Hedging

Suppose you hold 500 stocks in a microelectronics company called Chips-4-less. You have bought the stock at 80$ and the stock has risen to 120$, which is a nice profit. Summarizing this in table form:

Situation	Stock value	Profit/loss		Total:	Sum profit:
Before hedge	Up to 120$	Profit on stock:	(120$-80$)*500	+20,000$	+20,000$

The year results are coming up though in February and Chips-4-less will be making an official statement regarding the long term strategy. Which leaves you, the investor, with a dilemma. Either the statement will thrust the stock upwards, but it could also mean the statement won't be interpreted as a smart move which could plummit the stock. So you're left with the choice:

• Sell the stock and risk missing out on even more profit
• Keep the stock and risk all of your profits (and even a loss!)

Or not? The first hedge example is called the put hedge. Suppose you would be willing to risk about 20$ of profit in order to stay in the race for more profit. Furthermore, suppose the February put with a strike of 105$ is going for 3$. The put hedge in this example would be to buy 5 PUT FEB 105. Remember that buying 1 PUT contract actually means buying 100 actual puts, so 5 contracts corresponds with 500 pieces of stock.

 

Let's look at the possible outcomes in order to understand the hedge. Suppose the Chips-4-less crashes after the statement, the stock plunges to 64$. (120$ - 64$ = 56$ loss)

Situation	Stock value	Profit/loss		Total:	Sum profit:
no hedge	Plunged to 64$	Loss on stock:	56$*500	-28,000$	-8,000$
hedged	Plunged to 64$	Loss on stock: Profit on option: Paid premium:	56$*500 (105$-64$)*5*100 3$*5*100	-9,000$	+11,000$

You can calculate the losses from the stock crashing for a whole lot of values under 105$ for the Chips-4-less stock but you will always get the same result for the hedged situation. Your stock will always go down 1$ for each point it drops, but under 105$ the intrinsic value of a single put will go up 1$ for each point the stock drops. For 500 pieces of stock, the hedge of 5 PUT contract (which is 500 options) effectively cancels the loss on the stock for every value under a 105$. Above 105$ the put does nothing as the put becomes worthless nearing expiration, where the option value roughly equals the intrinsic value.

So that's good, the hedge protected the sum profit from turning into a loss! But of course, there is a catch as always, remember that reducing risk costs money. Suppose the Chips-4-less stock doesn't crash, but skyrockets to 150$ (150$ - 120$ = 30$ profit).

Situation	Stock value	Profit/loss		Total:	Sum profit:
no hedge	Skyrockets to 150$	Profit on stock:	30$*500	+15,000$	+35,000$
hedged	Skyrockets to 150$	Profit on stock: Profit on option: Paid premium:	30$*500 0 3$*5*100	+13,500$	+33,500$

 

So what has happened? Essentially, using a put hedge you are buying insurance that your loss will not increase in case the stock drops below the strike value. This limits the risk in the period from now untill the put expiration date. The cost of this insurance is equal to the premium. The less risk you are willing to take, the more cost. Limiting your risk for either higher strike value or for longer periods of time will cost a much more, as puts with a higher strike value or an expiration date further in the future have more premium on them.

 

Once again, you find yourself with 500 stocks in a microelectronics company called Chips-4-less which you have bought at 80$ in December. Summarizing this in table form:

Situation	Stock value	Profit/loss		Total:	Sum profit:
Before hedge	At 80$	Profit on stock:	0	0$	0$

You do not want to sell the stock because of longterm considerations, but you are sure it will not increase much (or even drop a bit) in the near future. Essentially, this stock is doing nothing for you right now, so you consider a covered call write.

For the covered call write you sell a number of CALL option contracts to hedge your position. When you buy a CALL contract, you are buying the right to buy 100 pieces of stock at the strike price on expiration date. Therefore, when you sell a CALL contract, you are agreeing to supply 100 pieces of stock at the strike price on expiration date. Because you own 500 pieces of stock in this case, it is called a covered call write as you can actually hand over the stock if necessary (writing is the same as selling).

First, let's look at the implications of a covered call write before going into technicalities. You sell 5 CALL 100 FEB for a premium of $1 per option (i.e. 500$ for 5 contracts). You were right and the stock goes for 85$ in February (85$ - 80$ = 5$ profit).

Situation	Stock value	Profit/loss		Total:	Sum profit:
no hedge	Up to 85$	Profit on stock:	5$*500	+2,500$	+2,500$
hedged	Up to 85$	Profit on stock: Loss on option: Received premium:	5$*500 0$ 1$*5*100	+3,000$	+3,000$

So that's good, the hedge increased profit! This time, the catch is that with the hedge the profit will not increase above 100$. Suppose the Chips-4-less stock skyrockets to 120$ (120$ - 80$ = 40$ profit).

Situation	Stock value	Profit/loss		Total:	Sum profit:
no hedge	Skyrockets to 120$	Profit on stock:	40$*500	+20,000$	+20,000$
hedged	Skyrockets to 120$	Profit on stock: Loss on option: Received premium:	40$*500 (120$-100$)*5*100 +1$*5*100	+10,500$	+10,500$

You can calculate the profit from the stock going up for a whole lot of values over 100$ for the Chips-4-less stock but you will always get the same result for the hedged situation. Your stock will always go up 1$ for each point increase, but over 100$ the loss on the sold call will go up 1$ for each point the stock increases. For 500 pieces of stock, the hedge of selling 5 CALL contracts (which is 500 options) effectively cancels the profit on the stock for every value over a 100$. Under 100$ the call is worthless (nearing expiration) so you don't have to pay the buyer of the option any money or stock.