Hedge effectiveness

[ammor]

Hi David,

Can you please explain in more details the concept of "Hedge effectiveness" by giving example?

Thanks.

Ammor

 

[David Harper CFA FRM]

Hi Ammor,

Sure.
Assume spot price volatility =20%, forward price volatility = 10% and correlation (rho) = 0.8.
So if we only have these two variables to regress (forward regress on spot), a key formula is:
the slope of the line (beta; aka, optimal hedge ratio) is covariance(spot, forward)/variance(forward).

In this case, slope = (0.8*20%*10%)/10%^2 = 0.4 optimal hedge ratio
... we can simplify slope = cov()/var() by canceling forward in numerator and denominator:
slope = correlation *spot volatility/forward volatility = correlation * "relative volatility"

Then Hull's hedge effectiveness is what, in a 2-variable linear regression, we call call the coefficient of determination (a metric of "goodness of fit), and it equals correlation^2 or R^2

so, since slope = correlation * spot volatility /forward volatility,
correlation = slope * forward volatility / spot volatility, and
correlation ^ 2 = slope ^2 * (forward volatility / spot volatility)^2
R^2 = slope ^2 * forward price variance/ spot price variance; where slope is the same as the "optimtal hedge ratio"
you might find helpful beta is one idea.

in this example, R^2 = 0.4^2*(20%/10%) = 0.64 = 0.8 correlation^2

hope that helps, David