What a Right Is Worth

Saviano describes a building “predator” from Campania. His talent, he writes, is finding unremarkable plots of land, buying them for next to nothing and waiting patiently until the price of every centimetre of ground and every pit has gone up a lot.

What is this man really buying? Not land. An empty plot outside town brings in nothing: nothing grows on it, you can’t let it, and you still pay the taxes. The predator is buying the right to build when building pays. If the city reaches his plot, if the zoning plan changes, if they run a road past it—the right turns into big money. If nothing happens, he’s left with a plot he paid next to nothing for, plus the taxes he’s paid.

That’s an option, though no developer would ever call it one. Economists call such things real options: the right to do something later, bought now. And the main question about any option is: what is that right worth?

The Tree of Outcomes

Let’s start simple. Say a share costs a hundred. In a year it will be either a hundred and twenty or eighty. What is the right to buy it in a year for a hundred worth?

If the share goes up, the right gives you twenty: you buy for a hundred something worth a hundred and twenty. If it goes down, the right is useless. Who pays a hundred for something worth eighty? So there are two outcomes: twenty or nothing. Out of the share and money in the bank you can put together a combination that gives exactly the same twenty or nothing. Whatever that combination costs, that’s what the right costs. Otherwise someone pockets the difference without any risk. That’s the binomial model: the world branches into “up” and “down”, and you find the price of the right step by step, from the end back to the start.

Now break the year into lots of little steps. At each one the share moves a little up or a little down. Make the steps infinitely many—and out comes the formula.

The Formula

In 1973 the economists Fischer Black and Myron Scholes published a formula for the price of an option, and the same year Robert Merton gave it a rigorous proof. According to the formula, the price of the right depends on five things: the current price of the asset, the price at which you can buy it, the time left, the interest rate, and how wildly the asset’s price jumps about. That last one is called volatility.

In 1997 Scholes and Merton got the Nobel Prize for it. Black didn’t live to see it: he died in 1995, and the prize isn’t awarded posthumously. And a year after the prize, a fund with Scholes and Merton on its board nearly brought down the world’s markets, as we’ve already discussed. The formula was right—within its assumptions. The world turned out to be crazier than the assumptions.

The Scarier, the Dearer

Of the five things, the most surprising is volatility. The more the price jumps about, the dearer the right. Why?

Remember: whoever buys an option has a limited loss. At worst you lose the premium. With a call bought on a share, the gain isn’t limited either: the price can fly as high as it likes. If the price barely moves, the right will almost never bring in much. If it jumps about wildly, there’s a chance it will fly very far up, and the fall hardly bothers you: you simply won’t use the right. A put has a ceiling. A share can’t fall below zero, so a put can’t bring in more than the agreed price minus the premium. But for a put too, big jumps, all else being equal, mean a better chance of a big win.

Uncertainty frightens the owner of a share. A bought option it makes dearer, all else being equal. Just don’t get confused: the right gets dearer because of the jumps the market expects. That doesn’t mean the option holder makes money on every bit of shaking. If the price jumps up and down all year and is back where it started by the date, the right to buy at that same price goes up in smoke.

Saviano explains a term from the Naples drug trade: the “stake”. It’s the sum the boss gives his lieutenant to buy a consignment. The term, Saviano writes, comes from the chaotic economy of cocaine: here you place bets, as at roulette. You put down a hundred thousand euros, everything goes well—and in two weeks it turns into three hundred thousand. The lieutenant was holding an option on someone else’s money. When it went well, as the investigation found, he hid part of the profit. When it went badly, the boss lost. The business was wild and unpredictable, so the option was worth a great deal. Here’s what it cost the boss: the lieutenants got rich and broke away, and a war broke out in Secondigliano.

The Fear Index

On the financial markets they’ve learned to measure volatility by the prices of options. Options getting dearer means big jumps are expected. In 1993 the Chicago Board Options Exchange began publishing an index that shows what swings the market expects over the coming month. It’s called the fear index. In calm times it sits somewhere around ten to twenty. In October 2008, at the height of the crisis, it went up during the day to nearly ninety. In March 2020, at the start of the pandemic, it closed at a record of over eighty-two. And on 5 February 2018 it doubled in a day. Several funds that made their money selling “fear”—that is, betting that the market would stay calm—went bust overnight.

Selling fear pays, as long as there isn’t any. That’s how an insurer collects premiums for years. Until the big fire comes.

The Don’s Yard

Don Vincenzo’s first laundry had an empty yard overgrown with grass. The restaurant next door wanted to buy it for years, to put a storeroom there. They offered good money. I thought we should sell: the yard brought in nothing, and we were paying tax on it.

The Don refused. “I don’t know whether I’ll need this yard,” he would say. “But if I do, there’ll be nowhere to buy one.” Twelve years later we put a second press in the yard and enlarged the drying room. Without the yard, the whole laundry would have had to move.

Later I sat down and did the sums honestly. After all, when I was urging him to sell, I’d counted only the taxes. And taxes aren’t the whole price. The restaurant’s money, which we didn’t take, could have been earning interest for twelve years. The taxes plus that interest were the premium on the option, and it came to a noticeable sum. The money itself hadn’t gone anywhere: it stayed in the land, the land didn’t get cheaper, and it could have been sold in any year. And moving the whole laundry would have cost more, even counting that interest. Had we not needed the yard, the sums would have come out in the restaurant’s favour. “An empty space,” the Don said, “is worth the most when you don’t know what to do with it. As long as you don’t know, anything is possible.”

The Bottom Line

You don’t pay for the right to do something later only in cash. The interest on money you turned down is a premium too. Hold on to the right while that premium is smaller than what the right could save you, and do the sums again every year.