How to Use Statistics and Probability for Quantitative Trading
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How to Use Statistics and Probability for Quantitative Trading

10 mins read

Many new traders make the mistake of starting with only their gut feelings when making trading decisions, and this often leads to costly losses.

Instead, you should rely on statistical analysis and probability to inform your investment decisions as much as possible. As you learn how to read charts and trend lines, how to identify support and resistance levels, and more, your confidence in trading will grow exponentially, and you’ll be more likely to make profitable trades because of it.

Types of Data

When it comes to quantitative trading, there are two main types of data that you need to be aware of: historical data and real-time data.

Historical data is what you use to backtest your trading strategies. Real-time data is what you use to execute your trades.

For example, a retail trader would get their data from the stock market’s trading platform whereas a quant trader would buy their data from Bloomberg or Reuters. A common misconception among traders is that they can make more money with less risk by using higher frequency trading (HFT).

In reality, HFTs have a larger drawdown period which makes them riskier than low frequency trading (LFT) methods. Higher frequency trading also has high transaction costs which can lead to significant losses if executed poorly. In order to reduce transaction costs, many HFTs trade in batches over several minutes instead of in one trade per second like other traders do.

Descriptive vs Inferential Statistics

When it comes to quantitative trading, there are two main types of statistics: descriptive and inferential. Descriptive statistics simply describe the data that you have collected. Inferential statistics, on the other hand, allow you to make predictions about future events based on your data. In order to be successful in quantitative trading, it is important to understand both types of statistics.

Many traders rely heavily on inferential statistics when developing their strategies; however, they also need to utilize descriptive statistics to analyze how well those strategies are working.

Traders often use these two types of statistics together, as one can complement the other depending on what type of analysis they want to do.

For example,

if a trader wants to know if a strategy works best with certain assets or market conditions then descriptive statistics may be more useful than inferential statistics. However, if a trader wants to find out which assets or market conditions work best with a given strategy then inferential statistics may be more appropriate than descriptive stats

Hypothesis Testing

In hypothesis testing, we start with a null hypothesis and an alternative hypothesis. The null hypothesis is usually that there is no difference between two groups, while the alternative hypothesis is that there is a difference.

We then use statistical tests to decide which hypothesis is more likely to be true. For quantitative trading, we can use hypothesis testing to test whether a trading strategy works or not.

If the null hypothesis is that the strategy does not work, and the alternative hypothesis is that the strategy does work, then we can use statistical tests to see if our trading strategy is likely to be profitable.

For example, if we wanted to test whether the strategy would have made money in 2008, one of the hypotheses would be There was a period of time in 2008 when the trade had positive returns. Another hypothesis would be There was no period of time in 2008 when the trade had positive returns.
The statistical measure of profitability is return on investment (ROI).


Using ROI as our statistic allows us to compare different investments over time by taking into account their original investment amount.

The probability that a particular trading strategy will generate profits depends on how much it costs per trade and how often it makes trades.

Regression Analysis

In statistics, regression analysis is a set of statistical processes for estimating the relationships between a dependent variable (often called the ‘outcome variable’) and one or more independent variables (often called ‘predictors’). These types of models allow you to assess how changes in certain factors might influence the value of your outcome.

There are many different types of regression analysis, each with their own pros and cons. The key question you need to ask yourself when performing any type of linear regression is What will my slope coefficient estimate be? For example, in basic linear regression, it will estimate how much your Y values change as X values increase by 1 unit.


Regression coefficients measure this change, either quantitatively (e.g., $1) or qualitatively (e.g., 10%). Regression analysis can also provide you with a standardized score that represents the magnitude of the relationship between an independent variable and a dependent variable- often known as beta coefficients.

You can also use them to find whether there’s an association between two categorical variables – such as male vs female- which can show up in two ways

Performance Attribution

When it comes to quantitative trading, performance attribution is the process of analyzing how different factors have contributed to the overall performance of a trading strategy.

This can be helpful in identifying which areas are working well and which may need improvement.

There are many ways to measure contribution, with some common examples being relative contribution (proportion of outperformance due to a factor), attributable return (direct effect on returns), total contribution (effect on both returns and risk).

The choice depends on what you’re trying to identify. For example, if you want to know where improvements could be made in order to increase profitability then relative contribution is your best bet. However, if you want information about how much each factor contributed then attributable return might be more useful.

If you want to know what caused the most volatility in your portfolio then total contribution would be appropriate. In addition, there are other types of attribution like frequency-based attribution and location-based attribution that rely on historical data and simulation techniques respectively.

Regardless of which type of attribution one chooses, they all require careful consideration before using them as the final word on whether an action should be taken or not.

Market Neutral Strategies

Statistical arbitrage and other market neutral strategies are based on the premise that securities prices are random and follow a probability distribution. In statistical arbitrage, the key assumption is that small price discrepancies between trading venues will eventually be eliminated.

In many cases, those discrepancies may be caused by imperfections in pricing models or data transfer speeds; when these errors occur, there is an opportunity to profit from them by buying at one trading venue while simultaneously selling at another with higher pricing.

For example, suppose you see an opportunity in which it appears as though Company A’s shares are priced 10 cents lower than Company B’s shares. We should use statistics for quantitative finance.

Your trade would involve buying Company A’s shares at one venue and simultaneously selling Company B’s shares at another venue (or vice versa). The difference in price will eventually be eliminated because of transactions like yours, leading to profits for those who time their transactions correctly: buy low, sell high.

Conclusion

In conclusion, statistics and probability can be extremely useful tools for quantitative trading. By understanding the underlying principles of these disciplines, traders can make more informed decisions about when to enter and exit trades.

Additionally, by tracking statistical trends in the market, traders can get a better sense of where the market is headed and make better predictions about future price movements.

With all this information at their fingertips, traders will have an easier time managing risk and putting together profitable strategies that fit their individualized investment philosophy.

As such, traders should take the time to understand how different distributions affect decision-making as well as how various probabilities play into everyday investing. For those who are interested in learning more about this subject, there are many resources available both online and off that discuss it in detail.

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