Markets: A Rigorous Course

M15 · Problem 22 ★★★ Check

What a continuous-series backtest measures

Yahoo's CL=F held NYMEX November 2026 WTI until its expiry on 20 Oct and December from 21 Oct. Daily bars in US dollars: CL=F on 19 Oct open/low/close 101.75/99.24/103.66 and on 20 Oct 103.43/101.04/101.79; on 21 Oct (December) it opened at 98.19. The December contract (CLZ26) on 19 Oct was 99.04/96.72/98.54 and on 20 Oct 98.24/95.25/97.82. USDINR closes: 94.99 on 20 Oct, 94.72 on 21 Oct. (a) The back-adjustment of 15.11.2 removes the roll gap: the rupee proxy of December's 21 Oct open minus November's 20 Oct close. Compute it. (b) In the back-adjusted series, every price before 21 Oct is shifted by this gap. Compute the adjusted 20 Oct low and compare it with the December-contract proxy low (95.25 × 94.99). The backtest's 16 Oct trade entered at ₹9,294.79 with N=₹170.80N = \text{₹}170.80. Was its stop hit on 20 Oct? Was the December-contract trade's stop at ₹9,134.51? (c) Compute the November–December spread on 19 Oct in dollars and the annualised roll yield 12ln⁡(F1/F2)12\ln(F_1/F_2) (M10 · 10.3). What does a spread of this size do to the difference between the two versions of the trade? (d) Which version should the base-rate table use, and how would you build a backtest that matches an MCX trader's roll two sessions before MCX expiry, given that Yahoo removes expired contracts?

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