Question

JQ Investor has 9,000 of DuPont currently valued at $56. He sets up a collar at $49 with a premium of $2.92, and $63 with a premium of $4.61. When the collar expires the stock is trading at $58.80

JQ buys _______ puts

and writes _______ calls.

The impact to the portfolio of this collar at the time it is put in place is $__________

The value of the portfolio at the close on the day the collar expires is $__________

Correct answers:

90 puts, 57 calls, -3.00, 529,127.00

Please tell me how to get to these solutions. Thank you!

Answer 1

Let us assume that the lot size of the options of DuPont is 100.

A Collar is set up to protect the investment against huge downside by buying an out of the money put option, and recovering the cost of buying such put option by writing an out of the money call option.

In this case, JQ holds 9000 DuPont and the lot size of 100.

Therefore, Put contracts to be bought are 9000/100 = 90 contracts.

Cost of buying 90 contracts will be Number of contracts×Lot Size×Price = 90×100×2.92 = $26,280

Now, covered calls will be written to recover $26280.

Number of call contracts to be written = Amount to be recovered/(Price×Lot Size) = 26280/(4.61×100) = 57 contracts.

Impact on the portfolio at the time of entering the collar

= Inflow from writing calls - Outflow from buying puts

= (57×100×4.61)-(90×100×2.92)

= 26277 - 26280

= $-3

Value of portfolio at the close of the expiry day

= Value of investment i.e. Closing stock price×9000 +/- Profit/Loss from Call +/- Profit/Loss from put

At expiry, stock price is 58.8. Therefore, both call and put are out of the money and hence will expire worthless. There will be no obligation on the call written and premium collected will be the profit. JQ will not exercise the put and premium paid will be the loss.

= [58.8×9000] + 26277 - 26280

= $529,197

Note: There seems to be a typo mistake in the answer mentioned along with the question. Kindly check the same.

(If this was helpful then please rate the answer positively. Thank You:)