Beta return

Not all of a portfolio's return is due to a manager's skill. Some of it is simply the reward for being exposed to the overall market going up or down — a reward any investor gets just by holding a diversified basket of shares, skilled or not.

Beta return is the name for this market-driven slice of the return. It measures how much return a portfolio earned purely because of its sensitivity to the broad market, separate from any extra return the manager added through skill, which is called alpha.

The Capital Asset Pricing Model (CAPM) splits risk into two parts: systematic risk, which cannot be diversified away and is measured by Beta, and unsystematic risk, which can be diversified away and for which an investor should not expect any extra reward. Under CAPM, a security or portfolio's required return is the risk-free return plus Beta multiplied by the market's excess return over the risk-free rate.

That second term, Beta times the market's excess return, is the beta return — the reward earned purely for the portfolio's exposure to market risk. Whatever the portfolio actually earns beyond this required return is the alpha return, the reward for the manager's skill in bearing non-market risk.

Required return = Rf + B x (Rm - Rf)

Beta return  = B x (Rm - Rf)
Alpha return = Actual return - (Rf + Beta return)

Rf = risk-free return
B  = portfolio Beta
Rm = market portfolio return

A portfolio returns 25% for the year. The market benchmark returns 15%, the portfolio's Beta is 1.5, and the Treasury bond (risk-free) yield is 5%.

Beta return  = 1.5 x (15% - 5%) = 15%
Alpha return = 25% - (5% + 15%) = 5%

Of the portfolio's 25% total return, 5% is simply the risk-free rate, 15% is the beta return earned for taking on 1.5 times the market's risk, and the remaining 5% is alpha, the manager's own contribution, over and above what the market and the portfolio's risk level alone would explain.

Chapter 16 (Portfolio Performance Measurement and Evaluation), section 16.2.9, 'Alpha and Beta return', works through the 25%, 15%, 1.5, 5% example above to decompose a portfolio's return under CAPM. Expect a question that gives a portfolio return, a market return, a Beta, and a risk-free rate, and asks you to calculate the beta return, the alpha return, or both.

• Beta return depends on the portfolio's own Beta, not the market's — a Beta above 1 amplifies the market's excess return; a Beta below 1 dampens it.
• Do not compute alpha as simply portfolio return minus market return — that gives the excess return, which the workbook distinguishes from the CAPM-based Jensen alpha, which also accounts for the risk-free rate and the portfolio's Beta.
• Beta return rewards systematic, market risk only — it says nothing about how well the manager picked individual securities, which shows up separately in the alpha.