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.
\nFor 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.
\nThe approximation is local. Basis risk, nonlinear payoffs, liquidity, and changing correlations can all make the realized hedge error larger than the linear estimate.
","contentMarkdown":"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.\n\nFor 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.\n\nThe approximation is local. Basis risk, nonlinear payoffs, liquidity, and changing correlations can all make the realized hedge error larger than the linear estimate.","dataUrl":"https://sharifhsn.dev/api/posts/linear-hedging.json","date":"2024-11-21","datePublished":"2024-11-21","description":"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, ofte…","site":"https://sharifhsn.dev","slug":"linear-hedging","source":"FE-535 | Risk Management","sourceUrl":null,"tags":["Risk Management","Hedging","Linear Risk"],"title":"Linear Hedging","url":"https://sharifhsn.dev/blog/linear-hedging/","version":"1","wordCount":98}