# Beta

Beta (or the ‘beta coefficient’) is a way to measure the relative riskiness of a share.

Using regression analysis, beta measures the systematic risk of a security relative to a benchmark. For example, if Apple (AAPL) has a beta of 1.3, this conveys the information that its risk, or volatility, is about 30% above that of the US stock market.

Beta is an input into the capital asset pricing model (CAPM) where the expected return of an asset is calculated based on its beta (ß), returns expectations, and a risk-free rate equal to the following:

Expected Return = Risk-free Rate + ß * (Expected Return of the Market – Risk-free Rate)

• A ß of 1 would give an asset the same expected theoretical return of the broader market.
• A ß below 1 would give an asset an expected return below that of the market (with the trade-off of it being less risky).
• A ß above 1 would give an asset an expected return above that of the market (with the trade-off of it being more risky).

Beta measurements are only accurate when a security possesses a high R-squared relative to the benchmark it’s being compared against. That is, if the actions of the benchmark are a poor predictor of the actions of the security, then it makes little sense to use the benchmark as a credible measure of evaluating its volatility.

Mathematically, the beta of a security is equal to the covariance of the security’s returns with the benchmark’s returns divided by the variance of the benchmark’s returns over a particular period of time.

ß = Cov(return of security, return of benchmark) / Var(return of benchmark)

Beta and its role in CAPM convey the basic idea that investors expect to be compensated for taking on more risk. But at the same time, it’s difficult to boil a security’s risk down into one particular number. Its volatility may also change over time, particularly for a startup company as it goes through its various stages.

Beta can nonetheless provide a reasonable proxy. If a stock’s beta is 0.9 and has a high R-squared with the S&P 500 or similar market benchmark, this might denote that it is likely to underperform the market by 10% in a bull market and outperform the market by 10% in a bear market.

Stocks with high betas include tech, mining, oil and gas, and highly leveraged firms. These are riskier but may provide higher return over the long-run. Low beta stocks generally include utilities and some consumer staples stocks, given the relatively predictable nature of their cash flows.

## Beta As It Pertains to Portfolio Construction

Beta is also one component of a trader’s return, in addition to the risk-free rate and alpha.

The risk-free rate is generally taken as the return on cash, where a three-month bond is taken as a proxy. However, some might take it to mean a 10-year bond, which, despite its volatility, could be a reasonable substitute for those with expected 10+ year holding periods. Those who prioritize real (i.e., inflation-adjusted) returns might use the rate associated with inflation-protected securities, such as TIPS.

Alpha is the value derived from managers deviating from the beta.

Beta can be defined as the excess returns of an asset class over the risk-free rate. For example, if the risk-free return is considered 1.5% and the expected return of mid-grade long-duration bonds is 4%, the expected beta of this particular subset of bonds is 2.5%. Similarly, if expected return of stocks is 7%, then the beta of equities would come to 5.5%.

The returns derived from indexing are a function of the risk-free rate and the beta. Deviating from the index provides the opportunity to generate alpha and improve over the returns generated from just the risk-free rate and beta.

Return = Risk-free rate + Beta + Alpha