complicate things by adding scaling algorithm into your day trading strategy to adjust position size according to the accumulated capital. However, that will turn the strategy dependent on the equity curve and distort the Sharpe Ratio from measuring the efficiency of the original design.

In other words, even if you have an exceptionally good day trading strategy created, all these trading platforms out there will report it as something mediocre. The better the strategy and the more consistently it performs over the years, the more penalty it will take from the standard Sharpe Ratio calculation. If all you do is gunning for a high Sharpe Ratio reported by these platforms, you are being misled all these years.

## How to Fix the Calculation

So how do we get the correct Sharpe Ratio for a day trading strategy without adding the burden of position sizing?

Once you realize that the periodic comparison is incorrect, all you have to do is substitute that with something that make sense. The only figure that makes sense is, of course, the initial capital. By computing the net percentage change based on the initial capital from the actual periodic net changes, and follow thru with the rest of the Sharpe Ratio formula, you will get the correct Sharpe Ratio for your day trading strategy.

This poses a difficult problem for many day trading strategy developers. The custom calculation is not readily available in their development platforms. So, it will be hard for you to see if one variation of your design is better than the other in terms of Sharpe Ratio.

Since not all platforms report the complete set of monthly return figures, you will need to generate that yourself through other means. For example, Tradestation does not provide the information in its strategy performance report but you can easily generate that through the use of a simple indicator.

## It Makes Sense

Since the purpose of Sharpe Ratio is to measure the return in terms of unit risk, the modified calculation above serve that purpose well.

If you are picky, you probably think of Sortino Ratio and other derivatives of Sharpe.

This is also what many readers have been asking me over the years – how do they tell if a day trading strategy is any good.

If the Sharpe Ratio you get based on the formula above is better than 1.5, your strategy is a reasonably good one.

## Using Big-Game Hunter ES as an Example

Big-Game Hunter ES is a day trading strategy designed to trade the Emini S&P. It has a very consistent performance over the past 23 years. Here is the net profit curve after commission and slippage.

With such consistent performance, you would expect it has a pretty good Sharpe Ratio, right?

Well, due to the fact that the performance you see here does not include position sizing, hence lacking the exponential growth effect, using standard way to calculate the Sharpe Ratio does not tell the true story of the strategy.

MultiCharts gives BGH a monthly Sharpe Ratio of 0.48 and Annualized Sharpe Ratio of 1.66. Sortino Ratio is reported at 1.96.

The shorter the backtest period, the higher the metric figures, no matter which part of the history you choose to backtest.

For example, if we cut short the backtesting to go up to the end of year 2009. The annualized Sharpe reported would be 1.93 and Sortino Ratio would be at 2.73. The problem, of course, is not that the trading strategy has degraded in performance afterwards. It is the way the original Sharpe Ratio formula penalizes consistently performing day trading strategies with no change to its position sizing.

Following is a table comparing the figures side by side.

From the table, it is clear that the standard calculation distorted the return and the variance, leading to a suppressed value of the Sharpe Ratio and exaggerated value of the Sortino Ratio.

My suggested modification to the formula would result in more consistent reporting of both figures no matter what the historical backtesting duration is.

## Summary

Day trading is the exploitation of intraday price movements. However, Sharpe Ratio was invented in a different era and its design is inheritedly not for the measurement of day trading strategy performance. Majority of those who are inspired to create their day trading strategies with a good Sharpe Ratio are probably surprised that Sharpe Ratio is not friendly towards responsible backtesting.

So is Sharpe Ratio useless then? Not necessary.

Finance industry has standardized their measure of performance using these metrics. Even for day trading, a fund manager deploying multiple day trading strategies will still need to fall back onto figures like Sharpe Ratio to allow them to compare their performance against the norm.

The issue I raised in this article is mainly a problem that during research and development, the standard Sharpe Ratio calculation and other related metrics on commercial trading platforms can easily mislead the research effort into giving up good strategies for the wrong reasons.

Part of my book project, Defensive Money Management Explained

## References

Sharpe Ratio at Wikipedia

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