# Can mathematics really help in identifying investment opportunities? Kane Kalas thinks so

Mathematician geeks appear frequently in TV shows and movies, applying their computational power to solve a variety of problems, from solving crimes to winning at tables in Vegas to making a fortune in the stock market. But can mathematics really help potential investors in the real world make huge returns in the stock market?

Kane Kalas, managing director of hedge fund Crystal Oak Capital, believes that mathematics can really help potential investors achieve superior returns. The trick, he says, is to analyze the data with a statistical lens to increase your chances of success and make the risk of ruin statistically impossible.

Can mathematical models beat the market?

Over time, mathematical models become more predictive for financial markets. High-frequency trading bots are common among financial companies and provide significant alpha. However, in 2021, a huge number of trades in the stock market are done at the direction of a mathematical trading algorithm.

The application of mathematics to trading is not as perfect as the mathematics itself

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

Kalas assured us that it is simply impossible to achieve a level of accuracy close to 100%. Typically, successful traders profit from 35-70% of their trades, depending on the average size of their losses compared to their winnings.

Gauss and Power Laws

Two mathematical laws that have proven popular with traders in recent years are Gauss’s laws and power laws. Gaussian mathematics calculates uncorrelated objects as they fluctuate randomly. The application to the stock market is obvious here; There are thousands of events that can change the price of a particular stock, many of which may be completely uncorrelated with each other.

However, it is important to remember that events, including stock movements, which are usually not correlated, can be correlated depending on the emotions of the investor. Gaussian logic cannot predict irrational stock market bubbles or dramatic stock market crashes caused by market mania and panic.

On the other hand, a power law calculates how a change in the value of one variable will affect another correlated variable — for example, how an increase in one company’s sales will affect stock prices in its sector. This law refers to the computation of standard deviation, a metric that is used in a number of risk calculations, including the Sharpe ratio and the Sortino score.

Both Gauss’s law and power law are far from ideal indicators of stock market performance. Prudent investors need to understand these limitations and are encouraged to use these laws only as one of many factors that can guide their overall investment decisions.

The power of quantitative analysis

According to Kalas, mathematics can indeed do well in investment markets in quantitative analysis. Quantitative analysis is a mathematical model that traders use to increase alpha and reduce risk. Quantitative models try to investigate the historical relationships between variables.

Although quantitative models are ineffective in predicting future results every time (correlations are often observed based on previous data in random or market conditions), investors must carefully consider why a correlation might have been observed between two variables and form an informed opinion about the likelihood that this correlation will continue into the future. …

Kalas notes that while even the most advanced mathematical systems cannot predict asset price movements with high accuracy, as technology and artificial intelligence improve, we are approaching an era where this will be possible.

Kalas considers himself to be both a quantitative and arbitrage investor. Unlike most quant traders who quickly enter and exit positions, Kalas uses quantitative algorithms and mathematical models to identify medium to long term investment opportunities. When asked about quantitative investments, Kalas replied:

“Computer models are increasingly superior to humans in all areas of game theory when given enough data. Algorithms can analyze correlations between countless variables and the price of securities, and this can often reveal relationships that human intuition could never have imagined. “

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