Greek attribution, the vanna residual, and what nine trades can prove

At entry the spread of Problem 15.11 had, per unit, net delta $-0.2690808$, net gamma $0.00030113$, net theta $-2.258465$ per calendar day, and leg vegas (per vol point) $\nu_L = 12.55455$ (long 22,750 put) and $\nu_S = 9.56296$ (short 22,450 put). Over the event day the forward moved by $\Delta F = -156.21$, the long-strike implied vol by $-0.647963$ points and the short-strike vol by $-0.770523$ points. The close-to-close change in the spread was $+47.25$ points. (a) Compute the delta, gamma, theta and vega terms of the second-order expansion and their sum. (b) Compute the residual and explain its sign using what happens to the spread's net vega as $F$ moves from above $K_1$ toward the midpoint of the strikes; name the cross-Greek responsible. (c) Over nine trades the rule of 15.6.2 had $\bar R = 0.153$ and $s = 0.417$. Compute the $t$-statistic, the $N$ needed for $t=2$ in expectation M03 (3.2a), the $N$ needed for 80% power (3.2b), and the number of years that $N$ takes at six RBI decisions a year with the rule trading nine decisions in eleven. (d) Name two features of this setup that would change within that horizon and so make old observations a different experiment.