$1.$ Mr$.$ X has a portfolio with a value of Rs$.23,00,000$ and the beta of the same is $1\mathrm{.}1.$ He wants to hedge the risk to this portfolio for the next one month. He plans to use one month futures contract on Nif index for hedging. Nifty is currently trading at $11,160$ and Nifty futures are $11,190.$ The Nifty lot size is $75$ per contract. Risk free rate is $7\%.$ Using the given information, you are required to:

I. Calculate hedge value and lots required for hedging. What position should the hedger take in Nifty futures?

II$.$ Calculate the payoff of Mr$.$ X in two situations if:

Nifty Spot falls by $7\%$ and Nifty Futures fall by $730$ points.

Nifty Spot gains by $4\%$ and Nifty Futures gain by $435$ points.