# Option question

John Doe has written put options on 10,000 shares of a stock with a strike price of 9 a share. The stock is currently trading at \$10 per share. The put delta is -.5. If the stock goes down to \$9 per share John Doe’s option position would have a gain or loss of? To hedge the option position, John Doe would?

Short fewer shares?

To hedge the position would John Doe buy call options on 10,000 shares of stock?

It doesn’t say John Doe ever had any shares, so to hedge he would short sell shares of the stock. The loss would be about 5000 dollars on the initial move down to 9 dollars a share.

I don’t think so. If you buy options and the stock decreases further, you are out the premium and still have to take the loss on the short put position.

CFAdummy Wrote: ------------------------------------------------------- > To hedge the position would John Doe buy call > options on 10,000 shares of stock? You wouldnt want to buy call options to hedge, becuase you are short put options. Your risk is to the downside, which is the same as buying call options

I think one of the answers was short 5000 shares. I’m not sure how they got this amount.

Thats about right if the delta was -.5. Although this question states that we start out at -.5 so the change in price would change delta a little bit, but for illustrative purposes, that is correct, you would short 5000 shares to hedge your option position.

The delta should move closer to -1 though so technically it should be fewer than 5000 shares? Am I thinking this through correctly?

If he has a puts on 10000 shares with a delta of -.5 wouldn’t his gain be \$5000 on the drop in price of \$1. Since he has a put position and doesn’t seem to have any stated long position in the underlying, to hedge, he would apparently need 5,000 shares of the underyling at the current delta, or more if the delta has now shifted closer to -1 which it most likely has.

He is short the put.

Actually, now I think that he should short more shares if the price drops because its # of options * delta. Delta will go from -.5 to say -.6 so now he needs to be short 6000 shares.

ooooh, guess I should read the question.

Yeah, so basically reverse everything I just said which gives you Nibs’s answer.

Nib, your thinking is exactly right, the only thing is, where does it say the investor has any short shares to start with. I take it as though he is short puts. Now 1 day later he wants to hedge. So he needs to short shares of the stock, not short MORE, because he never had any to begin with.

True, I just assumed when he went short the options he hedged himself.

I’m not sure how the negative delta affects the shorting the shares? Can someone show me the math? Sorry.

ok, hedge ratio=1/delta hedge ratio=2 hedge ratio*number of underlying shares=number of options necessary 2*x=100000 x=50000 part ii stock decreases one dollar change option=1-n(d)1*change in underlying change option=1-(-5)*\$1 =1.50 i think the second part is right…correct me where i am wrong

Did schweser even cover this hedge ratio stuff? I never seen it on the videos.

its in the books with the black scholes material