Parity, Verticals, and Calendars

I'm not going to tell you about all trading strategies. If you want that, you'll have to get a book about it. I highly recommend one written by a top professional poker player, Bob Feduniak (Futures Trading: Concepts and Strategies, by Robert Fink and Robert Feduniak). It's out of date in many details, but it's still the best combination of theory and practice available. Another essential is Dynamic Hedging by Nassim Taleb, a successful trader who does not play much poker. I discussed this book with both of them, and both have significant disagreements about some of the ideas, but I like their books, anyway. Finally, if you want the mathematics of finance explained with the brilliant clarity of real genius, get Paul Wilmott on Quantitative Finance.

However, to get the flavor of the trading game, we have to go beyond spotting obvious mispricings. It's essential to understand that this is a game, that there are strategies and moves. It's not just scanning lists of numbers and running to try to take advantage of them. It's coming up with new ideas. The three I'm going to talk about are old ideas (but still good ones) that give you the flavor.

If you buy a call option and sell a put option with the same underlying, strike, and expiry, you have effectively bought the stock. For example, suppose you buy the September 16 $50 call and sell the corresponding put on MWD. You'll pay $2.65 for the call, but get $0.35 for the put, for a net $2.30. On September 16, if MWD is above $50, the put will be worthless, but you'll exercise your call to buy a share for $50. If MWD is below $50, the call will be worthless, but the holder of the put you sold will execute it to force you to buy a share from her at $50. Either way, you buy a share for $50. Your all-in price is $52.30, a penny more than buying it for $52.29 in the market today (that's still a good deal, because you save a month's interest on $50, which is roughly a nickel).

If you like that sort of thing, see whether you can find some juicy violations of parity in the preceding list. You're looking for a situation where the strike price plus the call price minus the put price is significantly different from $52.29 (you can make money on deviations either way). There are five differences of more than a dollar; one is the January 2006 $45 strike. In this case you would sell the call and buy the put and the stock. You pay $0.70 for the put and get $9.40 for the call, ending up with $8.70. The stock costs $52.29, so you've spent a net $43.59. You'll collect $0.54 in dividends on the stock, bringing your investment down to $43.04. With interest until January, that's about $43.40. But on January 20, 2006, whatever the price of MWD is, you get $45, for a profit of $1.60.

With this and all the other trades, you don't really expect to hold it until expiry. Prices are out of line and tend to move back. When they do, you take your profit. With luck, they'll overcorrect, and you can make money getting out as well. However, you might get out if they go halfway back, giving up half your potential profit, but freeing up the capital and attention for more profitable trades.

There are some small risks in this trade. MWD might not pay the expected dividends, which reduces your profit but in this case does not cause a loss. The call holder might exercise early, but that doesn't hurt you beyond possibly losing some of the dividends. You get your expected profit early, which is good, and you get to keep the put for nothing (although it's unlikely to have significant value in any scenario in which the call holder would exercise early).

Verticals are buying a call or put, and selling the same kind of option on the same underlying with the same expiry, but at a different strike. For example, you could buy an October $50 call and sell the October $55 call. You would pay $3.30 and get $0.85, for a net price of $2.45. If MWD is above $55 on October 16, you make $5 (both calls are exercised, you buy a share of MWD for $50 with your $50 call, and you are forced to sell it for $55 to the person who holds your $55 call). If MWD is under $50, you get nothing (both calls are worthless). If MWD is between $50 and $55, you get the amount by which it exceeds $50 (the $55 call expires worthless, you exercise your $50 call, and you sell MWD at the market price).

When a stock is selling at the midpoint of a vertical-$52.50 in this case-the vertical has to be worth very close to half the spread-$2.50 in this case, because it's a $5 vertical. I'm not going to prove that-take my word for it. As the stock approaches the upper end of the spread, the call vertical is worth more than half the spread and the put is worth less. The amount more and less depends on the volatility of the underlying and the amount of time to expiry. The $2.45 price for the October $50/$55 call vertical is reasonable; it should be a little less than $2.50 because MWD is selling for a little under $52.50.

Can you spot any attractive verticals? You should see a lot. One example is the January 2006 $45/$60 call vertical. If we sell the $45 for $9.40 and buy the $60 for $0.65, we get $8.75 in our pockets. Since MWD is slightly below the $52.50 midpoint, this should sell for a little less than $7.50. So we've got our mispricing, but we haven't locked in a profit. We're getting paid $8.75, but we have to pay $15.00 if MWD is above $60 in January 2006. It's a good bet, but it's too risky to hold on its own. Fortunately, the same put vertical is selling exactly at $7.50 (it should be slightly above that level). So we sell the January $45 put and buy the January $60 put. We get $0.70 and pay $8.20, for a net expenditure of $7.50. That comes out of the $8.75 we got for the call vertical. Our net is $1.25.

Now what happens? We have $1.25 in pocket and a bet that pays us $15 if MWD goes below $45, but we have to pay $15 if it goes above $60. So we buy two shares of MWD. If it goes above $60, we make more than $15 profit on two shares of stock, while our payout on the bet is limited to $15. If the stock goes down, our put vertical covers any losses down to $45. We'll unwind the whole position before the stock drops below $45, almost certainly at a profit. We could make this position even safer by fiddling with the proportions of the four options we use, also by adjusting it as the stock price moves and time passes. It will still have some risk, but $1.25 is a significant overpayment to us to take it.

Finally, let's talk about calendar spreads. This means buying one option and selling another of the same type, with the same underlying and strike but a different expiry. Longer-dated options are more valuable than shorter-dated ones. The spread is most valuable near the current stock price and should decline in price for options at higher and lower strikes. Look at the January/October calendar spreads. For each strike price, I've taken the January option price minus the October option price:

As expected, all the numbers are positive (although this is not true for all the options in the table). The $50 and $55 strikes, the nearest to the current stock price of $52.29, are worth between $0.90 and $1.20. The ones $5 further away, at $45 and $60, sell for less, as expected, between $0.30 and $0.50-except the $45 calls. That calendar spread is too big. We should sell the January $45 calls and buy the October $45 calls, getting paid $1.10. As with the vertical spread, we need to offset the risk with another trade. We might be tempted to buy the $60 put spread at $0.30, which looks cheap. That's a good idea, but this position will take even more management than the vertical spread; we can't just hold it to expiry and collect our winnings. As a practical matter, there's not much difference. We're not going to hold many positions longer than a day, and none or almost none to expiry. Most of our profit comes from identifying mispricings and exploiting them before anyone else. We'll cash out when other people come in; in fact, we may be buying from people who were quicker than we were.

Every successful trader finds a niche, depending on taste and capital and skills. Although you're buying and selling with other traders, you all can be making money in theory. Just like in poker, that never happensthere are always losing traders. But you're not trading against anyone, not even some abstract "market." You're playing a game by certain rules. If you play well and have some luck, you win. If you play badly or have bad luck, you lose. Calling it a game, of course, doesn't mean you don't take it seriously. I care very much when it's my money on the line, and even more when it's other people's money-money from people who have trusted me. But it's a game in the sense that there are rules and a score, that you must both think ahead and react immediately to the moment. No one does this because it's useful for society, because no one can know the larger impact of their trades. Some have faith that the market is always right and their trades make it more efficient. Others have different faiths or don't care. No one does this for the money, either, despite what they may tell you (and the money can be very, very good). Everyone who does this does it because they love it.

Bonds

In 1982 I was hired by Prudential Insurance, but not as a trader. My job was to manage a bond portfolio that was used to fund annuity products sold by the company. For example, Prudential would agree to pay the retirement benefits of a pool of 1,000 workers for some company in exchange for a lump-sum payment today. Our actuaries would make projections about how much these payments would amount to every month far out into the future. They would estimate when the workers would retire, what payments they would qualify for, and how long they and their spouses would live. They had a century of experience doing that, and they sent me the results. My job wasn't to worry about that part of it; I started from the cash flows they produced.

The safest way to manage the portfolio would be to go out and buy a collection of U.S. Treasury bonds that would produce exactly the same cash flows as the projections. I could compute those bonds and add up the cost to make my bid for the business. But we'd never win anything that way. To get the price down, we had to use corporate bonds and mortgage securities, which paid higher yields. Also, it was too cumbersome to match every cash flow exactly. It didn't really matter if you had cash coming in a few months early or late 10 years from now. I won business and traded bonds every day; there was no point in balancing things exactly far out in the future.

However, I had to produce a daily report showing that my risk was within acceptable limits. The main risks were credit risk-what happened if some of the bonds I bought didn't pay off as promised-and mismatch risk-what happened if we had an obligation to pay in January and the money to pay it didn't come in until June. There were other risks as well. I had to show what would happen in various stress scenarios, such as a sudden spike in interest rates or a sharp decline in credit quality of all banks.

If I won a bid, I had to go buy bonds for the portfolio. I also had to reinvest cash that built up and occasionally sell some bonds to rebalance. I had two ways to do this. I could call a big bond dealer, like Merrill Lynch or Salomon Brothers, and talk to a salesperson. These banks had bond traders, but customers like me dealt with salespeople who dealt with the traders. With some smaller banks I dealt with the trader directly, but I was still a customer, not a trader.

Like most investors in high-grade bonds, I didn't ask for specific issues such as the 8 percent coupon Ford Motor Credit bonds due August 2000. Instead, I'd say something like, "I'm looking for about $100 million of A-rated corporates with five- to seven-year maturities, and I can't take any more financial or auto paper." The salesperson would go through the firm's inventory, or bonds she thought could be bought from other shops, and suggest some names. Prudential had a credit department that had opinions on the soundness of different issuers, plus I had reports from public rating agencies like Standard & Poor's, Moody's, and Fitch. Good salespeople earned my business by having other useful information, especially about the trading outlook, such as whether this same bond was likely to be cheaper tomorrow. I could decide on bonds with the highest returns that kept the portfolio within its overall risk parameters and place orders. Or I could wait for the salesperson to call me back when something new came up, especially a new issue her firm was bringing to market.

The other option was to go to Prudential's bond traders. The firm employed two of them for the kinds of things I bought. They worked in a trading room with computer screens showing bonds bid and offered from lots of different brokers. Some portfolio managers used the traders as order takers (traders hate that) standing over their shoulders and pointing out the bonds they wanted. Others would give general instructions at the beginning of the day and trust the trader to find good deals.

It took me only a couple of months to get tired of that. Prudential didn't hire me as a trader, but I still thought of myself as one. The best opportunities could not be constructed one bond at a time. There might be a new issue with a very attractive yield, but not at the right maturity point and from an industry I was already overexposed to. I could buy it, but only if I sold something else and also bought another bond with a complementary maturity. The trouble is that once I made the buy, I was completely committed to doing the other two trades, so I would get bad prices and give away any gain from the initial purchase. I could try to negotiate package swaps with salespeople, but they never gave me good overall prices. I could ask the traders to try to pull it off, but the markets moved too fast and they had too much other work to do it.

Believe it or not, all of this bond management was done by hand. Prudential did buy me some time on a time-share mainframe with a dial-up 128-baud modem, and I programmed some routines in FORTRAN to help. I also had a home computer that I programmed in FORTH for the job. But then Prudential bought a first-generation IBM PC. I never found out who bought it or what it was for, but one day it appeared in an empty office. I immediately typed in my portfolio and wrote a BASIC program to tell me what kinds of bonds would help me the most. I got a list and went up to the trading room, where I picked off several of them from the screen. I went back down to enter the trades, got a new list, and went back up. With the computer to help me, I didn't need to calculate each trade by hand, and I could make some trades that threw me out of balance, knowing I could fix it on the next trip up and downstairs.

I didn't plan it this way, but I couldn't have devised a better way to get permission to trade for myself. I was driving the traders crazy, especially when the market was moving fast. I got my own chair at the desk (the corner, but still on the desk) and screen (only one, while other traders had three, but a screen). The one thing I didn't get was permission to move the PC into the trading room; I still had to run up and down the stairs.

I stayed in fixed-income securities until 1988, eventually becoming the head of mortgage securities at Lepercq, de Neuflize, a small French investment bank active in that business. I never gave up my trading, although I never did it as my only job. This was a slower kind of trading than options on the floor, but the dollar amounts were much larger (my Prudential portfolio had grown to $3 billion by the time I left). The game was pretty much the same: Look for some basic price relationships, pick off the exceptions, balance everything so you didn't care which way the market moved, and wait for things to come back in line to take a profit. The calculations were more complicated and the universe of securities larger, but I had computer power and people working for me instead of being on my own doing things in my head.

Дата добавления: 2015-10-26