FRM Fun 6 (optimal versus effective hedge) In the FRM, both authors Hull and Geman define the futures basis (b) = S(t) - F(t). In words, the basis is the difference between the spot price and one of the (any of several quotable) futures prices. Geman further defines basis risk as the variance[S(t) - F(t)]; i.e., the variance of the difference between two random variables. Then Geman defines a "classical measure of effectiveness of hedging a spot position with Futures contracts" as given by h = 1 - variance[basis]/variance[S(t)] = 1 - variance[S - F]/variance[S(t)]. While Hull defines the minimum variance hedge ratio (aka, optimal) as given by h* = correlation(S,F)*volatility(S)/volatility(F). What is the relationship between Geman's hedge effectiveness (h) and Hull's optimal (h*), if any? for example, are they demonstrably equivalent? unrelated? is one superior?