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A New Language

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Here's a sentence taken from an anecdote told by a former floor trader (Sheridan, CBOE Webinar): "I buy 500 with a 50 delta. That's 25,000 deltas long. I have to immediately sell 25,000 shares of the stock to hedge my position."

Can you interpret what he was saying? If not, you will be able to do so by the end of this article. You'll also understand a little more about what delta has to do with managing risk.

About once a year, I cover delta in these Trader's Corner articles, thinking each time that it will likely be the last time I do so. Delta, along with gamma, vega or tau, theta and rho comprise the Greeks, components of options pricing. Inevitably, questions from subscribers prompt a review or, in this case, a different twist on the discussion. Usually those questions have to do with why their purchased options aren't profitable when the underlying moved in the right direction. However, I believe that this discussion of delta also ought to concern how it can be used to monitor risk.

The reason those options aren't as profitable as readers expect them to be often involves an explanation of delta. In OPTIONS AS A STRATEGIC INVESTMENT, Lawrence G. McMillan summarizes delta by saying that it measures "how much current exposure" an option trader's "option position has as the underlying security moves." Perhaps, if you haven't studied the Greeks of options, that summarization doesn't make any more sense than the anecdote that began the article, but hang on. It will.

Another explanation of delta is one that perhaps both McMillan and the floor trader reference: delta's prediction of the option's probability of being in the money at expiration. A delta of 0.55 suggests that the option is estimated to have a 0.55 or 55 percent chance of being in the money at expiration.

Another definition exists, and this one typically makes the most sense. Delta provides a measurement of how much an option's price is likely to move as the underlying such as KO, MSFT or the SPX moves. Delta ranges in value from 0.0 to 1.0 for calls and -1.0 to 0.0 for puts, but for most options on most quoting sources, it's expressed as a decimal such as 0.32 or -0.25. On a few sources, such as ivolatility.com's free service, the delta is expressed as a percentage, such as 58.53 percent or -41.87 percent. The differences in quoting conventions relates to the delta's two purposes: showing how much an option will change in price for each point change in the underlying or giving a percentage chance that the option will be in the money at expiration.

When a call option has a delta of 0.32 or 32 percent, the option's price will increase approximately 0.32 for each point the underlying moves higher and has an estimated 32 percent chance of being in the money at expiration. If you have a call on KO with a delta of 0.55, and KO moves up a point, your call should be worth about $0.55 more if all other inputs such as volatility remain the same. If you have a put on KO with a delta of -0.78, and KO's value falls two points, your option should be worth about $1.56 more, with a caveat that will be discussed later.

Many brokers offer quotes that include the deltas for the options you're considering. If your broker's site doesn't include information on delta, ivolatility.com does. At the top of the front page, you'll find a slot for typing in the symbol of the underlying. Type in KO, for example, and click through to find out that with KO closing at $57.80 on 10/15, KO's OCT 55.00 strike call had a delta of 82.92 percent (or 0.83) and the OCT 55 strike put had a delta of -18.51 (or -0.19).

Why are deltas positive for calls and negative for puts? That's because calls increase in price when the underlying moves up, but puts decrease in price when the underlying moves higher. The negative sign shows that for each point the underlying moves higher in price, the put option decreases by the delta.

Conversely, calls lose money when the underlying drops; puts gain in that circumstance. For each drop of a point in the underlying, the put will gain by the delta. For those for whom the concept isn't intuitive, an example might be easier to understand.

XYZ @ $15.00
Front Month Call Strike 15 has a delta of 0.50
Front Month Put Strike 15 has a delta of -0.50

Two hours later, the following is true:
XYZ @ $17.00
Front Month Call Strike 15 is worth approximately $1.00 more (2 x 0.50)
Front Month Put Strike 15 is worth approximately $1.00 less

The increase or decrease in options prices in the example isn't exact because delta changes as the price of the underlying moves closer or further away from the strike of the option. For our purposes, we'll consider it steady at 0.50 or -0.50 throughout the two-point price change, but that wouldn't strictly be true.

Notice that the call in our example had a delta of 0.50 and the put, -0.50? That's because these calls and puts are at the money, with the underlying at 15.00 and the strikes at 15.00, too. At-the-money (ATM) options have deltas of approximately 0.50 or 50 percent.

On October 15, with KO closing at $57.80, ivolatility pegged the OCT 57.50 call's delta at 58.50 percent (or 0.59) and the OCT 57.50 put's delta at -42.69 percent (-0.43). KO had moved away from that 57.50 strike, moving higher, so the call's delta had increased a little above .50 or 50 percent and the put's had decreased a little below .50 or 50 percent. The deeper an option is in the money (ITM), the closer the delta's absolute value will be to 1.00 and the further it is out of the money, the closer the delta will be to 0.00.

That means, for example that a deep-in-the-money put will move almost a point for every point the underlying drops. A far out-of-the-money one won't move much at all unless the underlying drops precipitously.

That leads directly into the problem that prompts subscribers to write me. A subscriber might have bought an SPX put, for example, and the SPX moved down 4 points, but the put didn't change much in value. That's usually because the option was so far out of the money that the delta was low.

For example, at the close on October 17, with the OEX at 719.70, an OCT 700 put had a delta of 0.06 or 6 percent. The bid/ask spread was 0.15 for that option. That means that, all other things held constant, the OEX would have to drop almost three points just to cover the distance between the bid/ask spread, and even further to cover the costs of the commission, and that would just get you to breakeven, not even to a profit. When I was daytrading the OEX, I would buy options as deep in the money as I could afford, but I wanted a delta of at least 0.70. That usually allowed me to make a profit, albeit sometimes a small one, on a three-point move in the OEX. McMillan goes further. He says if you're going to be daytrading, buy the stock, not an option. This whole delta problem is one of the reasons--along with the wide bid/ask spreads--that some former options traders switched to futures.

Did you notice that in our hypothetical XZY stock at $15.00, the deltas of the ATM call and strike added up to zero (-0.50 + 0.50 = 0.00)? The position is called delta neutral. What does that mean? It means that, theoretically, the position will not suffer from price movement. If XZY moves up, the call's price would theoretically increase as much as the put would decrease, at least at first. Of course, it's not always quite that easy and this ignores other risks.

Risks to options positions come mainly from price movement, volatility changes and time decay. Either the price moves against you, volatility drops or escalates or time passes without enough movement. A delta-neutral position temporarily wipes out the price risk, but depending on how it's structured, it may suffer from other risks. For example, what if you bought that XYZ straddle at with a strike of $15.00 (i.e., one 15.00 call and one 15.00 put) and the price of XYZ stays near $15.00 right into expiration? Time decay eats away at the value of the options you bought. In addition, volatility will likely decrease and that also will decrease the value of both the call and the put you purchased.

It's not always possible to wipe out all risks, but the former floor trader who bought "500 with a 50 delta" and turned around and sold "25,000 shares of the stock to hedge" was trying to create a delta-neutral position, one that wouldn't suffer from adverse movements in the stock. Stock is considered to have a delta of 1.00. Why? For each point a stock moves, the stock gains or loses that same value. When a stock is sold, you're short the stock and so the delta is now -1.00. For every point the stock moves down, your position gains a point.

That floor trader who bought the 500 contracts with a delta of +.50 was at risk if the stock dropped. For every point the stock dropped, the floor trader would theoretically have lost $25,000 (500 contracts x 100 multiplier/contract x .50 delta = 25,000 deltas). Yikes. That's a tremendous risk. No wonder that trader wanted to "immediately" sell 25,000 contracts.

What happens then if the stock drops a point after the floor trader had hedged? The value of the options position theoretically drops $25,000, but he's offset that by gaining $25,000 in his short stock position. Floor traders don't last long if they don't control both price and volatility risks, say former floor traders, and you can see why.

Delta-neutral positions don't always stay neutral. Imagine the floor trader's case. If the stock were to drop five points, for example, the call he bought is further out of the money and the delta has dropped. Imagine that it had dropped to 0.41, for example. The trader is then long 20,500 deltas (0.41 delta x 100 multiplier/contract x 500 contracts), but he's short 25,000 due to the stock he shorted. What does he do? He could buy-to-cover 4,500 of those shares of stock he shorted if his only goal was to keep a delta-neutral position.

He might have other goals. He might be also be trying to keep his entire portfolio gamma/delta-neutral. What's gamma? That's the topic of next week's article.
 

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