Question

A collar is established by buying a share of stock for $62, buying a 6?month put option with exercise price $56, and writing a 6?month call option with exercise price $68. On the basis of the volatility of the stock, you calculate that for a strike price of $56 and expiration of 6 months, N(d1) = .7247, whereas for the exercise price of $68, N(d1) = 0.6564.

a. What will be the gain or loss on the collar if the stock price increases by $1? (Round your answer to 2 decimal places. Omit the "$" sign in your response.) Collar ____ by _____

b-1. What happens to the delta of the portfolio if the stock price becomes very large? (Omit the "$" sign in your response.) Delta of the portfolio approaches $ _________

b-2. What happens to the delta of the portfolio if the stock price becomes very small? (Omit the "$" sign in your response.) Delta of the portfolio approaches $ ________

Answer 1

A). The delta of the collar is calculated as follows:

Delta

Stock 1.0000

Short call –N(d1) = –.6564

Long put N(d1) – 1 = –.2753

Total = 0.0683 or 0.07

If the stock price increases by $1, the value of the collar increases by $.07. The stock will be worth$1 more, the loss on the short put is $.2753, and the call written is a liability that increases by $.6564

b -1). If S becomes very large, then the delta of the collar approaches zero. Both N(d1) terms approach 1. Intuitively, for very large stock prices, the value of the portfolio is simply the (present value of the) exercise price of the call, and is unaffected by small changes in the stock price.

b - 2). As S approaches zero, the delta also approaches zero: both N(d1) terms approach 0. For very small stock prices, the value of the portfolio is simply the (present value of the) exercise price of the put, and is unaffected by small changes in the stock price.