Puts, Calls and Hedge Time in Paris

Alan in Paris writes:

I've been granted options on my company's stock that will vest in December. I want to protect the downside -- even to the point of not accepting any upside from here.

If I could exercise my options today, I'd get 1,000 shares at $50. Because the stock now trades at $100, I'd take a $50,000 profit. I fear between now and December, though, the stock could go down to $50, leaving me with nothing.

Could I buy out-of-the-money puts to stem some of the potential equity loss? What if I short the stock instead?

Dr. Option responds:

Why on earth would you think about hedging stock options when you live in Paris? Good grief, man. Eat! Drink! Paint!

But if you insist...

Let's start from square one. By the grace of your company, you own (or will own in December) a $50 call on 1,000 shares. Now your stock's in a $100 world so, as you've correctly pointed out, there's 50 points of intrinsic value in the call. You've earned it with sweat equity, meaning you've got a cost base of zero. You say you'll vest in December, but you don't specify an exercise/expiration date for the option. You seem to be saying you would exercise immediately upon vesting if the option's in the money, so I'll just assume vesting and exercise/expiration dates are coincidental.

You're looking for a hedge against price risk. In other words, insurance. But you don't say how much you're willing to pay for it, nor how much "self-insurance" or deductible you're willing to accept. Those would be the same questions you'd address in any insurance-buying decision.

A full hedge is established when a diametrically opposite position is undertaken to counterbalance the risks of an existing market stance. The simplest hedge, then, is the opposite of the existing position. That means the exact hedge for this position is actually short calls, struck at $50, on 1,000 shares. If we make fairly modest volatility and interest-rate assumptions, such a sale could rather handily bring in enough call premium to hedge the granted call's current intrinsic value.

But that's not a good trade for you, mon ami Parisien. Since you don't own the underlying shares, and since your long call is contingent and held away, your broker would treat you as if you were writing naked calls. That would subject you to a pretty steep margin requirement. To be exact, at least $20,000, or 20% of the current value of the underlying shares. To boot, writing in-the-money calls subjects you to a greater risk of early assignment. And you can't afford that since you ain't got the shares.

Zut alors! How can you get opposite price exposure to your existing position without selling calls?

We gotta first ask a question here, "What's the yardstick by which we measure price risk?" Yep, it's delta, the rate of change in the option's price for every $1 move in the stock.

Running your options grant through an options-pricing model would most likely generate a delta position of plus 1,000. Because your granted call is so deep in the money now, it behaves pricewise as if it were a long position in 1,000 shares. To be fully hedged (delta neutral), you'd need to establish an equivalent short (negative delta) position.

In your question, you wonder if a short sale of the stock is a possible risk remedy. It would, in fact, give you just the sort of delta position you need today (minus 1,000) to become delta neutral. But it may not be what you want tomorrow. The delta of stock never changes; the delta of an option does. Those changes would create a hedge imbalance.

There are a couple of very important considerations to keep in mind, though. First, this trade requires margin. Big margin. You'll have to put up equity of at least $50,000 initially. That's more equity than required for the short-call hedge. And if you couldn't do short calls, you certainly can't do short stock.

You say you also pondered buying puts as a possible hedge. Let's consider using the closest out-of-the-money put struck at $95 for that. In our hypothetical world, with a stock at $100, we might find the December $95 put offered at 6 1/2. Buying puts in a 1:1 ratio to the "calls" granted by your company (10 puts equals 1,000 shares) would leave you still bullish.

Your net position would be equivalent to owning about 660 shares. That's because the put delta is only minus 0.34 per share. So, you'd be only tempering your bullishness with this trade. Still, that may be OK. As you have no cost base in the granted call, a profit's generated as soon as the call is in the money. Then it's just a matter of ensuring that any potential put-premium losses don't swamp the call gains. And that, at present market levels, looks imminently doable. The potential payouts look like those depicted below.

1:1 Put Position Expiration payouts
Stock price	P/L $50 call grant	P/L 10 $95 purchased puts	Net
120	$70,000	-$6,500	$63,500
110	60,000	-6,500	53,500
100	50,000	-6,500	43,500
90	40,000	-1,500	38,500
80	30,000	8,500	38,500
70	20,000	18,500	38,500
60	10,000	28,500	38,500
50	0	38,500	38,500
40	0	48,500	48,500
30	0	58,500	58,500

Above the current market, an opportunity cost of up to $6,500 is incurred. That's simply the cost of the insurance cover -- the put premium. For some range below that level (i.e., 90 to 50), the hedge retains a portion of your present $50,000 intrinsic value. The "deductible" in this case is equal to the puts' original out-of-the-money amount together with their premium. But it's only at levels below 38 1/2 that the hedge returns more than present intrinsic value. So, in essence, for a $6,500 cash investment, you end up hedging the entirety, or more, of the intrinsic value only in a severe downturn well below the granted call's strike price.

So, can you create a more effective hedge with out-of-the-money put purchases -- one that offers protection over a broader range of prices? Mais oui! You can establish a delta-neutral hedge with puts, but you're going to need about three times as many puts (1 divided by 0.34 equals 2.9) to do so. Constructing the hedge with 29 of the puts requires an $18,850 cash investment and produces the expiration payouts shown here.

Delta Neutral Hedge Expiration payouts
Stock price	P/L $50 call grant	P/L 29 $95 purchased puts	Net
120	$70,000	-$18,850	$51,150
110	60,000	-18,850	41,150
100	50,000	-18,850	31,150
90	40,000	-4,350	35,650
80	30,000	24,650	54,650
70	20,000	53,650	73,650
60	10,000	82,650	92,650
50	0	111,650	111,650
40	0	140,650	140,650
30	0	169,650	169,650

Obviously, aside from the disparate capital commitments required, the two put hedges differ in market outlook and risk tolerance. As a hedge of the $50,000 intrinsic value, the 1:1 put position is more aggressive. It gives away less upside potential above the current market but carries more downside risk. Inherently, this position provides less catastrophic insurance than the delta neutral hedge. The delta neutral hedge is more conservative in that it exposes the current intrinsic value to diminution through the much narrower price range highlighted in the above illustration.

So, Alan, the good news is that there are indeed ways to hedge your stock option's current value. The bad news is that without knowing your current capitalization or risk tolerance level, Dr. Option finds it impossible to offer a specific prescription. But, at least now you have an idea of the how the medicine might taste. Chacun a son gout.

(Everyone to his own taste.)

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