Markets: A Rigorous Course

M10 · Problem 5 ★★ Check

Roll yield with a moving curve

(a) Derive (10.12): the one-period excess log return of a futures position with fixed time-to-maturity τ\tau is Δln⁡S−ctΔ+(ct+Δ−ct)(τ−Δ)\Delta\ln S - c_t\Delta + (c_{t+\Delta} - c_t)(\tau - \Delta). (b) Evaluate it for τ=2/12\tau = 2/12, Δ=1/12\Delta = 1/12, St=7000S_t = 7000, ct=12%c_t = 12\%, St+Δ=7100S_{t+\Delta} = 7100, ct+Δ=20%c_{t+\Delta} = 20\%. Check by computing the two futures prices directly. (c) Which term would a calendar-spread trader be trading?

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