Diversification can reduce risk. In some cases it can eliminate it. But these cases are not typical, because there are important limits to diversification. We can see the most important reason for these limits by returning to Lloyd’s one more time.

In Lloyd’s early days, there was one important hazard facing British shipping other than pirates or storms: war. Between 1690 and 1815, Britain fought a series of wars, mainly with France (which, among other things, went to war with Britain in support of the American Revolution). Each time, France would sponsor “privateers”—basically pirates with official backing—to raid British shipping and thus indirectly damage Britain’s war effort.

Whenever war broke out between Britain and France, losses of British merchant ships would increase. Unfortunately, merchants could not protect themselves against this eventuality by sending ships to different ports: the privateers would prey on British ships anywhere in the world. So the loss of a ship to French privateers in the Caribbean and the loss of another ship to French privateers in the Indian Ocean would not be independent events. It would be quite likely that they would happen in the same year.

When an event is more likely to occur if some other event occurs, these two events are said to be positively correlated. And like the risk of having a ship seized by French privateers, many financial risks are, alas, positively correlated.

Here are some of the positively correlated financial risks that investors in the modern world face:

When events are positively correlated, the risks they pose cannot be diversified away. An investor can protect herself from the risk that any one company will do badly by investing in many companies; she cannot use the same technique to protect against an economic slump in which all companies do badly.

An insurance company can protect itself against the risk of losses from local flooding by insuring houses in many different places; but a global weather pattern that produces floods in many places will defeat this strategy. Not surprisingly, insurers pulled back from writing policies when it became clear that extreme weather patterns had become worse. They could no longer be confident that profits from policies written in good weather areas would be sufficient to compensate for losses incurred on policies in hurricane and drought prone areas.

So institutions like insurance companies and stock markets cannot make risk go away completely. There is always an irreducible core of risk that cannot be diversified. Markets for risk, however, do accomplish two things: First, they enable the economy to eliminate the risk that can be diversified. Second, they allocate the risk that remains to the people most willing to bear it.