Question

A hedge fund manager shorted 800 shares of XYZ stock at $65/share and she plans to close out her short position in nine months. She decides to put options to fully hedge her short sale against price risk. 9-month XYZ put options have a strike price and premium of $60 and $.15, respectively. Find her total profit/loss (stock and options combined) if XYZ sells for $59 when the options expire.

• -4120
• 4120
• 4920
• -4920

Find the manager's total profit/loss (shares and options combined) if the stock trades for $72 when the options expire.

Answer 1

Manager's profit or loss if XYZ sells for $ 59 is computed as follows:

Since Manager shorted 800 shares of XYZ so he will be gaining when the stock falls:

Hence profit if stock falls to $ 59 is

= $ 65 - $ 59

= $ 6 per share

So profit on 800 shares would be

= 800 x $ 6 per share

= $ 4,800

But for hedging he has short put which is a reversal of going short, means if the stock rises he will gain. But in this case the stock falls to $ 59. So the loss in this put is

= $ 60 - $ 59 - $ 0.15 (Premium is deducted because in this case the manager must have received the premium at the time of shorting the put option)

= $ 0.85 per share

So loss on 800 shares would be

= 800 x $ 0.85 per share

= $ 680

So the net profit would be

= $ 4,800 - $ 680

= $ 4,120

So the correct answer is option b i.e. $ 4,120

Manager's profit or loss if XYZ goes to $ 72 is computed as follows:

Since Manager shorted 800 shares of XYZ so he will be losing when the stock rises:

Hence loss if stock rises to $ 72 is

= $ 65 - $ 72

= $ 7 per share

So loss on 800 shares would be

= 800 x $ 7 per share

= $ 5,600

But for hedging he has short put which is a reversal of going short, means if the stock rises he will gain. In this case the stock rises to $ 72. So the profit in this put will be restricted to the premium amount only since in case of shorting the put option the maximum gain is the premium amount only

= $ 72 - $ 60

= $ 12 but restricted to premium amount only i.e. $ 0.15 per share.

= 800 x $ 0.15 per share

= $ 120

So the net loss would be

= $ 5,600 - $ 120

= $ 5,480

So the net loss is $ 5,480.

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