Coefficient R^2

Ludwma

Member
Subscriber
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

David Harper CFA FRM
Subscriber
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,
 
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