2. (Proportional carrying charges o) Suppose that a forward contract on an asset is written at time zero and there are M periods until delivery Suppose that the carrying charge in period k is qS(k), where S(k) is the spot price of the asset in period k Show that the forward price is F = (1-9)MS d(0, M)

[Hint Consider a portfolio that pays all carrying costs by selling a fraction of the asset as required. Let the number of units of the asset held at time k be x(k) and find r(M) in terms of x(0)]