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Alpha and Beta are key components of the Capital Asset Pricing Model (CAPM), a theory of finance that has been widely taught for the last 50 years. The CAPM is used to evaluate individual positions in a portfolio as well as to evaluate managed portfolios against an index. The CAPM is predicated on the Efficient Market Hypothesis being true.

The truth or failure of the Efficient Market Hypothesis is the subject of much debate. You can read more about the Efficient Market Hypothesis in our White Paper: What about the Efficient Market Hypothesis? It can be found in our Information Center.

Calculating Alpha and Beta for a portfolio against its index consists of

  1. Create an Excel spreadsheet containing ordered pairs consisting of the percentage returns per (day, week, month, quarter) from a given portfolio and from the index for that same time period. The numbers for any given time period must be next to each other on the same row.
  2. Use linear regression – Excel has a built-in function to do this – to fit a straight line through these data points: the portfolio returns (conceptually) plotted on the Y axis and the index return for the same period plotted on the X axis. The resulting line will be of the form:

    rp = αp + βp * rindex

  3. This formula is called the Security Characteristic Line (SCL), where the "security" in this case is the portfolio being evaluated against the index.
  4. The αp is called the "alpha coefficient" and βp is called the "beta coefficient"

A beta coefficient above 1.0 means that the portfolio swings more aggressively than the market. If the beta is less than 1.0, the portfolio moves less than the market. More specifically, a stock that has a beta of 1.5 goes up or down with the market, but does so by a factor of 1.5. A negative beta means the stock moves in the opposite direction as the market. By definition, the beta of the market must be 1.

The alpha coefficient is the Y intercept of the SCL. It is interpreted by followers of the CAPM as meaning the return of the portfolio over and above the return of the index. By definition, the alpha of the market must be 0.

If you set "stats" to TRUE in your Excel function call, it will report the Coefficient of Determination, R², of the regression. This number varies from 0 to 1. Zero means that no part of the actual values of the portfolio returns could be explained by the SCL (with its alpha and beta); it means that the alpha and beta are meaningless as descriptors of the behavior of the portfolio. An R² of 1 means that all of the returns of the portfolio can be explained by the SCL and that the alpha and beta are excellent descriptors of the returns of the portfolio.

Alpha, beta, and R² are widely used metrics in evaluating portfolios, although we remind the reader that they come from the Capital Asset Pricing Model which assumes the Efficient Market Hypothesis to be true.