Basis risk

On 5 Nov 2026 a fund that tracks the Nifty 50 exactly knows it must sell 6,500 index units' worth of its basket on 20 Nov 2026. It sells 100 lots of the Dec future at 24,719.10 and buys them back on 20 Nov when it sells the basket. (a) Show that the effective sale price per index unit is $F_1 - b_2$. (b) On 20 Nov the Dec contract has 39 days left. Using the carry model, compute $b_2$ and the effective price for $S_2 \in \{24{,}000, 25{,}000\}$ and net carry $r - q \in \{3\%, 6\%\}$. (c) Which source of uncertainty in the effective price dominates, the level of the Nifty on 20 Nov or the carry? Why would the Nov contract (expiring 23 Nov) have been a better hedge instrument for this date, and what risk would that have introduced?