A beta-matched put hedge

On 5 Nov 2026 the Nifty was at 24,536.6 and the 25 Jan 2027 23,500 put settled at ₹175.95 (lot 65; 81 days to expiry). A ₹80 lakh portfolio has $\beta = 0.9$. (a) Compute $N^\star$ from (14.24) and the premium for the nearest whole number of lots, in rupees and as a percentage of the portfolio. (b) Using Proposition 14.30, compute the worst loss at expiry as a percentage of the portfolio for an exactly beta-matched hedge, before and after the premium (scale the premium to $N^\star$ lots). (c) With the whole-lot hedge, the Nifty falls 20% by expiry and $\varepsilon = 0$. Compute the portfolio loss, the hedge's net payoff after premium (ignore charges and STT) and the hedged result as a percentage of the portfolio. (d) Annualise the premium of (a) as a drag. Why does the hedged result in (c) beat the floor of (b)?