Charlene Trump manages a $600 million equity fund which tracks the performance of the TSX/S&P 60 index. Charlene wants to ensure that the value of the portfolio doesn't drop by more than 4.5% within the next four months. The portfolio has a volatility of 30% and dividend yield of 1.65% p.a., roughly equal to those of the TSX/S&P 60 index. The risk-free rate is currently at 1.9% p.a..
a. Please help Charlene figure out how much she should sell her holdings in order to execute a synthetic-put-option insurance. Suppose the market drops by 3.2% immediately afterwards. How much additional equity does she need to sell?
b. Suppose instead Charlene wants to use 9-month TSX/S&P 60 futures to execute the synthetic hedge. How many contracts does she need to short? How should she adjust the futures position after the 3.2% drop? (The current level of TSX/S&P 60 is 910, and one TSX/S&P 60 futures contract is 250 times the index level.)