Beta hedging and what is left

A ₹12 crore portfolio has $\beta = 0.9$ against Nifty futures. (a) How many Dec Nifty lots must be traded to reduce beta to 0.3? Round to whole lots and report the effective beta. (b) Over the next month the Dec future rises 4% and the portfolio rises 5.1%. Compute the P&L of the hedged position and decompose it into the target-beta part, the rounding residual, and $\alpha + \varepsilon$. (c) Explain why a manager who believes in her stock selection but fears a market fall would choose $\beta^\star = 0$ rather than selling the portfolio.