Assume you have a $1,000,000 equity portfolio under management that approximately has the risk profile of the RUSSELL-2000 index of small cap companies. You would like to hedge the risk of this portfolio by buying put options on IWM, an ETF on the RUSSELL-2000 Index. The current price of IWM is $177.50. The volatility of the IWM price is 33%. The risk-free rate is 0.6% continuously compounded, for all maturities. Assume that IWM does not pay dividends.

(a) Use the Black-Scholes formula to find the price of a European Call option on IWM that expires in 28 days and has a strike price of $185.

(b) Find the price of a European Put option on IWM that expires in 28 days and has a strike price of $165.

(c) Find the delta of the call option in part (a) and the delta of the put option of part (b).

(d) Consider the put options of part (b) that expire in 28 days and have strike prices of = $165. How many shares of IWM is one put option contract (100 put options) equivalent to?

(e) How many put options contracts (the put options that expire in 28 days and have strike prices of = $165) are needed to -hedge the downside risk exposure of your $1,000,000 equity portfolio? What will be the cost of buying those put options?