Investment XYZ

Monday, May 22, 2006

Cuban's Collar -- Anatomy of a Famous Trade

Mark Cuban's collar trade is one of the most famous trade using derivatives during the internet bubble time. Here I will analyze in detail how options make this ingenious trade possible and how both sides of the trade work.

Costless Collar

Back in 1995, Mark Cuban and partner Todd Wagner created, a multimedia behemoth providing streaming audio and video of live radio, TV and sports. They sold the company to Yahoo! for $5.7 billion (yes, "B"). Yahoo's market cap at the time was about 130 billion -- Today it is 44 Billion, in between Yahoo's market cap reached almost 300 billion and crashed down to about 10. The ingenious option trade Mark Cuban made allowed him to protect his billions, without paying any insurance premium. At the time he had 14.6 million shares of Yahoo traded at $95. Thus he had a market value of $1.4 billion (I'm not sure about the rest of the total $5.7 billion, but that's not the concern of this article). Probably because there was a lock-in period for him to sell the Yahoo share, or he used these Yahoo shares as collateral for a bank loan, or he didn't want to miss the opportunity if Yahoo continued to rally, he chose to enter a collar to lock in his share value without selling the shares. Here is the detail of the option trade:

1) For each 100 shares of Yahoo stock, 1 contract of put (strike 85) was bought and 1 contract of call (strike 205) was sold. In total there were 146,000 contracts of calls and 146,000 contracts of puts traded.

2) The premium of the put exactly offset the premium of the call, thus there was zero cost for this trade (not sure about the whether Cuban had to pay the commission but it is likely the commission cost was rolled into the premium as part of the total deal between Cuban and the counterparty bank).

3) All options expired in 3 years.

Such option structure is called collar. A collar consists of two legs: buying a downside put and selling an upside call. A costless collar has the premium of the put offsetting the call's exactly so that there is no cost to enter the collar trade.

After Cuban's collar trade was entered, Yahoo's share price reached the stratosphere of $237 in January 2000. Such a collar trade seemed not so smart. Then the internet bubble burst, and the Yahoo reached the abysmal of $13 in late 2002, the collar turned out to be a stroke of genius, a great risk management trade that cost nothing to have. Cuban was able to pin down on the value of the share (or 90% of it), no matter how the subsequent movement of the stocks.

Several interesting observations of this trade. Even though the Call price equal to the Put price, the Call was $110 out-of-money, while the Put was only $10 out-of-money, that seemed to be a huge disparity. Was that the Call way too much underprice or the Put was well too much overpriced?

Actually the pricing is not so outrageous as it appears. There are two factors in working here: 1) Skew; 2) Interests. The first factor, skew, means the market always prices downside protection (puts) more expensive than upside (calls), thus puts are usually more expensive than the calls in the same out-of-money amount. Such market phenomenon is called skew, which can be measured in several ways (one way is to describe the skew by the pricing of a collar).

Another factor is more important in this case. Calls can save the holder interests than holding stock (since you don't need to shell out cash to buy stock until exercise time), while puts cost you interests that you should get if you short stock instead of buying put. Thus the combination of the two (sell call and buy put) - both costs interests -- means collar is costly in interests. Supposed Cuban didn't do the collar trade but sold the stock instead. The proceeds from the stock sales could earn him interests for the subsequent 3 years, no matter whether the market was up and down. While with the collar he would lock in the stock value (just as cashing out), but without the interests. Thus collar would be unfavorable to holders, unless such interests consideration is priced in. Thus 3 years of interests would discount call price and increase put price: the same effect as skew.

Did He Miss Something?

Even though in retrospect this collar trade was smart in protecting Cuban's original share value, he might have missed out on two things: 1) he might have overpaid for skew which typically is overpriced in the market place due to psychological factors of investors; 2) He missed out on the interests he deserved. If he really wanted to lock in the share price rather than speculating on the upside potential of the stock price, he could do 85/95 collar (buy 85 put, sell 95 call) which should give him quite substantial amount of premium income (since 95 call should have much higher premium than 85 put). Such income should be roughly equal to the interest income he should received if he liquidated his Yahoo shares into cash. The banks that marketed such costless collar to big investors like Cuban would like them to forget about the interest aspect and focus on the "costless" feature of collar. To construct such costless collar, it ends up with a collar with two far apart strikes (such as 85 put and 205 call), containing a huge speculative upside potential (which is attractive to the speculative mind). Basically it is a way of encourage the investors to forgo their interest income to exchange for some speculative opportunity. In Cuban's case, the banker might present the "benefit" that even when Yahoo should rise to 200, his share would not be called away so that he would still participate in the rally.

In the end, that collar worked more like a put (while the upside call financed the cost of the put), and the "only" thing Cuban lost was potential interests he would have received if he just sold the stock. How much? The interests for 3 years would amount to $200 million or more.

The Counterparties of the Trade

Cuban's collar helped him protect his billion. So did the party on the opposite side of the trade lose billion when Yahoo tanked? Let's use this trade to look at how the option market works for both sides of the players.

On one side, Cuban now owned puts and short calls, with his existing holding on Yahoo stock. His counterparty of this trade, the market maker or the bank, would short puts and long calls. So what would happen to these huge positions on the opposite end of the trade?

Obviously if the market maker did not do anything and just hold the short puts and long calls, the short puts would wipe a billion or more off him when Yahoo tanked. However, contrary to common belief that options are zero-sum game, the market makers do not gamble against customers, namely the customers and the MM may not typically on the opposite ends of a bet on the speculative part of a trade (see my earlier article on this). Instead, MM would hedge. In this case, to hedge the options, they should short almost the same amount of Yahoo stocks as Cuban was holding. Thus it almost looks like the counterparty sold (as short) all the shares Cuban would like to sell but couldn't (either because of regulations, or taxes or loan requirements, etc.). Thus when Yahoo stock dropped to $13, Cuban was safe, so was the counterparty.

Actually there is more to that.

In real life though, since the trade is so huge (292,000 contracts of calls and puts) which entailed many aspects of risks no matter how you hedge it with stock, the counterparty would typically lay off the risks to many other parties, which included 1) other market makers; 2) proprietary traders, who might take on part of the trade for reasons other than speculating on direction (for example, the short put leg might seems very juicy in volatility that some volatility traders might want to assume portion of the risk of the short put trade); 3) Speculators/investors (for example, the long 205 calls may be transferred to the hands of investors who were extremely bullish about Yahoo stock).

So how could the counterparties of this trade make profit (or loss), since we all know Cuban had lock in his money even when Yahoo share price plunged to $13 in 2002? The profits of the counterparties came from

1) Bid/Ask spread.

2) Interests.

3) Volatility.

4) Speculation.

The first one is obvious. The market makers provide a service for liquidity (they have the obligation to take the other sides no matter whether the investors want to buy or sell), so they deserve to profit from the bid/offer spread. The second one, interests, is less obvious. Suppose there was a single party holding exactly the opposite positions as Mark Cuban's: long 146K contracts of calls, short 146K contracts of puts, and short 14.6 million shares of Yahoo stock, how much he would make by the time when the option expired? He would make roughly $200 million in interests, while Cuban got to protect his Yahoo stock value. That was a pretty cool trade for both parties -- a win-win.

The interests show the glacier power of money. Many investors look at the few percent of interests with distain and focus their eyes on the quick money that might come from the fast movement of stocks. Actually I have not heard anyone commenting on the potential "loss" of $200 million for this famous trade, and everyone extols on the virtues of protective power of the costless collar.

The third point, volatility is more technical and less certain, and just like the fourth point, both are speculative and the profits and losses depend on the movement of stocks. It is difficult to estimate the total gains or losses of these two types, but it is unlikely they would lose billion.

So supposed the counterparties of this trade had only one type: the market makers who hedged. What would be the total value of this trade when we add the two sides' profit and loss together? Was it zero? Not at all. The net should be at least $200 million, not counting the instant profits for MM on the bid/ask spread, the commission, and the overpricedness of downside volatility, all these were in the profit side of the equation for the counter parties (while they did not add to the loss side of Cuban). So magically, a collar trade could create net positive value in substantial amount.

That's the way how the option market has the potential to create net profits and distribute risks: On one side, Cuban had a particular interest to create this huge collar trade for protection (with a tack of speculation on upside); on the opposite end of the stick, this huge trade would be broken down into many smaller pieces and the risks would be transferred to many parties with many different goals, each one had their own way of making or losing money. But in the end, the net sum is not zero, but likely a positive number. It shows the power of risk transfer function of options in a very complex space, which is not a zero-sum game as many people believe.

(The author can be contacted at

Friday, May 19, 2006

The Myth of "Max Pain"

There is a now commonly known option phenomenon called "Max Pain": on option expiration Friday, stocks typically are attracted to the nearest strikes where there are large option open interests. For example, if QQQQ price is at 39.2, and there is big option open interest at strike 39 and strike 40, it is likely the stock will close at 39 or 40. For simplicity, I will refer to this phenomenon as "pin" or "Max Pain ™" (

Why is it called "Max Pain"? The theory is that option market makers like to push the stock price to a particular strike so that all the options on that strike would go poof -- all become worthless. The assumption is most likely the investors would be the option holders so such "pin" would cause maximal pain to the investors who see their investments in option disappear worthless -- thus the name "Max Pain". Sounds like a conspiracy theory (MM vs the poor investors, a very common source of conspiracy theory). The term "pin" is more neutral, it means the stocks tend to be attracted to the strike and then pinned down there.

Stickiness Around Strike on Expiration Dates

Before we try to understand "why" there is such phenomenon and how people interpret it, let's see whether there is such thing really exists. My cursory observation tells me that there is not a large percentage of stock showing such tendency, but the few that show does looks quite obvious. For investors, statistics probably doesn't matter, what matter is whether such "Max Pain" falls on the names he is holding.

Just look at the just past expiration (5/19/06). Among total 909 symbols which have market cap > $1 billion and have options, there 165 names showing "pin" - with stock settling with 0.1 of a strike. That's 18%. No prevailing, but very substantial. Statistically, if the stock prices are randomly distributed and the average strike spacing is $5, the chance of stock closing at within 0.1 of a strike is about 4%.

Among then pin names, here are a few examples that stocks are pinned down to within 5 pennies (stock closing prices in parenthesis, the second number is the price change on Friday): LFG (65.0, +0.5), RIMM (67.49, -1.74), DNA (80.03, +4.1), SNDK (62.49, +0.88), SLAB (40.04, +0.37), LEH (67.48, +1.27). Considering how volatile some of these names are (such as RIMM, SLAB, SNDK, LEH), it looks like volatile as they are, they still end up within pennies of the strike when the market close. Quite magical. The conspiracy theory seems quite well founded.

So the fact of “pin-to-strike” is established. Let's look at how much truth to "Max Pain" explanation of the "pin".

First of all, all expiring options, no matter what strikes, will go poof on expiration Friday after the market. What exactly I mean is the volatilities go poof, disappear, zip. For example, supposed on expiration Friday morning, a strike 40 call is priced at 1.5 with stock at 41.3, that means there is 0.2 volatility value in the option. When the market closes, if the stock is closed at 42, the option is worth $2, or the intrinsic value. The volatility value of 0.2 disappears. If the stock is closed at 40, the option is worthless, so is the 0.2 volatility. In other words, the volatility value disappears on expiration, no matter whether the option is in-the-money, at-the-money or out-of-money.

Disappearing of Volatility Value

So should the market makers try to push the stock prices to the strikes to make the options disappear, if they can push? Probably not necessary for them to do that. First of all, market makers would always hedge their options (which require calculating "Delta" of options using some model), and on expiration date, the hedging is relatively easy to understand without complicate math: option is either in-the-money or out-of-money, so the delta is either 1 (call), -1 (put) or 0 (mathematically, it means on expiration date, Delta becomes a discontinuous function, and Gamma becomes a Dirac-Delta function). As we see above, the volatility value of the options always evaporate away on expiration, so as long as an option is hedged, the market maker can capture (if he is short) or lose (if he is long) the volatility, no need for them to push the options to the strikes. Furthermore, market makers can be long or short options, so the disappearing volatility value may be good or bad for them, namely, the "max pain" may be exerted on themselves, which obviously doesn't make sense.

For investors who hold options and do not hedge, the disappearing volatility value works against them, no matter whatever the stock price is settling in. Unhedged options (purchased by investors) are to speculate on the intrinsic value (as the direction of stock), not on the volatility value. The volatility value is a premium that gives investors two benefits (thus the cost money to have it): 1) leverage: holding a $1.5 option in the morning (stock at 41.3), and stock closes at 42, the option increase to $2, that's 33% return, while if you hold stock, it gives you 1.7% return. So even though the investor loses the 0.2 volatility value, he should be happy since options give him a huge return rate that stock can't give him. 2) protection. If stock drops down to $39, the option expires worthless, so the option holder would loss $1.5, while the stock holder would lose 41.3 - 39 = $2.3.

Investors tend to feel the options (a contract) is less tangible than stock (equity), thus if an option disappears entirely when the stock settles on the strike, they feel they are lost something forever. Actually that is quite naive thinking. If they miss their stock, all they need to do is to buy the stock at the strike, and you have exactly the same results when the option expires in-the-money.

Can Hedging Cause It?

Nevertheless, I wouldn't whisker away the conspiracy theory altogether. The "pin" phenomenon may be actually related to trading behavior on expiration day. First of all, let's see who are trading options. In general there are 3 types: 1) investors who speculate on stock direction (option as a leverage tool); 2) market makers who take the opposite side of a trade and hedge (and make money on bid/ask spread); 3) Proprietary traders who trade on some dimensions other than delta (such as volatility traders, dividend traders). #1 (investors) typically won't hedge, 2) and 3) typically hedge.

Hedging activities on expiration tend to occur around the strike. Let's look at an example to see how it works: a trader longs a call (strike 40), stock is moving from 39.9 upward. When the stock crosses 40 line, now his position suddenly changes from no delta to 100 delta, so he has 100 shares per contract to sell (short). If the stock drops back below 40, he can buy the stock back, thus longing an option give he opportunity to scalp around a strike and make some extra profit. Conversely, if he shorts the call, the hedging is a risk management process to limit loss that can cause by stock movement. The moment the stock go above 40, he should immediately buy stock to hedge, if the stock drops below 40, he should immediately sell the stock. Such buy high/sell low would in general cause loss which should in theory (statistically), offset the volatility premium he should collect. In both cases (long and short), the hedging activities all center around strikes, which tends to pin down the stock there.

So who is more likely to cause the pin-to-strike, the long side or the short side? For the long (doesn't matter they long call or put -- "long" means long volatility, not long Delta), the scalping is some "extra" profit they can get if the stock does whipsaw around the strike. So when the stock price is above the strike, they would sell stock; below the strike, buy stock (sell high/buy low). If you have 500 contracts, that means you can sell 50,000 shares of stocks. Such selling action can certainly push the stock back down below the strike, where they can buy back the 50,000 shares. Of course if the stock moves above the strike and keep going, that can become a windfall for the long if he does not hedge. But typically the market makers or the hedgers won't take huge delta risk like this and would hedge instead. On the short side, any price move across a strike (up or down) is a big risk. A 5c option can suddenly become tens or hundreds times more expensive (remember GOOG on 1/20/06 expiration Friday, dropping almost $40 going through 3 or 4 strikes – that can be a big disaster for anyone shorting options and not hedge quickly and correctly). So moving the stock price toward a strike is not a good thing for the short side, and because he has to buy when the stock goes up, sell when the stock goes down, the hedging action on the short side can cause the stock to move further away (not toward) the strike.

So the "max pain" theory explains such pin-to-strike incorrectly in three areas: 1) You don't need to move the stocks to strike to make the option worthless. Volatility value will evaporate on expiration date, no matter what stock price is close on Friday. 2) The pin is likely due to hedging activities, rather than some MM conspiring to move the stock to strike; 3) The option traders (MM and proprietary) who might cause the pin is the long side, rather than the option writers (as the max pain theorists claim).

The Automatic Exercise Rule

So all these "Max Pains" are not the results of some conspiracy trying to cause pain on investor? Probably not as the "Max Pain" theorists commonly believe, but for a different reason. Option automatic exercise rule is the true reason behind such pain. After options expire, not all the in-the-money option are automatically exercised. The rule (which was recently updated, and may vary from broker to broker) states that only options more than 10c in-the-money will be automatically exercised. Those within the 10c limit, the option holders have to call their broker to give exercise instruction if they want to exercise. If you do not exercise them, they become worthless even theoretically they are in-the-money. Why there is such rule (which seems extremely unfair to the long side)? There are some understandable reasons behind it. Exercising an option involves two major risks: 1) after exercise, you hold stock thus no longer have the protection of an option. For a 5c option, if stock drops $10 on the Monday after expiration, you would just lose 5c/share, while if you exercise the 5c option into stock, you would lose $10/share. 2) You need to come up with capital to buy the stock. Imagine you own 10 contracts of GOOG 400 call, stock settles at 400.05, you decide to exercise to save the 0.05, you need to come up with $400,000 cash to buy 1000 shares of GOOG at $400.

Such 10c rule, though not unreasonable, can cause a windfall for the short side if the option holders decide not to (or more unfortunately, forget to) exercise. 10,000 contracts (a typical size of open interest of one option strike) of 10c options have a value of $100,000 that would be in the hand of the short side if not exercised. That is certainly a lot of risk-free money involved for one strike.

Is that a conspiracy again the investors who may not be so knowledgeable or vigilant? I doubt, considering the risk and capital requirement for exercising. But that certainly puts some responsibility in the investors' hand, and requires them to really know what they are doing and pay attention to their options when are near the strikes. Forgetting to exercise a 10c in-the-money option is unforgivable for a responsible investors.

What lesson can investors learn here?

1) Watch out for the automatic exercise rule of your broker. Check with your broker before the expiration date. Typically it is more than 0.1 in-the-money, but some may be 15c.

2) Watch out for your options holding that may end up out-of-money and fall into the non-automatic realm. If you do not intend to own the stock (which would cost you capital), make sure you sell the option BEFORE 4pm EST, even sell it at 0.05 is better that out-of-money. Before 4PM, you can usually sell it above the intrinsic value.

3) Even though option market close at 4PM EST, your right to the options actually still in your hand until 5PM or 5:30PM. So you can still exercise an out-of-money or non-automatic exercise option, if you want to. Why do you want to do that? Let's look at a fictitious example. You hold a DIA (1/100 of DJIA ETF) 115 put, and it closes at 115.01, so your option is out-of-money. At 4:30PM EST, President Bush eats a pretzel and chokes himself, unconscious (may be dead). So DJIA after-market drops 100 points ($1 in DIA). What can you do? You call your broker and exercise your put option, which effectively establish a short stock position at 115 (while at this point the market is trading at 114). If you don't want to wait until Monday morning to take profit (it is possible that Bush survives the incidence and end up like nothing happen for the market on Monday), you can buy the stock on the after-market at 114, thus lock in the profit immediately ($100/contract), without taking any uncertainty on Monday.

So "pin-the-strike" may still be a reasonable "technical indicator" to predict where the stock may end up on expiration Friday (I'm not for or against such analysis), but what cause it may be quite different from what is commonly believed.


In October 2006, the OCC (which governs the option trading regulations) change to the automatic exercise threshold for in-the-money options from 10c to 5c.

(The author can be contacted at

Wednesday, May 10, 2006

Why the Deluge of GM Calls

On May 9, 2006, a GM May 20 Call (which had about 10 days to expiration and was in-the-money), spiked in trading volume to a jaw-dropping 288,000 contracts traded in a single day. The normal trading volume on this option is only a few hundreds to a few thousands, the Open Interest on this strike before this day was 22,215. The turn-over rate of this option on this day was not just much much higher than regular volume, but much higher than open interest.

What was going on? If you asked an option trader, he was sure to snicker: "It's a dividend play."

What? Isn't it because people are very bullish about GM? On that day, GM got an upgrade, and the stock made a huge $2.25 jump, a big jump for GM since it is slowly recovering from a junk-bond state reached in April. Also, stock trading volume was huge. Since there was a huge short interest in GM stock, there was speculation of creating the possibility of a short squeeze. All these seem to be along the same line as the huge volume in this May 20 Call. So wasn't this call buying part of a bullish stock buying orgy? Had it anything to do with a dividend?

The GM ex-dividend (ExDiv) date was the following day, 5/10/06 with a dividend amount of 0.25 (which was cut in half since last quarter). On ExDiv day, the stock should open at a price 0.25 lower than the previous day's closing pricing, before the stock can start its random walk. For stock investors, there is absolutely no arbitrage opportunity (there may be some tax consideration, but that's individual dependent). If you buy the GM on 5/9/06 at a closing price of 25.8, the next morning, your equity is worth 25.55, plus you get 0.25 in cash, no change at all in your total value. Any subsequent change in value results from the random walk of the stock price, thus it has risk. In other words, for stocks, there is no risk-free arbitrage opportunity at all.

Then how about the calls? Are they just like stock, no chance for arbitrage for some risk-free money?

A Call is the "right" to buy stock at a certain price. The GM May 20 Call, which is an American style option, is "a contract for the holder to buy the GM stocks any time before 5pm EST, May 19 2006 at $20/sh". When you hold this contract and do not exercise it, you do not own any stock on the day before the Ex-Dividend date, thus the holder of the Call contract is not entitled to a dividend distribution (the dividend is distributed only to stock holders settled on 2 trading days after the ExDiv date, which is to say, you have to hold or buy stock on the day before the ExDiv date because the stock trade takes 3 trading days to settle). If you buy the Call and exercise the right on 5/9/06, you are entitled to the dividend, thus the net result is exactly the same as buying stock.

What happens if the holder forgets to exercise? On 5/10/06, the Call will open with a drop of $0.25, just like the stock. However, the stock holder will get the $0.25 dividend in return so that there is no change in value, while the call holder does not. Thus he would just lose $0.25 per share overnight, without any risk involved. In his opposite, the option writer who was not assigned will simply pocket the risk free money of $0.25, or $25 per contract. For 300,000 contracts, that $7.5 million potential risk free money in the option seller's hand. However, the actual arbitrage potential is much smaller. Only a small portion, typically 5%, of option holders who belong to the "dumb customer" class, forget to exercise the calls on the day before ExDiv, so there is likely "only" $375,000 riskfree money.

How would the option writers catch this risk free money? All he needs to do is to hedge this call exactly as stock immediately after the call is sold. The next day, if the option is assigned, his stock is called away and he has not gain or loss; if the call is not assigned, he has a net profit of $25 per contract.

Now an interesting question: how can the option writers create such a huge volume? There can't be so many "dumb customers" showing up to buy calls on this day...

Actually all these trades are done with the market makers, who would never forget to exercise the options (it is part of the standard operation in option market making). Then isn't that the trade is totally wasteful, if the long sides are sure to exercise the calls?

The magic lies in the "lottery" system of option assignment in the option clearing house. After an option is traded, the two sides of the trade no longer have any link to each other (thus there is no counterparty risk). All the trades are consolidated and netted out in the clearing firms (and ultimately at Options Clearing Corporation or OCC). When an option is exercised, the clearing house can no longer trace back to the other side of the contract. Thus a lottery system is employed. The short sides are randomly drawn from a pool to be assigned for the exercise orders. Thus as long as there is a percentage of option holders forgetting to exercise, there is a chance for the short side not to be assigned, and that chance is independent of who is your counterparty in the initial trade.

Let's look at an example: supposed the open interest of a call option is 1000, which means there are 1000 contracts on the short side and 1000 on the long side. If one contract holder (on the long side) wants to exercise his 50 contracts, he is holding, here is what will happen in the process: he sends the exercise order to his broker, who will inform OCC -- the organization who take track of exchange traded option open interests, besides many other functions related to option exchanges. How can the OCC picks from the 1000 contracts of short positions and decide who should be assigned? Since it is no longer possible to trace back to who was the counterparties of the 50 contracts to be exercise, a lottery system is certainly a fair way for such situation. OCC will randomly choose 50 from the 1000 contracts short positions, and whoever get picked would be assigned -- which means a short call position becomes a short stock position. In another word, every short holder has 1 in 20 chance being assigned when a 50 contracts exercise order coming into a 1000 contract pool. In such a lottery system, the short option contract holders have no idea when he will be assigned until he is actually being informed. Even at the option expiration, if the option strike is very close to stock price, there is great uncertainty for the short holders whether he will be assigned or not.

Now back to the GM Call option story. Why did the heavy trading occur at this strike (20 Call)? What about GM May 25 Call? For a call option to be exercised before expiration ("early exercise"), the option should 1) be deep in-the-money; 2) have little time value left; 3) have a substantial dividend. Comparing to the May 20 Call, the May 25 Call is near the money and has too much time value embedded. Then what about the dividend that can cause the stock to drop? Is it a bad deal to hold onto a May 25 call that will suffer the drop but is still not worth to be exercised? No, its option price should be still fair: the dividend is already built into the price thus no sudden drop in call price before and at the ExDiv date.

For the May 20 call option trades on May 9, why there is still such risk-free money in the market place? Arbitrage, or risk-free money is what keeps the market fair and consistent. For example, the old fashion cross-market arbitrage fulfills the "social responsibility" of getting everyone a single price at all liquid markets at any moment. The call-exercise arbitrage as in this GM case goes a little deeper than other no-brainer arbitrage situation. In cross-market arbitrage, the opportunity disappears when there are many arbitrageurs piling in on the same trade. While in the call-exercise case, you trade (write) as many such calls as you can -- the opportunity never goes away, but only a small percentage of trades can be profitable. Such arbitrage requires data sophistication as well as a certain percentage of "dumb customers" (who do not know about the exercise to capture the dividend) in the total investor population.

In fact, selling a Call to capture the "leak" in dividend is not a true arbitrage in another sense: there is a potential huge risk involved: selling the deep in-the-money call is the same as selling a way out-of-money put (when the short Call is hedged with stock). In case the calls are not assigned, the call writers can get hit by a sudden large drop in stock price. Such a risk is even more prominent if the call is in the border line of whether it should be exercised or not (namely, the call is not very deep in-the-money).

In any cases, some traders who have the sophistication of data and hedging are willing to take such risk for the dividend opportunity for any stocks that distribute large dividends. Interestingly, this trade only depends on the size of the dividend, not on the stock price (thus it is not necessary to find a high yield name for such trades). Recent examples: C, WFC, GS, PG, and a big one: PD (which had a large special dividend on May 12, 2006).

Are there any lessons to be learned for investors playing options? Yes, just be careful when you hold a deep in the money call option. It may behave just like stock -- most of the time except when it gets close to the ExDiv date. So make sure you check the dividend and ExDiv date, if you are not sure whether you should exercise or not, just sell the option before the ExDiv date.

(The author can be contacted at

Friday, May 05, 2006

Put/Call Ratio: A Tea Leaf Indicator?

Investors love indicators, they give people some talking point for justifying their view. After all, if the stock market is a big random walk with 50/50 chance of going up and down, any indicators, including tea leaf and the cracks of turtle shell, can help pointing a direction and wouldn't be terribly wrong.

One of the popular indicator is the put/call ratio, the ratio of put volume over call volume, roughly speaking. There are two versions of such ratio: the classic CBOE version and the ISE "Sentiment Index" version (ISE version ISEE is defined as call/put ratio, but here for comparison we will inverse it as put/call ratio). Put/call ratio is now taken as the most popular indicator for investor sentiment. High Put/Call ratio indicates bearish sentiment ("more people buying puts"), low indicates bullish. To add another twist, the so-called "sentiment analysis" theory would use this as contrarian indicator, bullish means bearish, bearish means bullish. Even the palm reader are not so smart in employing such contrarian dialectics.

Here I'm not going to discuss the "contrarian" part of the theory, but just look at the how true it is to infer put/call ratio as bull/bearish sentiment.

Let's lay out some facts first.

When an option is traded, two sides of a contract is open: one side is long, one side short. Typically one side initiates the trade (either long or short) thus it takes the market (most of the time) -- taking the market means buy on ask price, sell on bid price. The other would make the market -- buy on bid (lower price) and sell on ask (higher price). That's the price of liquidity: if you (typically the investors) take liquidity (initiate the trade), you have to pay for the bid/ask spread, while the passive side (the market makers who "provide the liquidity") get to enjoy the bid/ask spread but have to do the trades whatever side the investors want. For investor sentiment, who should only for the side that initiate the trade, not the side that passively take the trade to provide liquidity.

Typically the initiated trades come from two types of people: 1) investors/speculators who use options as leverage tools to bet on stock direction; 2) proprietary traders who trade on mathematical models, or trade on a view on volatilities, dividends or interests. The first type of traders would not hedge away the "delta" since that's the only factor they bet on, the second type would typically hedge away the delta and expose the residue risk on other dimensions such as "vega" (volatility), "rho" (interest rate) or dividends. On the passive side (the market makers), they always hedge away the delta.

When we take about "bullish/bearish" sentiment, it is always associate with "delta" (stock direction). Long delta = bullish; short delta = bearish. The investor bullish sentiment is associates with the following two strategies: 1) buy call (mostly take the price as ask); 2) sell put (mostly sell at the bid). Both are long delta. Conversely, the bearish sentiment is associated with 1) sell call (mostly take the price as bid); 2) buy put (mostly buy at the ask).

Thus the key to figure out the investor sentiment is in finding out how the investors (who bet on delta) initiate the trade (long or short).

There is some discount to the above sentiment relationship: if the trade is to close an existing position, then the strategy is for taking profit or cut loss, rather than a committed indication for bullish/bearish sign. For example, an investor initiates to sell a call he bought at lower price, he is taking profit rather than really indicate a bearish sentiment.

How can we recognize a trade as "closing a position" or truly initiated? You might think of open interest, but that won't work. Even when the investor initiates a trade to close an existing position, the market may still need to open a new contract (thus increase the open interest), because the investor might had bought the original call from a different market maker, so that after the closing trade, the investor has no position, while one market maker has a short call, another has a long call.

Since there is no easy way to recognize a trade as closing or opening a position, we will just ignore this factor but at least we should keep in mind of such discounting factor.

To associate trading volume with bull/bear sentiment, we need to know:

1) The initiated side is investors/speculators, not proprietary traders.
2) Need to know a trade is done on the bid or ask price so that to determine the investor initiates to buy or sell.

Only the put/call ratio that is calculated using the subset of volume that satisfy both of the above two conditions would be a meaningful indicator for bull/bear sentiment.

The classic CBOE version of put/call ratio simply take the entire trading of volume of call and put into the calculation. ISE version trying to do a little better, excluding the volume initiated from broker/dealers, who are mostly likely to hedge delta. ISE version is close to satisfy the first condition above. We can indeed assume non-broker/dealer trades are all initiated by investors

However, ISE version includes only the "Opening" positions (which presumably means increase in open interest). As discussed above, open interest does not related to open/closing of investor positions. For now we would just ignore the distinction of "open" vs "close" trades, whether it is meant for actual positions or open interests.

My version of put/call ratio that would closely related to sentiment is:

Sentiment Ratio = (Put_Ask + Call_Bid) / (Call_Ask + Put_Bid)

Put_Ask (Call_Ask) is the investor volume of put (call) bought at ask price, Put_Bid (Call_Bid) is the investor volume of call sold at bid price.

The high this ratio, the more bearish the sentiment is.

Let's put in some number and see a detail example. Supposed the total call trade volume is 10000 contracts, of which 4000 are from broker/dealers, put volume at 7000 contracts, of which 3500 are from broker/dealers. Of the portion attributed to investors, 3000 calls and 1000 put are initiated on ask price.

Total Call Trading Volume = 10000
Total Put Trading Volume = 7000
Non-Broker/Dealer Call Volume = 6000
- Traded on Ask Price = 4000
- Traded on Bid Price = 2000
Non-Broker/Dealer Put Volume = 3500
- Traded on Ask Price = 1000
- Traded on Bid Price = 1500

Here is what we would get for the three versions of put/call ratio:

CBOE version = 7000 /10000 = 0.7
ISE version = 3500 / 6000 = 0.58
My version = (1000 + 2000) / (2500 + 4000) = 0.46

The actual numbers here do not mean anything except just to show the wide range you can get.

The CBOE version would be just a statistics that may have certain meaning except it has little to do with sentiment. The ISE version is better in its exclusion of broker/dealer volume, but doesn't mean the number is any close to the sentiment (or my version) -- the rebalance of the volume traded on bid or offer can make ISE version as far away from truth as anything else (for example, if all the investor put volume comes from the selling on bid, the sentiment is totally opposite to attributing all these volumes to put buying). Thus improving a little in the quality of the data does not make the number any close to truth. Furthermore, to separate the broker/dealer volume out of the total volume, you need the option exchange to document and publish such distinction. That's why ISE version include only the volume traded in ISE, one of the six option exchanges.

My version of put/call version is good on paper but pretty useless -- presently there is no way to get these data from the option exchange or option data publisher (OPRA who distributes all the option pricing data).

So what can we learn from these ratios? Nothing. But that's better than misleadingly associate them with something (like investor sentiment). Just like reading tea leaf to predict the future. There can be many theories on that, many people build a career on that, but the best way to deal with it is to know nothing about it.

That's the whole point of this article -- do not take the put/call ratio (as the available forms) as any indication of investor sentiment. Until we have a better categorization of trade volume data, it is better to have no indicator that to have a wrong one.

By the way, Doctor "J" on CBOE TV ( is pretty good in gauging the investor sentiment on the individual stocks. Since he is trading in the option exchange, right on the frontline, he knows all about whether any big size trades happen on bid or ask prices, and that's the way he uses to gauge whether the investors are bullish or bearish on a particular name -- exactly the same principle I propose for the sentiment put/call ratio.

As for the "contrarian" theory (bullish sentiment means bearish future, simply put), maybe a contrarian on some wrong numbers will get it right? The magic of any stock prediction is usually you can get 50% right, which, unfortunately, many investors feel comfortable about that.

(The author can be contacted at

Thursday, May 04, 2006

Is Option a Zero-Sum Game?

Is option trading a zero-sum game? That sounds strange to ask such question. All option textbooks say that: option trade is like betting: an option contract has two sides: if you buy a call and win, the other side who sold you the call would lose. Isn't it obvious?

The Fear of Trading Against MM

If option trades are zero-sum, investors seems to be in a wrong crowd: they are usually betting against the other crowd who are professional option market makers (if you want to buy, they create the contract and sell it to you; if you want to sell, they buy it from you), and this crowd usually win. So if it is zero-sum, the investors must be on the losing side -- at least statistically speaking. No wonder people love to guess which side MM (market makers) is at and trying the stand on the same side.

Such belief is totally untrue. In many cases, the so-called MM (in the option market) are actually bogie-man that people create to scare themselves. It is a useless effort trying to stand on the same side as MM, because they have no side. They stand on both sides and make money on the bid/offer spreads.

Here is how the option market works: when an investor opens an option contract (for example, buy a call), the investor is speculating on the direction (wish the market to go up), while the other side, the market maker, has no view (up or down), but has the obligation to write the contract (the investor is on the long side, the MM is on the short side). After the contract is opened, the investor would sit on it and hope his speculation is correct (wish the stock to rise for calls), while the market maker would immediately hedge the position. In this example, the MM short call, so he buys stock to neutralize the delta. Furthermore, he has to "dynamic hedge" this position when the stock moves up and down.

It is easy to figure out whether the investor has a good trade or not: if his call option rises, he makes money; if drops, he loses. For MM, it is less obvious, because the total profit/loss of the position has to accumulate the entire path of hedging, including both the stock and option positions. However, statistically, MM would make money on the two factors: 1) bid/ask spread; 2) option volatility.

Thus the unhedged option trades by investors will earn the profit/loss from the speculation of direction, while the hedged MM opposite side of the contracts will earn it from bid/ask and volatility. Of course, some MM would also speculate on the direction, thus that may justify the fear of betting against some big guy who knows more than you. But in the option market (both the public exchanges and OTC), all MM hedge.

Thus option trading is absolutely not zero-sum. To the contrary, stock trading is absolutely zero-sum. If you buy stock, someone else in the market has to sell that stock to you (there is no equivalence to the option market that you can create a contract out of blue -- that's the so-called fungibility of options and futures).

A Win-Win Example

Let me illustrate a case that would show you how an option trade can be win-win for both sides: you (the investor) bet the stock would rise at earning release (ER), so you buy 10 contracts of at-the-money call at $1.5 (total cost = $1500). The MM now short 10 contracts of call, and buy 500 shares of stock to hedge. The earning release comes and your speculation is right, stock jumps up $2.5, now the call becomes $2.5, you make $1000. Does the MM loss $1000? His option part loses $1000, his hedging stock gains $1250, thus his net gain is $250! How nice, you win, the MM wins too. The ending seems better than a classical fairytale.

The scenario for the profit/loss for the MM in the above case is much more complicate than the investor. For you, if the stock drops after ER, say down $1, option drop to $0.75, you loss $750, the MM would has a gain of $750 - $500 = $250 -- magically he would still make money. For investors, this trade is 50/50 chance of making it out (just as the stock has 50/50 chance of going up and down). For MM, it is a non-linear surface: he would make money if the stock price change (up or down) is within a certain range, but would lose -- and can loss big -- if the change (up or down) is huge.

That's the end of the "option is zero-sum game" myth. Welcome to the myth of "risk transfer".

If the stock speculators still like to play the game of "standing in the same side with MM", they'd better pick the stock MM, not the option MM. However, with the electronic markets and the huge liquidity in stock trading, it is hard to pin point who are the professional MM and who is the speculators. In contrast, MM in option market is a special class of traders.

So don't try to guess the mind of MM in the option market. They are a bunch of "delta neutral" guys, believe in nothing except liquidity.

(The author can be contacted at

Wednesday, May 03, 2006


Appreciation 升值
Arbitrage 套利/套汇
Arbitration 仲裁
Ask(Offer) 买方叫价
Asset 资产
Bid 卖方出价
Bond 债券
Breakeven 收支平衡点
Capital 资本/资本金
Cashflow 现金流
Commission 佣金
Depreciation 折旧
Derivatives 衍生证券
Dividend 股息/红利
Equity 股票/股本/权益证券/证券
Futures 期货
Hedge 套期保值/对冲
Hedge Fund 对冲基金
Interest Rate 利率
Liability 负债
Mark to Market (MTM) 以市值计价
Mortgage 按揭
Mutual Fund 共同基金
Option 期权
Assignment 指派
At-the-Money (ATM) 价平
Call 买入期权/看涨期权
Early Exercise 提前实施
Exercise 实施
Expiration 期满日
In-the-Money (ITM) 价内
Put 出售权/卖入期权/看跌期权
Option Chain 期权链
Out-of-the-Money (OTM) 价外
Strike 协约价
Writer 立权人
OTC (Over-the-Counter) 场外交易证券
Position 投资持有量/头寸
Premium 溢价
Private Placement 私募
Returns 回报
Risk 风险
Split 拆股
Spot Market 现货市场
Spread 价差
Swap 掉期/换期/互换协议
Swaption 换期期权
Underlying 标的物
Underlying Stock 基础股票
Volatility 涨落
Warrant 认股权证
Covered Warrant 备兑权证

Tuesday, May 02, 2006

Buffett's WMD

Press in last few days has noted about Warren Buffett’s recent big short positions in far-term international index put options (news). Since it is Warren Buffett, the Bloomberg reporter was talking glowingly of this trade, even mumbling something like “he will make money whether market goes up or down.” What’s a change. I wonder whether she can tell the difference of “call” and “put”, “long” and “short”.

From the press, the size of the Buffett trade is 14 billion, with duration 15 to 20 years, on 4 major indices, 3 of which are outside US. The 14 billion is the notional value, namely the maximal loss he can occur if all the indices drop to 0. However, it is not clear about the detail structure of the deal, is it a swap, or just a plain put with long duration? Who is the counterparty? Obviously it is also impossible to know what kind of implied volatility the trade is sold at.

I’m a bit baffled by this trade, but also amused by the reaction. Many people would immediately link such a massive deal with Buffett’s famous remark calling derivative as “Financial Weapons of Mass Destruction”. To be exact, his original remark was on the “OTC Derivatives”, not regarding the exchange traded derivatives. But still, this deal is obviously OTC. The longest exchange traded index options are only of 3 years in duration at most.

Buffett’s WMD remark was based on his observation that OTC derivatives 1) are complex and has hidden liabilities that may not be fully disclosed or understood; 2) Difficult to value since there is no public market for them. If his deal is in plain vanilla put with extended expiry, the first point won’t apply here. The second point is valid for this deal.

So is Buffett talking from both sides of his mouth -- on one hand chiding the investment world on the evil of OTC derivatives, while on the other hand, doing a massive deal on OTC derivative himself? Moreover, he is doing it on the short side -- the side that he would be blown up in case the WMD should went off. So what's the deal here?

If you read a little bit about Buffett, you would find that actually he is an old hand in derivatives, thus give him the talking rights for that famous WMD remarks. Remember LTCM? The press loves to talk about LTCM since the media and the public can blame anything that is hard-to-understand on it. In fact, Buffett almost did a deal to "rescue" LTCM with his own money. If the deal would had gone through, Buffett would get a tremendous good deal on all those LTCM derivative positions (and LTCM would get rescued -- but would incur big loss though saving the disgrace of being rescued by the Fed orchestrated effort). Buffett would get those huge short volatility index options at an extremely high implied vol (now look at the current deal he just doing, any similarity?), and he would get those bond arbitrage positions and risk arbitrage trades when the spread is widest (and with our 20/20 hindsight, we all know eventually those index volatilities dropped like a rock, and all those spread collapsed -- even LTCM, under the supervision of the several banks that take over their entire book, would eventually make money for their investors). Buffett is certainly not just a savvy stock investors, but a very savvy derivative investor.

Another fact: the equity investments that Buffett made his first mark was in insurance (those wacky GEICO ads should remind everyone of Buffett?) which in essence is the business of selling puts. In such perspective, this recent deal seems to be quite natural for Buffett rather than out-of-ordinary.

What baffles me about this trade is not of the fact that it is a massive OTC derivative trade, but by the timing of this trade. Why sell volatility and long delta now? The exchange market implied volatility is at a quite low level at this point, thus it can reasonably guess that Buffett's OTC put deal can't be done at a very high implied vol (the counter party that does this deal with Buffett is certainly no dumb farmer, but savvy investment bank that deals with implied volatility every day). The other similarly structured OTC derivatives, the LTCM deal (if Buffett would had got it) would had been shorted at a very high vol, thus almost certain it would be profitable, while this current deal, if shorted at the present exchange market vol, profitability would only be 50/50.

Shorting put has the magical enticement of letting you making money right away, and making money day in and day out, until one day suddenly it hits you with a hammer at the most unexpected moment. For savvy traders, they would hope to sell put when the market is panicking (while all the investors are buying puts at a sky-high premium), and cover it (buy the put back) when the market calms down (or keeping the fingers crossed to wear out the options to expiration, if it is not too far away). For Buffett, both of these two profit-locking methods won't work for him -- it is OTC derivative, thus it is very hard to buy it back, and it is very far term (15 to 20 years), so your fingers get tired trying to keep it crossed for 20 years.

In fact, it is not the question of whether this trade will be profitable or not -- it is highly likely that this trade will be profitable in the end (just like most of LTCM trades are profitable in the end). If Buffett marks his book by model (which is likely the case because there is no market for these OTC options, he has to mark to model), it is almost certain that he already has positive P/L for this trade so far. The serious question is, during the next 15 to 20 years, at the moment when market crashes (which is almost certain to happen), will he be solvent?

More of an interest rate play?

Interest rate usually is a minor factor in option valuation when comparing with volatility and other factors. However, for such a long duration, the sensitivity of the current option value to interest rate may rival to volatility. Shorting put means Buffett is long on interest rate. If interest rate rises from the current level in the next 15 years, these put would go down in value. With such long duration, 100 basis point change in the interest rate would have 3 or 4 time larger impact in value than 1 pt change in implied volatility. Another way to look at this: if there is no earnings growth in the stock market in the next 15 years, the market has to just sloth through at the rate of interest in average just to get even with the cost of money. Just such “slow” growth would make all these currently at-the-money put way out of money so that Buffett can keep all the premium with a safe distance to protect some market crash. That seems to be a pretty good trade, isn’t it?

Counter to common belief, shorting put is actually less risky than owning stock. Obviously if you short a lot of puts, it might be very risky, just as owning a lot of stocks. The most risky strategy is selling a lot of out-of-money put – sell a lot just to get enough juicy premium.

Though we don't know the detail of the structure, it seems the strike of these put are at the money. So obviously Buffett is no reckless traders selling tons of out-of-money front month put. However, the following situation is quite likely: market goes up thus these put become way out of money, thus making Buffett a lot of "mark-to-model" profits. Now Buffet take those profits and use it in some other places. At this point these out-of-money puts would become dangerous time bomb that is barely visible.

Shorting Put

History of Shorting Put is littered with dead bodies with spectacular flameout: Nick Leeson of Barings in 1995 (loss $2 billion shorting Nikkei put to wipe out the 233 years old British bank), Victor Niederhoffer shorting front month put in October 1997 (lose 150 million overnight to wipe out his own fund), both unhedged; and LTCM shorting European index volatility (presumably hedged).

Buffett is in a different league. However, now that we all know about this trade (just as we all know about his short dollar trade), when the next market downturn or crash comes, we all would wonder about how this elephant would be doing in Buffett's book.

Whether this trade is good or bad, one thing is quite high certainty: in 15 to 20 years, both Warren Buffett and Charles Munger (Berkshire Hathaway’s CEO) might be dead when the options expire. So why worry now?

(The author can be contacted at

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