Portfolio alpha and beta

Alpha and beta are two measures that describe a portfolio relative to the market, that is, to a chosen benchmark such as the S&P 500 or the WIG index.

Beta: sensitivity to the market

Beta shows how much the portfolio’s return changes on average when the market moves 1%. It is calculated as the covariance of portfolio and market returns divided by the variance of market returns.

• Beta = 1: the portfolio moves with the market on average.
• Beta above 1, e.g. 1.3: the portfolio reacts more strongly, rising and falling 1.3% on average for a 1% market move.
• Beta below 1, e.g. 0.6: the portfolio is less sensitive to the market.
• Beta close to 0: the portfolio’s results barely depend on that market, as with bonds relative to stocks.

Alpha: results beyond expectations

Alpha (classically, Jensen’s alpha) is the difference between the portfolio’s actual return and the return you could expect given its beta:

Example: the portfolio earned 12%, the market 10%, the risk-free rate was 4% and the portfolio’s beta 1.2. The expected result is 4% + 1.2 × 6% = 11.2%, so alpha is 0.8 percentage points. The portfolio beat the market by 2 points, but most of that edge came from taking more risk, not from skill.

Both measures need a long history of returns and depend on the chosen benchmark. A beta calculated against a poorly matched index, such as a Polish stock portfolio against the S&P 500, says little.