Risk Reduction Potential
The risk reduction potential (RRP) indicates how much the standard deviation of a portfolio can be reduced by hedging out the systematic component of its risk. It varies from 0% (risk cannot be reduced), to 100% (all risk can be hedged).
If Rt is the return at time t of a portfolio, and Rf,t is the return at time t of a tradable risk factor, then we can model the portfolio as:
Rt = α + βRf,t + εt
where, α and β are constants, and ε is a mean zero error term. βRf,t represents systematic risk, which can be hedged using the risk factor, and εt represents idiosyncratic risk, which cannot be hedged. If we short β of the risk factor, we will be left with only with the idiosyncratic risk:
This is the lowest standard deviation portfolio possible. Let σB denote the standard deviation of the portfolio before hedging and σA denote the standard deviation of the portfolio after hedging. If ρ is the correlation between Rt and Rf,t, then the RRP is defined as:
When ρ = 0% the RRP is 0%. When ρ = 100%, the RRP is 100%. In between RRP is non-linear. If ρ = 20%, RRP = 2%, but if ρ = 60%, RRP = 20%. Attempting to hedge with instruments with low correlation to the existing portfolio will not reduce the standard deviation of the portfolio significantly.
For further discussion and derivation of the formula, see our white paper, Risk Reduction Potential.