A trader would like to protect her equity portfolio with a put option. The portfolio is worth $280 million and the desired put option would have a strike price of $260 million with a maturity of 12 weeks. The current volatility of the portfolio is 26% and the dividend yield on the portfolio is 2.0% per annum. The risk-free rate is 4.0%. Because this option is not available on any exchange, the trader decides to create a synthetic option by maintaining a position in the underlying portfolio with the required delta. What percentage of the original portfolio should be sold and invested at the risk-free rate?

a. Initially at time zero?

b. After 4 weeks, when the portfolio value is $300 million?

c. After 10 weeks when the portfolio value is $260 million?