(AR(1) for a futures basis)

Let $X_t$ be the deviation, in index points, of the Nifty near-month futures basis from its cost-of-carry fair value (M07). Model it as an AR(1) with mean 0, $\phi = 0.9$ per day and innovation standard deviation 4 points (illustrative). Today $X_t = 12$. (a) Give the 5-day-ahead forecast and its standard error. (b) Give the half-life of a deviation and the unconditional standard deviation of $X_t$. (c) A Nifty futures lot is 65 units (as of 2026-11-05). What is the expected convergence in rupees per lot over 5 days, and why is this not a riskless profit?