Coefficient R^2

[Ludwma]

Hi David,

In the question 153.4, I see following formula to compute R^2:

R^2 = h*^2 * var(F)/var(S)

Where does this formula mean?

Thanks,

Fabiano

 

[David Harper CFA FRM]

Hi Fabiano,

This sort of encapsulates Hull on hedging with futures. The hedge is based on a univariate regression (spot price change regressed against futures price change). The SLOPE of the regression line is the optimal hedge ratio (h*):
h* = beta (Forward with respect to spot= cov(F,S,) / variance(F) <-- must know this; same as capm beta = cov(security, market)/variance(market)
h*= correlation(F,S)*volatility(S)*volatility(F)/ volatility (F)^2 = correlation(F,S)*volatility(S)/ volatility (F). Therefore,
correlation(F,S) = h* vol(F)/vol(S). In a univariate regression, R^2 is correlation^2, so:
R^2 = [h* vol(F)/vol(S)]^2 = h*^2 * var(F)/var(S)

Thanks,