Exporter and the minimum-variance ratio

An exporter expects USD 750,000 on 15 Jan 2027 and hedges with January futures sold at 94.8650. From weekly changes over the past year (illustrative) $\sigma_{\Delta S} = 0.38$, $\sigma_{\Delta F} = 0.40$ (₹ per USD), $\rho = 0.98$. (a) Compute $h^*$, the number of lots, the tailed number of lots (same tail factor as Problem 11.20), and the hedge effectiveness. (b) Give two reasons why $\sigma_{\Delta F} > \sigma_{\Delta S}$ and $\rho < 1$ even though the future settles on the same exchange rate. (c) On 15 Jan spot is 93.90 and the January future 93.95. With 690 lots, compute the exporter's rupee receipts per dollar, and compare with a full 750-lot hedge. (d) How much more than spot on 5 Nov did the exporter lock in with the full hedge, in rupees? What is this amount economically?