Linear Hedging
- Risk Management
The linear-risk notes approximate a portfolio's change by its sensitivities to risk factors. A hedge chooses positions whose factor exposures offset the portfolio's exposures, often by solving a covariance-weighted least-squares problem.
For a single factor, the minimum-variance hedge ratio is proportional to covariance divided by the variance of the hedging instrument. The unitary hedge examples show why the sign and units must be checked: a hedge ratio is a position size, not a probability.
The approximation is local. Basis risk, nonlinear payoffs, liquidity, and changing correlations can all make the realized hedge error larger than the linear estimate.