Mathematical prodigies often appear in TV shows and movies, applying their computational advantages to an array of tasks from solving crime, to winning at the tables in Vegas, to earning fortunes exploiting the stock market. But in the real world, can math really help prospective investors reap enormous profits in the stock market?

Kane Kalas, the managing principal of Crystal Oak Capital, a hedge fund, believes that mathematics can indeed help would-be investors achieve superior returns. The trick, he believes, lies in analysing data from a statistical lens to improve your chances of success and to render the risk of ruin a statistical impossibility.

**Can The Market Be Beaten By Mathematical Models?**

Over time, mathematical models are becoming more predictive of financial markets. High-frequency trading bots are commonplace among financial firms and produce considerable alpha. Nonetheless, in 2021, a huge minority of trades executed in the stock market are at the behest of a mathematical trading algorithm.

**Applying Mathematics To Trading is Not as Perfect as Mathematics Itself**

There is a general misconception that a successful trader will be accurate almost 100% of the time. While mathematical trading systems cannot perfectly predict what’s going to happen in the future, they can certainly increase a trader’s chance of success.

Kalas reassured us that a level of accuracy of a stock trade anywhere near 100% is simply impossible to achieve. Generally, successful traders turn a profit on anywhere from 35-70% of their trades, depending on the average size of their losses vs. their wins.

**Gaussian Laws And Power Laws**

Two mathematical laws that have proven popular with traders in recent years are Gaussian laws and Power laws. Gaussian math calculates uncorrelated entities as they randomly fluctuate. The application to the stock market here is obvious; there are thousands of events that could move a particular stock’s price many of which could be entirely uncorrelated from one another.

It’s important to remember though that events including stock movements that are normally uncorrelated can become correlated based on investor emotion. Gaussian logic cannot predict irrational stock market bubbles or dramatic stock market crashes emanating from market manias and panics.

Power law, on the other hand, calculates how the value changes of one variable will affect another correlated variable – for example, how one company’s increase in sales will affect stock prices within its sector. This law relates to the calculation of standard deviation, a metric that is used in a number of risk calculations including the Sharpe ratio and Sortino score.

Both Gaussian law and Power-law are far from perfect indicators of stock market performance. Prudent investors must understand these limitations and are advised to only use these laws as one of many factors that may guide their overall investment decisions.

**The Power Of Quantitative Analysis**

Where math can truly excel in the investment markets, according to Kalas, is in quantitative analysis. Quantitative analysis is the mathematical model that traders use to increase alpha and reduce risk. Quantitative models attempt to examine historical relationships between variables.

While quant models are not efficient at predicting future outcomes every time (often correlations observes from previous data in random or market conditions have changed) investors should carefully consider why a correlation might have been observed between two variables and form an educated opinion about the likelihood of that correlation continuing into the future.

Kalas points out that while even the most advanced mathematical systems cannot predict movements in asset prices with pinpoint accuracy, as technology and artificial intelligence improves, we are approaching an age in which this may be possible.

Kalas considers himself a quant as well as an arbitrage investor. Unlike a majority of quant traders who enter and exit positions rapidly, Kalas uses quantitative algorithms and mathematical models to identify medium-to-long-term investment opportunities. When asked about quant-based investment, Kalas opined,

“Computer models increasingly outperform humans in every field that involves game theory as long as they are given sufficient data. Algorithms can analyse the correlations between countless variables and a security’s price, and this can often reveal relationships which human intuition could never have imagined.”

This is the basis on which Kalas makes a majority of his investment decisions for Crystal Oak Partners, the hedge fund that he owns and manages. The fund uses quantitative data to trade foreign and US securities with a long-short trading strategy.

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