Definition

Beta estimates the sensitivity of an investment's periodic returns to a selected market's periodic returns. It is a fitted relationship over a stated sample. It depends on the market proxy, dates and return frequency, and it can change through time.

Beta formula

For a single-factor excess-return regression:

beta = covariance(portfolio excess returns, market excess returns) / variance(market excess returns)

Use aligned observations and a consistent risk-free return. A zero market variance makes this coefficient undefined. The regression intercept is alpha, while beta is the slope. Neither is simply a ratio of cumulative or annualized compound returns.

Correlation describes the strength and direction of a linear association. Beta also reflects the relative scale of the two return series. Thus two portfolios can have similar correlation with a benchmark and different betas. A high beta describes exposure in the fitted sample; it does not promise a particular return on the next trading day.

Why a leveraged ETF name is not a portfolio beta

The U.S. momentum study uses TQQQ and TECL as risk assets, together with defensive ETFs. In most of its reported risk-on months the leveraged holdings each carry about a quarter of the portfolio alongside a defensive holding. The full portfolio is not continuously invested entirely in a single 3x fund.

The U.S. strategy comparison reports that system's 29.9% CAGR and -21.1% maximum drawdown over May 2016 to October 2026. Those figures do not determine a regression beta. Estimate beta from the actual periodic portfolio return series against the chosen market.

Leveraged ETFs generally target a multiple of a daily index move. Their multi-day return depends on the path and resets. The SEC investor bulletin explains this daily objective. A daily leverage target should not be read as a measured long-window portfolio beta or a multiple of long-run CAGR.

Practical interpretation

Choose a benchmark that reflects the question. SPY and QQQ represent different market exposures, so a beta to one need not match a beta to the other. Inspect the fitting window and consider whether a strategy's cash allocation or leverage changes across regimes.

A rolling beta can show exposure changes, but shorter windows also increase estimation noise. Check the underlying positions before attributing every change to a stable economic relationship. The backtesting guide explains how portfolio construction and benchmarks enter the research process.

Frequently asked questions

Is a low beta portfolio safe?

Low sensitivity to one benchmark does not remove concentration, liquidity, credit, tail or model risk. Inspect drawdown and Sharpe alongside the exposure estimate.

Can beta be negative?

Yes, a fitted negative slope means the investment tended to move opposite the selected market in that sample. The relationship may change and can be uncertain.

Read alpha, information ratio, CAGR and the quant glossary.

For education and research only. This is not investment advice. Historical performance does not guarantee future results.

Last updated: 2026-10. Author: FinLab Quant Research.