John Williamson is a recently retired executive from Reston Industries. Over the years he has accumulated $10 million worth of Reston stock and another $2 million in a cash savings account. Table 3: Regular and Exotic Options (Option Values) Reston S&P 500 European call $6.31 $6.31 European put $4.83 $4.83 Table 4: Reston Stock Option Sensitivities Delta European call 0.5977 European put -0.4023 Williamson would like to consider neutralizing his Reston equity position from changes in the stock price of Reston. Using the information in Tables 3 and 4 how many standard Reston European options would have to be bought/sold in order to create a delta neutral portfolio? A) Buy 497,141 put options. B) Sell 497,141 put options. C) Buy 370,300 call options. D) Sell 370,300 call options.
either A or D, but I think we need the share price unless I am completely missing some other step. But to hedge a long you buy puts or write calls.
I agree w/ budfox, don’t you need the share price to know what c+, c- are as well as how high or low the stock might go?
D. He doesn’t have enough money to buy the put option.
Well done…I forgot the price. Reston Stock Price = $50.00 Strike = $50.00
Ahhh… clever… ARGHH!!!
No D is not the correct answer. Any other idea?
then it’s (10 000 000 / 50) / (-.4023) = -497 141.437 A.
A
Here is the answer. I thought the rule when long stock was to divide the number of stock by a number of SHORT CALLS, not puts… The correct answer was A. Number of put options = (Reston Portfolio Value/Stock PriceReston)/-DeltaPut Number of put options = ($10,000,000/$50.00)/-0.4023 = -497,141 meaning buy 497,141 put options. Selling put options does not deliver any downside protection but it aggravates the losses when the stock decreases in value. Buying call options will increase the exposure to Reston.
Here is the way you can understand creating delta neutral portfolio: Delta of Stock = 1 Delta of Call / Put = As per the question = delta For a particular portfolio having long stock and short calls, total delta should be zero: so, (Delta of Stock)*(number of Stock) - (Delta of Calls)*(number of calls) = 0 First term is positive because you have longed the stock and second is negative because you have shorted the calls. Since delta of stock = 1, we get, number of stock - Delta of Calls*(number of calls) (solve the equation) for case when you long put and long stock: we have, (Delta of Stock)*(number of Stock) + (Delta of put)*(number of puts) = 0 Both the terms are positive as I have longed stock as well as puts. we have, number of stock = -(delta of put)*(number of puts) (solve the equation)
Thanks, it’s very clear now! I just did not get from Schweser that you could create delta neutral portfolios using put.
Just to check my understanding / logic, D would have been correct had the # been 334,616?
That was the figure I was expecting to see in the proposed solutions when I did the test, as I went directly to use the formula: Ncall to short = NStock / Delta call