A collar is established by buying a share of stock for $64, buying a 6-month put

Question

A collar is established by buying a share of stock for $64, buying a 6-month put option with exercise price $58, and writing a 6-month call option with exercise price $70. On the basis of the volatility of the stock, you calculate that for a strike price of $58 and expiration of 6 months, N(d1) = .7116, whereas for the exercise price of $70, N(dl)-0.6443. 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.) a. Collar gain by b-1. What happens to the delta of the portfolio if the stock price becomes very large? (Omit the "$" sign in your response.) Delta of the portfolio approaches S b-2. What happens to the delta of the portfolio if the stock price becomes very small? (Omit the "$" sign in your response.) Delta of the portfolio approaches S

Explanation / Answer

delta of call=N(d1)
delta of put=N(d1)-1

Hence, in collar if stock price increases by 1, profit will be
1 on stock
0.6443-1 on put
-0.7116 on call

Total profit=1+0.6443-1-0.7116=-0.0673

Delta of portfolio will be 1+delta of put-delta of call

If stock price becomes very large, delta of call will become 1 and delta of put will become 0
So, total delta=1+0-1=0

If stock price becomes very small, delta of call will become 0 and delta of put will become -1
So, total delta=1-1+0=0

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