We receive questions every week from readers and students. Recently I got a good one about using put options as protection for a stock position. Here is the question:
Let’s suppose that I purchase 100 shares of a stock at $30.00 and I wish to protect that stock against any loss for a given period. If I buy 1 $30 put (at the money) on the stock, that would give me the right to sell the 100 shares of the stock back to the put writer for a total of $3,000 at any time during the option period. Thus, setting aside the cost of the option (which I know could be costly), I would have fully insured against any decrease in the price of the stock during the option period.
With the put being ATM, it would have a delta of -0.5. I understand this to mean that I would need to purchase 2 puts to have a fully hedged position on 100 shares. Since in the previous paragraph I determined that only 1 put was necessary to provide the downside insurance, I am assuming there must be a difference between being “insured,” in the sense I used such term in the previous paragraph, and being “fully hedged” as that term is used in this paragraph. I am having difficulty reconciling the two concepts. Can you enlighten me?
Great question. Many people loosely use the terms “hedged,” “insured” and “protected” interchangeably, but in fact they are not the same thing. Here is the short answer:
A position that is perfectly hedged against stock price movement will show no overall gain or loss today if the stock price changes today within a small range.
A protected position (or “insured” position), on the other hand, will gain or lose overall as the stock price moves today; but the maximum loss is limited.
Note the word “overall” above. This means considering both the value of the stock and of the put options used to hedge or to protect it. We cannot “set aside” the cost of the options with either type of position. In the case of the hedge, the whole point is that the change in value of the stock and that of the options must offset each other exactly. And in the case of the protected position, it would not make sense to pay $10 to protect against a loss of $5.
It’s pretty clear why someone might want to protect a stock position, to make it into one where the maximum loss is known and limited. So who would use options hedging and why?
Let’s illustrate with a real-world example, with a real $30 stock. On August 3, HPQ (Hewlett-Packard) was at $30.02. The September puts, with 45 days to run, were at $1.43.
The delta of these options (options’ price participation percentage), as in the reader’s question, was approximately -.50. This means that if HPQ dropped by one dollar per share today, the put’s value would increase in value by .5 * $1.00 = $.50 per share today. Conversely, if HPQ were to rise by $1.00, the put would drop by $.50.
First, let’s say we owned 100 shares of HPQ and bought a single put option for $1.43 to protect the position. If HPQ then dropped by $1.00, we would lose $100 on the stock. The puts would increase in value by only $.50 per share, to $1.93, gaining back $50 for us. We would thus have lost $50 overall (a hundred-dollar loss on the stock and a fifty-dollar gain on the puts). In the worst case (flat or lower stock price) we could have an overall loss on this position of up to the $1.43 per share that we paid for the puts. Every penny that the stock moved up (if any) would improve on this. Our upside profit potential would still be unlimited, but whatever that profit was, it would be $1.43 per share less than without the puts.
Now let’s look at the situation with a position that is completely hedged against stock price movement. Such a position is called a delta-neutral hedge. There are many ways to construct one. In this case we could make it by buying a hundred shares of stock; and also buying not one but two puts. Now, if the stock drops by a dollar we would still lose $100 on the stock but we would gain $50 on each of the two puts, replacing that hundred-dollar loss entirely.
The hedge might be what we were looking for if we knew there was an event coming up that would move the stock, but we didn’t know which way and didn’t want to take the chance. We might think it was worthwhile to forego the chance of a profit in exchange for eliminating the chance of a loss. Once the event is past, we could then decide to remove the hedge (sell the puts) and be back in a position to make a profit or loss on the stock.
Another reason for a neutral hedge would be to attempt to profit from a change in implied volatility (crowd expectations for future stock price movement), without having exposure to actual stock price change. If implied volatility were very low then we would be able to buy the two puts cheaply. If implied volatility then went back to its normal higher level, the two puts would increase in value even without any change in the stock price. And if the stock price did change the two puts would offset it. This would work if the increase in volatility happened soon, before the puts lost too much time value.
In summary, a protected position limits our loss, at the cost of the put premium. A hedged position freezes us in place until it is removed. Options hedging has its uses as does protecting stock positions, depending on what we are trying to accomplish.
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