Portfolio beta

The portfolio beta is simply the beta of a portfolio rather than a single security. It is most often used as a measure of how risky a portfolio is, and as such is used in performance measurement, for example in the Treynor index.

The portfolio beta may be calculated in the same way as the beta of a security by calculating the covariance of the portfolio with the market. This approach may be preferable when assessing the past risk (e.g. for risk-adjusting past performance) of a portfolio the composition of which has changed over the period of interest.

The beta of a portfolio as it is at a point in time is the weighted average of the betas of its constituents. The weighting is simply the proprtion of the portfolio in that security: so the beta of a portfolio that is invested 15% in a, 40% in b and 45% in c is simply 0.15 × βa + 0.4 × βb + 0.45 × βc. This is simpler if the composition of the portfolio has not changed over the period being looked at, or if the changes have not significantly changed the beta.

Copyright Graeme Pietersz © 2005-2019