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Subject 4. Calculation and Interpretation of Beta PDF Download

Beta (β) is the standardized measure of systematic risk.

Since all investors want to hold the market portfolio, a security's covariance with the market portfolio (Covi,M) is the appropriate risk measure. Covi,M is an absolute measure of the security's systematic risk. Its magnitude is affected by the variability of both the security and the market portfolio (recall that Covi,j = pi,j x σi,j x σi,j). To standardize the measure of systematic risk, divide Covi,M by the covariance of the market portfolio with itself (CovM,M). Therefore, the standardized measure of systematic risk (beta) is defined as β = Covi,M / CovM,M = Covi,M / σM2 = ρi,M σi/σM.

  • The market portfolio has a β of 1.
  • If β > 1, the security is more volatile than the market.
  • If β < 1, the security is less volatile than the market.

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