Development of Investment or Trading Strategies with G*Power-like Functionalities
Abstract
This post explains how G*Power, a tool for statistical power analysis, can be applied to evaluate investment or trading strategies — especially to determine how many observations are needed to detect meaningful performance (e.g., a substantially positive Information Ratio). It demonstrates using a paired-sample t-test in G*Power and replicates the calculation in R and Python, showing how to compute the required sample size to ensure robust strategy validation before deployment.
Why Hypothesis Testing Matters in Finance
In quantitative investing, the robustness of a strategy is no longer judged solely by historical performance but increasingly by its statistical validity. Whether you're comparing a new portfolio model to a benchmark, assessing the added value of a machine-learning-enhanced strategy over a traditional one, or evaluating two competing risk models, statistical hypothesis testing is foundational. It enables practitioners to formally specify and test assumptions, determine whether observed improvements are meaningful, and avoid misinterpreting random variation as skill. This analytical framework underpins tasks such as: portfolio performance evaluation, backtest validation, asset allocation, and regime-based strategy design. It is important to emphasize that the framework of statistical hypothesis testing is foundational and is deeply embedded in the curricula of globally recognized programs such as the CFA® and FRM®.
Types of Power Analysis in G*Power
G*Power offers five analysis modes to accommodate different inferential goals:
- A priori – Compute the required sample size for given \(\mathrm{\alpha}\), power (\(1-\mathrm{\beta}\)), and effect size.
- Compromise – Determine α and power jointly, given effect size, sample size, and error ratio.
- Criterion – Derive \(\mathrm{\alpha}\) from given power, effect size, and sample size.
- Post-hoc – Calculate the achieved power for a given \(\mathrm{\alpha}\), effect size, and sample size.
- Sensitivity – Compute the smallest detectable effect size, given \(\mathrm{\alpha}\), power, and sample size.
G*Power can perform such analyses across several dozen types of statistical tests, including those related to correlation and regression, means, proportions, variances, and generic tests.
Example: Using G*Power to Determine Sample Size for Detecting a Presumed Information Ratio
In the development and evaluation of trading strategies, we often care not just about raw returns, but about risk-adjusted performance — typically captured by metrics such as the Information Ratio (IR). The IR, computed from sample observations, measures how much average excess return (mean of active return, \(\mathrm{\bar{R}}_{\mathrm{active}}\)) a strategy generates per unit of active risk—the volatility of return differences versus a benchmark, also known as tracking error (\(s_{R_{active}}=s_{R_{strategy}-R_{benchmark}}\), or TR):
\[\mathrm{IR}=\frac{\mathrm{\bar{R}}_{\mathrm{active}}}{\mathrm{s}_{\mathrm{R}_{active}}}=\frac{\mathrm{\bar{R}}_{\mathrm{strategy}}\mathrm{ }-\mathrm{\bar{R}}_{\mathrm{benchmark}}}{\mathrm{s}_{\mathrm{R}_{active}}}\]
In this post, the Information Ratio is treated as a standardized mean difference (effect size) for the purpose of statistical power analysis. It should not be interpreted as an annualized portfolio Information Ratio commonly reported in performance evaluation.
A natural question arises:
How many daily observations are needed to statistically detect that the Information Ratio is greater than zero, assuming it is truly equal to some specific positive level?
In other words, we want to know minimal sample size that allow to reject \(\mathrm{H}_0\) in favor of \(\mathrm{H}_1\) where:
\[\mathrm{H}_0:\mathrm{IR} \le 0 \quad \text{vs} \quad \mathrm{H}_1:\mathrm{IR} > 0\]
This is where the specific functionalities of G*Power become a practical tool in financial analysis. Although it doesn’t directly reference the term Information Ratio, G*Power’s paired-sample t-test framework can be used to address this exact question — because the IR is mathematically equivalent to the standardized mean difference, or scaled effect size (\(\mathrm{d}_z\)), used in such tests:
\[\mathrm{IR}\equiv \mathrm{d}_z=\frac{\mathrm{\bar{d}}}{\mathrm{s}_{\mathrm{d}}}\]
where:
- \(\mathrm{\bar{d}}\) is the mean of excess returns (strategy minus benchmark)
- \(\mathrm{s}_{\mathrm{d}}\) is the standard deviation of these excess returns
The paired-sample t-test is suitable here because we’re comparing daily returns from a strategy and its benchmark, observed over the same time periods. This creates a natural pairing of data points.
Setup the Test Parameters in G*Power Input
Suppose an Information Ratio (IR) of 0.6 (daily) is assumed, representing a performance level that could be considered quite decent relative to the benchmark.. The goal is to determine how many daily return observations are required to statistically detect positive performance—that is, to test whether \(\mathrm{IR}>0\). To this end, we use a one-tailed paired-sample t-test with the following parameters: a significance level \(\mathrm{\alpha}=0.05\) (the probability of a Type I error — incorrectly rejecting the null hypothesis when it is true), and a desired test power \(1-\mathrm{\beta}=0.9\) (the probability of correctly rejecting the null hypothesis when it is false). The effect size is set at \(\mathrm{d}_z=0.6\), reflecting the expected standardized mean difference. These parameters are entered into the corresponding fields in the Input Parameters section of G*Power, as shown in the screenshot below.
Power analysis in G*Power for a one-tailed paired t-test with an effect size of 0.6, alpha = 0.05, and 90% power, showing that 26 daily return observations are needed to validate a trading strategy’s Information Ratio.
Interpretation of G*Power Output
Referring to the Total sample size field in the Output Parameters section of G*Power, we find that, under the assumed effect size, significance level, power, and paired-sample t-test framework, the required sample size is 26 paired observations. This means that if we collect at least 26 daily return pairs from our strategy and its benchmark, we will have a 90% probability (power) of correctly detecting that the true Information Ratio exceeds 0—assuming it truly does—while accepting a 5% probability (\(\mathrm{\alpha}\)) of making a Type I error—that is, falsely rejecting the null hypothesis that \(\mathrm{IR }\le \mathrm{ }0\) when it is in fact true.
The calculation assumes independent paired observations, as required by the classical paired-sample t-test framework. In financial applications, however, return series may exhibit serial dependence, volatility clustering, or other departures from the model assumptions. As a result, the effective sample size may be smaller than the nominal sample size, and the number of observations required in practice may exceed the value obtained from the power analysis.
G*Power-like Sample Size Calculation in R and Python
Below are minimal examples replicating G*Power’s functionality to calculate the required sample size for detecting a presumed effect size (e.g., an Information Ratio of 0.6) with 90% power at a 5% significance level using a one-tailed (right-tailed, since we are testing for positive excess performance) paired t-test.
Script in R
library(pwr)sample_size <- pwr::pwr.t.test(d = 0.6, power = 0.9, sig.level = 0.05, type = "paired", alternative = "greater")
sample_size$n
Script in Python
from statsmodels.stats.power import TTestPoweranalysis = TTestPower()
sample_size = analysis.solve_power(effect_size=0.6, power=0.9, alpha=0.05, alternative='larger')
sample_size
Summary
This post demonstrated how G*Power’s power analysis can support the evaluation of investment or trading strategies by determining the sample size needed to detect an assumed Information Ratio. Equivalent tools in R (pwr) and Python (statsmodels) offer the same functionality in a reproducible, code-based workflow. Notably, G*Power’s capabilities may be far more useful in designing and validating investment and trading strategies than illustrated here.
For a rigorous treatment of backtesting methodology and statistical inference in trading strategies, see my textbook: Scientific Backtesting.
For a comprehensive treatment of synthetic data generation and inferential backtesting workflows, see: Synthetic Data in Inferential Backtesting.
G*Power Documentation and Downloads
Download the Code Scripts
G*Power Sample Size Scripts (R + Python)
