Futures and options

Next in line were the commodity exchanges. Commodity contracts are agreements to exchange a fixed amount and grade of some commodity, such as wheat or pork bellies, at a specified location, for a fixed amount of money within a fixed delivery window in the future. The classic example you will find in finance textbooks is a farmer who uses the contract to sell his wheat. For example, suppose he has a crop he expects to harvest in June. It's now early April, and the price for June delivery is $3.00 per bushel. He can lock in that price today with a commodity contract, or he can wait until June and hope the price goes up. If he does that, however, he could lose if the price goes down. On the other side, a miller knows she needs to buy wheat to grind in June, so she can also lock in the $3.00-per-bushel price today rather than taking a chance on the price going up. Viewed in this light, commodity contracts are the opposite of gambling. The farmer and the miller use them to avoid gambling with each other.

It should come as no surprise at this point that the farmer story is a fairy tale. Almost no farmers use commodity exchanges, nor did they in the past. Millers and other processors of agricultural products do, but they generally sell the commodity in the future instead of buying it. That looks as if they're doubling up so they make twice the profit if the price of wheat falls but take twice the loss if it rises. The vast majority of traders have no connection to the physical commodity at all-they don't grow it, transport it, or process it. The only time they use it is when they buy a loaf of bread in the grocery store like anyone else.

Futures markets are vital to the economy and were even more vital in the past, but not because they help farmers strike price bargains with millers. In a simple story, a crop steadily gains in value as it moves from being in the ground on a farm to harvest, then to movement to a city for processing, through cleaning, grinding, and packaging in final consumer goods. If that's true, there's no need for futures markets. At each step of the way people can make economic decisions based only on current prices.

That kind of "myopic" planning works well when there aren't any options for shipping and processing, when change is slow, and when infrastructure is already in place. None of those conditions applied in, say, 1880 Kansas City. Myopic planning would have led to alternating shortages, when the city's expensive processing facilities are idle, and glut, when commodities are rotting on the sidings. The economic solution to this problem required deliberately added randomness to the commodity prices, induced by exchange manipulation. Without that randomness, the supply network could not be robust and dynamic, and the people to run it would not have bothered to come.

How can options be portrayed as anything but gambling? An MIT professor named Robert Merton shared the 1997 Nobel Prize in economics for coming up, in 1973, with an original argument. Options aren't gambling games, he said, they are derivatives. Merton's argument was highly mathematical, but the essence is simple. It is possible to re-create the option payoff by buying and selling the underlying security, and the return on that strategy can be computed in advance. Therefore, an option is just a convenient packaging of other financial transactions and should sell for the same price as the "replicating portfolio."

To see how this works, suppose the Yankees are playing the Braves in the World Series and it's tied 2-2. The first team to win four games wins the series. Therefore, whichever team wins two out of the next three games will win. A bettor approaches you and wants to bet $100 that the series will go the full seven games. Assuming you can bet on each individual game at even odds, what is the fair price for this bet?

You can bet $100 in the sixth game against whichever team wins the fifth game. If you lose that bet, the same team won the fifth and sixth games, the series is over in six games, and you don't have to pay off on the seven-game bet. If you win that bet, the series is tied 3-3 and will go to seven games. In that case you will have $200, so that is the fair payout for the seven-game bet. Figure 4.1 shows the results of betting on the fifth game. You end up with $0 if the series ends at six games and $200 if it goes to seven, just like making the sevengame bet.

Figure 4.1

This seems similar to the argument that if each game is a 50/50 coin flip, the probability that the series will go to seven games is 0.5, so $200 is a fair payout for a $100 bet. But that argument is a gamble. It depends on the probability of each team winning, while Merton's argument depends instead on the betting odds, which do not have to be the same as the probabilities (although you wouldn't expect them to get too far out of line, or smart bettors could get rich). Moreover, the probability argument is just a long-run expected value; Merton's argument guarantees the bookie will have the $200 to pay off every time.

What if the betting line is not even? Suppose betting on the Braves pays 2:1 (for each $1 you bet, you win $2 more if you win) but Yankees bets pay 1:2 (for each $2 you bet, you get $1 more if you win). Now the hedge is a little more complicated. In the fifth game, you bet $25 on the Braves. If they win, you have $150, which you bet on the Yankees. If the Yankees win, so you have to pay off on the seven-game bet, you have $225. However, if the Yankees win the fifth game, you lose your $25 bet, so you have $75, which you bet on the Braves. If the Braves win the sixth game, so you have to pay off on the seven-game bet, you will have $225. So now the fair price for the seven-game bet is $225, and you still have no risk (see Figure 4.2).

This example may be a bit tedious to go through, and I've got some more coming up. But they are crucially important to understanding modern derivatives markets. If you can follow them in World Series betting, you know the basic principle that drives financial engineering.

Although no one seemed to notice it at the time, the riskless hedge argument was a complete reversal from all other financial markets. Insurance companies, stock exchanges, and foreign exchange and interest rate dealers all argued that their customers were not gambling. These financial institutions admitted that they acted as casinos, taking lots of bets from customers and relying on diversification to cancel most of the risk. But it wasn't evil gambling, even though it used the same principles, because the customers were engaging in prudent and socially useful activities.

The options markets ignored the question of what the customers were doing. They claimed that options weren't gambling because there was no gamble. The exchanges weren't acting like a casino, diversifying many customer bets. They were acting like a sports bookie, setting the line so that they made money whichever team won the game. Options dealers didn't care whether the stock went up or down, for the same reason a sports bookie doesn't care if the Yankees or the Braves win the World Series. As long as the bet amounts are equal on both sides, the exchange and the bookie make a riskless spread.

Figure 4.2

In one sense, this is a more honest argument. It doesn't invent silly nursery stories about what customers are doing. But in another sense, it's much more dangerous. It says that derivatives aren't gambling because there is no risk. Putting perfume on risk and calling it hedging is silly, but denying that it exists at all is insane.

The refusal to admit options were gambling led to the inevitable disaster. If you believe options are derivatives, then you can buy or sell any amount with no risk, as long as you offset the trades with borrowings and transactions in the underlying stock.

Remember, you quoted $225 for the $100 bet that the series would go seven games. You bet $25 on the Braves in the fifth game and lose. Now you have $75, which you expect to be able to bet at 2:1 on the Braves, so you win $225 if the series goes to seven games. But suppose when you try to place that bet you find out that the odds on the Braves have dropped down to even (1:1)? Now if you bet the $75 on the Braves you will get only $150 if they win, so you will take a $75 loss. If you don't know what the future betting odds will be, derivatives have risk.

Дата добавления: 2015-10-26