Strategic Risk Taking: A Framework for Risk Management

Appendix 1: Mean-Variance Framework and the CAPM

Consider a portfolio of two assets. Asset A has an expected return of µ_A and a variance in returns of σ²_A, whereas asset B has an expected return of µ_B and a variance in returns of σ²_B. The correlation in returns between the two assets, which measures how the assets move together, is ρ_AB. The expected returns and variance of a two-asset portfolio can be written as a function of these inputs and the proportion of the portfolio going to each asset.

µ_portfolio = w_A µ_A + (1 − w_A) µ_B

σ²_portfolio = w_A² σ²_A + (1 − w_A)² σ²_B + 2 w_A w_B ρ_AB σ_A σ_B

where

w_A = Proportion of the portfolio in asset A

The last term in the variance formulation is sometimes written in terms of the covariance in returns between ...