## Quant Trading (and HFT): Performance 101

*Understanding the Core Principles of Trading Performance*

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It’s hard to believe that 10 years have passed since the publication of the second edition of High-Frequency Trading: A Practical Guide to Algorithmic Strategies and Trading Systems (Wiley, 2013). I am grateful for all the positive feedback and the nearly 700 citations the book has accumulated over the years, according to Google Scholar.

In the age of Artificial Intelligence (AI), it is very tempting to focus on the latest technologies and sideline the core principles of trading. This article attempts to address the very basic concept of trading: trading performance. Perhaps this can be useful to students of trading, academics and, potentially, some practitioners as well.

Most of the trading process is about successful prediction, and AI can be enormously helpful with that. To trade successfully is to profit, and to profit one needs to buy low and sell high, in any order of operation. Can you predict with reasonable accuracy whether the markets are going up? If so, you buy a market ETF, like SPY, and wait for your prediction to come true, then sell to realize the gain. Or, you can run a sophisticated portfolio management model to predict which combination of assets to buy and sell to maximize your gain. You may also predict whether futures and options are a better bet given the current market conditions. Separately, you may examine corporate strategy and financials to predict if a given firm is in danger of default or a bankruptcy, like Virgin Galactic.

Consider Wrapped Ethereum (WETH), for example. Figure 1 shows the price chart of this crypto currency. The appreciation of WETH in the post-COVID boom attracted many crypto enthusiasts. Many turned into HODLers (Holding On for Dear Life), even as the industry hit “crypto winter” with rapidly decaying numbers. An objective measure like Sharpe Ratio may be helpful to investors not only as a measure of past performance, but as a decision tool about the future investing as well, as this article attempts to show.

The key question we look at in this note is how do you actually know if your prediction is worthwhile. Many current and prospective traders have differing opinions on the subject. Some perhaps beginner traders look at the overall positive gain and consider it to be a “good enough” success. Others swear by the historical probability of correct predictions, or “hit rate.” Mathematically, these measures are interesting, but we can do better. And the better and widely established measure of success is Sharpe Ratio developed by William Sharpe (1954).

Dr. Sharpe is a brilliant Academic, a Nobel Prize winner, and a consultant. According to a legend, he developed the Sharpe Ratio while being tasked by his client, a large pension fund, to create a simple metric that would objectively capture various statistical components of various investments, be it stocks, investment portfolios or something else.

Dr. Sharpe looked at the fundamental properties of financial returns. A simple return is a percentage change in the given asset’s price: the difference in prices divided by the price at the beginning of the measurement period. The return can be measured over a year, a day, or in the high-frequency world, over a millisecond. The high-frequency volume clock, developed by Cornell University professors David Easley, Marco Lopez de Prado and Maureen O’Hara (2012) even suggests calculating returns over fixed trading volume intervals instead of actual time.

In financial engineering, researchers often use logarithmic returns instead of simple returns mainly because logarithmic returns easily lend to differentiation and are therefore useful in various derivative equations. The return properties of simple and logarithmic returns, however, are very similar.

Once the returns are computed, the financial desirability of the investment can be estimated as the average returns divided by the returns’ standard deviation. This relation is known as the Sharpe Ratio. Sharpe Ratio effectively measures the average return per unit of risk, the latter measured by the standard deviation of returns. Many may also recognize Sharpe ratio as a Z-score or a t-statistic used in numerous linear regression studies.

To compare investments of different time durations, researchers annualize the Sharpe ratios, that is convert the Sharpe to the annual basis. To annualize the Sharpe ratio, one needs to multiply the per-period Sharpe ratio by the square root of the number of computational periods in a year. Thus, to convert the Sharpe computed based on monthly returns to the annualized Sharpe, multiply the monthly Sharpe by the square root of 12. To convert the daily Sharpe into the annualized Sharpe, multiply the daily Sharpe by the square root of the number of daily trading intervals per year: roughly 251 for equities, and 365 for cryptocurrencies and other digital assets.

How big does the Sharpe ratio need to be for a successful investment? The simple answer is “the bigger, the better”. The simple returns and the computed Sharpe ratio typically do not include the trading costs, which will eat into the actual performance. The Sharpe ratio of 3.5 is often considered to be the minimum required for any professional investments. To be hired as a trader at a successful organization like Citadel, one probably needs a Sharpe ratio of around 10. Successful HFT strategies can deliver a Sharpe of 40.

Going back to Wrapped Ethereum (WETH) and measuring its Sharpe ratio based on daily buy and hold returns from February 2, 2018, through June 7, 2023, we obtain 0.68. Granted, it’s been a crypto winter. Would things look drastically differently in, say, May 2020? The Sharpe ratio based on WETH daily returns from February 2, 2018, through April 30, 2020, we obtain an even worse 0.22. Well, how about at its peak in May 2021? Sorry, HODLer folks, it was still just 0.91.

Of course, here we did not consider any prediction strategies at all. Lots of room for improvement exists. HFT and AI both can be deployed to supercharge returns and raise Sharpe ratios to acceptable levels. The beauty of the Sharpe ratio is that it universally applies to all strategies, all instruments and all time horizons and allows us to knowledgeably choose better trading and investment opportunities.

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