Beta measures the relationship between a stock or portfolio’s returns and those of a benchmark.
It effectively aims to answer the question: how much more volatile is this asset compared to a related benchmark?
It’s important that the benchmark chosen is related to the stock or portfolio we’re looking at. For example, the S&P500 would be a useful benchmark for a long-only portfolio of US stocks but less useful in the context of looking at a UK government bond ETF.
To calculate beta, we would then compare the historical returns of the stock or portfolio with those of the benchmark and find how they are related.
A portfolio beta of close to 1 means that the portfolio is about as risky as the benchmark and would likely generate returns broadly similar to it.
A portfolio beta of, for example, 1.3 means the portfolio was 30% more volatile than the benchmark, which means an increased chance of an excess return but also increased downside risk.
A large aim of many fund managers, particularly within hedge funds, is to aim for a high upside beta and a low (or negative!) downside beta - meaning when the market goes up, the fund increases by a more than proportional amount, but when the market goes down, the fund is protected from a large fall in value.