In the early days of Lloyd’s, British merchant ships traversed the world, trading spices and silk from Asia, tobacco and rum from the New World, and textiles and wool from Britain, among other goods. Each of the many routes that British ships took had its own unique risks—pirates in the Caribbean, gales in the North Atlantic, typhoons in the Indian Ocean.

In the face of all these risks, how were merchants able to survive? One important way was by reducing their risks by not putting all their eggs in one basket: by sending different ships to different destinations, they could reduce the probability that all their ships would be lost. A strategy of investing in such a way as to reduce the probability of severe losses is known as diversification. As we’ll now see, diversification can often make some of the economy’s risk disappear.

Let’s stay with our shipping example. It was all too likely that a pirate might seize a merchant ship in the Caribbean or that a typhoon might sink another ship in the Indian Ocean. But the key point here is that the various threats to shipping didn’t have much to do with each other. So it was considerably less likely that a merchant who had one ship in the Caribbean and another ship in the Indian Ocean in a given year would lose them both, one to a pirate and the other to a typhoon. After all, there was no connection: the actions of cutthroats in the Caribbean had no influence on weather in the Indian Ocean, or vice versa.

Statisticians refer to such events—events that have no connection, so that one is no more likely to happen if the other does than if it does not—as independent events. Many unpredictable events are independent of each other. If you toss a coin twice, the probability that it will come up heads on the second toss is the same whether it came up heads or tails on the first toss. If your house burns down today, it does not affect the probability that my house will burn down the same day (unless we live next door to each other or employ the services of the same incompetent electrician).

There is a simple rule for calculating the probability that two independent events will both happen: multiply the probability that one event would happen on its own by the probability that the other event would happen on its own. If you toss a coin once, the probability that it will come up heads is 0.5; if you toss the coin twice, the probability that it will come up heads both times is 0.5 × 0.5 = 0.25.

But what did it matter to shipowners or Lloyd’s investors that ship losses in the Caribbean and ship losses in the Indian Ocean were independent events? The answer is that by spreading their investments across different parts of the world, shipowners or Lloyd’s investors could make some of the riskiness of the shipping business simply disappear.

Let’s suppose that Joseph Moneypenny, Esq., is wealthy enough to outfit two ships—and let’s ignore for a moment the possibility of insuring his ships. Should Mr. Moneypenny equip two ships for the Caribbean trade and send them off together? Or should he send one ship to Barbados and one to Calcutta?

Assume that both voyages will be equally profitable if successful, yielding £1,000 if the voyage is completed. Also assume that there is a 10% chance both that a ship sent to Barbados will run into a pirate and that a ship sent to Calcutta will be sunk by a typhoon. And if two ships travel to the same destination, we will assume that they share the same fate. So if Mr. Moneypenny were to send both his ships to either destination, he would face a probability of 10% of losing all his investment.

But if Mr. Moneypenny were instead to send one ship to Barbados and one to Calcutta, the probability that he would lose both of them would be only 0.1 × 0.1 = 0.01, or just 1%. As we will see shortly, his expected payoff would be the same—but the chance of losing it all would be much less. So by engaging in diversification—investing in several different things, where the possible losses are independent events—he could make some of his risk disappear.

Table 20-2 summarizes Mr. Moneypenny’s options and their possible consequences. If he sends both ships to the same destination, he runs a 10% chance of losing them both. If he sends them to different destinations, there are three possible outcomes.

You might think that diversification is a strategy available only to those with a lot of money to begin with. Can Mr. Moneypenny diversify if he is able to afford only one ship? There are ways for even small investors to diversify. Even if Mr. Moneypenny is only wealthy enough to equip one ship, he can enter a partnership with another merchant. They can jointly outfit two ships, agreeing to share the profits equally, and then send those ships to different destinations. That way each faces less risk than if he equips one ship alone.

In the modern economy, diversification is made much easier for investors by the fact that they can easily buy shares in many companies by using the stock market. The owner of a share in a company is the owner of part of that company—typically a very small part, one-millionth or less. An individual who put all of his or her wealth in shares of a single company would lose all of that wealth if the company went bankrupt. But most investors hold shares in many companies, which makes the chance of losing all their investment very small.

In fact, Lloyd’s of London wasn’t just a way to trade risks; it was also a way for investors to diversify. To see how this worked, let’s introduce Lady Penelope, a wealthy aristocrat, who decides to increase her income by placing £1,000 of her capital at risk via Lloyd’s. She could use that capital to insure just one ship. But more typically she would enter a “syndicate,” a group of investors, who would jointly insure a number of ships going to different destinations, agreeing to share the cost if any one of those ships went down. Because it would be much less likely for all the ships insured by the syndicate to sink than for any one of them to go down, Lady Penelope would be at much less risk of losing her entire capital.

In some cases, an investor can make risk almost entirely disappear by taking a small share of the risk in many independent events. This strategy is known as pooling.

Consider the case of a health insurance company, which has millions of policyholders, with thousands of them requiring expensive treatment each year. The insurance company can’t know whether any given individual will, say, require a heart bypass operation. But heart problems for two different individuals are pretty much independent events. And when there are many possible independent events, it is possible, using statistical analysis, to predict with great accuracy how many events of a given type will happen. For example, if you toss a coin 1,000 times, it will come up heads about 500 times—and it is very unlikely to be more than a percent or two off that figure.

So a company offering fire insurance can predict very accurately how many of its clients’ homes will burn down in a given year; a company offering health insurance can predict very accurately how many of its clients will need heart surgery in a given year; a life insurance company can predict how many of its clients will … Well, you get the idea.

When an insurance company is able to take advantage of the predictability that comes from aggregating a large number of independent events, it is said to engage in pooling of risks. And this pooling often means that even though insurance companies protect people from risk, the owners of the insurance companies may not themselves face much risk.

Lloyd’s of London wasn’t just a way for wealthy individuals to get paid for taking on some of the risks of less wealthy merchants. It was also a vehicle for pooling some of those risks. The effect of that pooling was to shift the supply curve in Figure 20-5 rightward: to make investors willing to accept more risk, at a lower price, than would otherwise have been possible.