Question

Myles Houck holds

500

shares of Lubbock Gas and Light. He bought the stock several years ago at

$ 47.91

and the shares are now trading at

$ 75.50

Myles is concerned that the market is beginning to soften. He​ doesn't want to sell the​ stock, but he would like to be able to protect the profit​ he's made. He decides to hedge his position by buying

5

puts on Lubbock​ G&L. The​ 3-month puts carry a strike price of

$ 75.50

and are currently trading at

$ 2.73

a.  How much profit or loss will Myles make on this deal if the price of Lubbock​ G&L does indeed​ drop, to

$ 61.50

a​ share, by the expiration date on the​ puts?

b.  How would he do if the stock kept going up in price and reached

$ 91.50

a share by the expiration​ date?

c.  What do you see as the major advantages of using puts as hedge​ vehicles?

d.  Would Myles have been better off using​ in-the-money

putslong dash—that

​is, puts with an

$ 86.50

strike price that are trading at

$ 10.58?

How about using​ out-of-the-money

putslong dash—​say,

those with a

$ 71.00

strike​ price, trading at

$ 1.10?

Explain.

Answer 1

1. Consider a 1 lot of Put have quantity size of 100. So total of 5 lot will have a quantity of 500

Since Myles have right to sell at 75.50, he will exercise

Gain on the Put =${ (75.50-61.50)- Premium} * 500

=$(14-2.73)* 500

=$ 5,635

The underlying are currently are in profit of = (61.50-47.91)*500

= $ 6,795

b) Since stock has went beyond his Put strike of 75.50, He will not exercise it and he will lose the premium he paid which is =$ (2.73*500)= $ 1,365

He has gain in the underlying stock which is at present value of $91.50 per share giving him total gain of $(91.50- 47.91)*500 = $ 21,795

c) Since Myles have the underlying stock and if he is in the view that market will soften and the share price may reduce it is better to hedge using the put option. In worst case if the market go against his view, he will lose the premium that he had paid and can participate in the further appreciation. If the market react as per his view he will lock the price at the strike price of the put he has bought at the expense of the premium. As we have seen in the above scenario where the share price fell down to 61.50 from 75.50, still he had right to sell at the strike price of 75.50.

d) Case 1. Buy Put of Strike Price $ 86.50 at the of $ 10.58

Scenario 1. share drop to $ 61.50

Myles will have right to sell at 86.50 so total gain in that case is $[ (86.50-61.50)-Premium]*500

= $ 7210

Scenario 2. Share reached at $ 91.50 per share

Myles will not excerise the put as current price is higher than the strike price and he will lose the premium of 10.58 per quantity which is $ 5290

Case 2 : Buy put strike of $ 71.00 at premium of $ 1.10 per quanity

Scenario 1 share drop to 61.50

Myles will have right to sell at 71.00 so total gain in that case is $[ (71.00-61.50)-Premium]*500

= $ 4200

Scenario 2 : Share reached at $ 91.50 per share

Myles will not exercise the Put and he will lose the premium of =1.10*500= $ 550 and he has full participation in the market

As per the above , it is better to hedge using slighly out of the money optin as he has less premium risk in case market reacts against his views.