Stale-NAV arbitrage

(a) Prove Proposition 6B.2.1(b): a purchase of $S$ at a stale NAV $v_s$ when fair value is $v_s(1 + \varepsilon)$ transfers $S\varepsilon/(1 + f)$ to the buyer, with $f = S/(Nv_s)$, and show that the old holders lose exactly this amount. (b) An international equity fund has net assets of ₹2,000 cr at its stale NAV. A trader knows that the fair NAV is 1.8% higher and buys ₹100 cr. Compute the transfer and the old holders' loss as a percentage of their fair wealth. (c) The trader redeems the next day at a NAV that has caught up. What is the trader's return on the ₹100 cr? Why is it below 1.8%? (d) Explain which of the Indian rules of 6B.2 (cut-off time, realisation of funds, forward pricing) would stop this trade, and which feature of a fund's holdings could still create a stale price in India.