Definitions: Beta & Alpha

Before delving deeper into the topic of market efficiency and active vs passive, it may be helpful to briefly review the definitions of beta and alpha.

Beta

At it’s simplest, beta can be defined as the volatility of an asset relative to a benchmark. The benchmark is often an index of a specific sector or an entire asset class. For example, a US large-cap stock that is 20% more volatile than the S&P 500 index has a beta of 1.2. Or if the volatility is 20% less than the index , it’s beta is .8. Beta is a measure of relative volatility.

Alpha

Within the Capital Asset Pricing Model (CAPM), this same beta is used to forecast returns. Under CAPM, higher beta leads to higher returns and lower beta results in lower returns. In other words, a fund with more volatility should have higher returns and a fund with lower volatility should have lower returns. Reality rarely unfolds as modeled, so an ex-post CAPM equation was created. It adds a variable called alpha to account for the difference between an asset’s actual return and it’s expected return (which CAPM predicts to be the benchmark return, adjusted for volatility). Below are a couple of examples on calculating alpha:

  • An investor invests in large-cap domestic stocks and reports a 10% return, while the Russell 1000 returns 7%. The investor has produced 3% alpha.
  • An investor invests in global equities and reports a 9% return, while the MSCI All Country World Index returns 13%. The investor has (negative) alpha of -4%.
Beta, Colloquially

The term beta is often used to refer to the risk and return characteristics of a benchmark. Some examples: US large-cap beta may refer to the Dow Jones Industrial Average or the S&P 500, investment grade bond beta is often synonymous with the Barclays Agg index, or tech beta may simply refer to a tech-sector ETF. I often refer to index ETFs as cheap, liquid beta. Some may compare large-cap beta to small-cap beta or consumer staple beta to consumer discretionary beta, when discussing risk and returns. Below are some examples of how someone might refer to beta:

  • Utility sector beta is sensitive to interest rates.
  • An index fund may be called beta exposure.
  • An investor holds investment grade bonds and reports a -1% return while the Barclays Agg is down 3%. Some might say that the beta return was -1% (and alpha was positive 2%).
To recap:
  • Beta is an asset’s volatility, relative to a benchmark.
  • Alpha is an asset’s return above it’s benchmark, after controlling for differences in volatility.
  • Technical definitions notwithstanding, the term beta is often shorthand for a benchmark or may refer to the benchmark’s risk and return characteristics.

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