Standard Deviation of Pool

For a two-asset portfolio, total risk depends on each asset’s volatility and on how the two assets move together.

Formula:

${\sigma }_p=\sqrt{w_1^2{\sigma }_1^2+w_2^2{\sigma }_2^2+2w_1{w}_2\text{Cov}(1,2)}$

Where:

• w = portfolio weight
• \sigma = asset standard deviation
• Cov(1,2) = Covariance between the two asset returns

Key idea:

• If assets do not move perfectly together, portfolio risk can be lower than the weighted average of individual risks.

That is the math behind diversification discussed in Risk and Return.