Chapter 6 begins with a discussion of the banking crisis of 2007. The author acknowledges that the crisis is “mind-bogglingly complicated.” In order to explain it in an accessible way, he introduces an example: In 2010, a British woman named Fiona Exon bought a carton of six eggs and discovered that all six of them had double yolks. Newspapers reported that the chances of this happening was less than a quintillion to one. This meant that a discovery like Exon’s should only happen roughly once every 400 years. However, after newspapers reported on her astounding discovery, many other people came forward and announced that it had also happened to them. Harford was asked to speak on national radio to explain the mathematics behind this incident, and several listeners called in to say that they had also discovered a carton of six eggs with double yolks.

Harford says that the main problem was that newspapers made the assumption that double-yolk eggs do not come in clusters. If the calculations were changed to factor in that they could, the chances of all six eggs in a carton having double yolks would increase “a million billion fold” (146). He says that double-yolk eggs could indeed come in clusters because it turned out that employees in egg-packing plants could easily identify double-yolk eggs by holding them up to the light. They would separate them out and place them in cartons to take home for breakfast. If there were extra cartons that no one wanted to take home, they would simply place them back on the production line to ship out. That makes Exon’s discovery a lot less remarkable and the newspapers’ calculations—that the chances of this happening were less than a quintillion to one—hugely incorrect. Harford says that this is “roughly—very roughly” what happened in the 2007 banking crisis (147).

Essentially, the banking crisis occurred because banks were taking huge bets on the chance of events that they thought were incredibly rare and almost impossible. The truth was that, like Exon’s eggs, they made incorrect assumptions about the “process producing those events” (147). The banks’ version of egg cartons was called “mortgage-backed securities,” and the eggs inside were the now well-known “subprime loans.” Banks bought the subprime loans from the companies that originally made them. The banks bundled them into “financial products,” which provided the buyer with the rights to the stream of mortgage payments and the risks that the mortgage would never be paid. The benefit of these packages was that they created “financial assets that promised a safe and predictable income” with a low chance of defaulting (148). However, if the worth of those packaged assets was miscalculated, they would collapse and threaten the companies that owned them with bankruptcy.

To understand this further, imagine that the egg cartons of the mortgage-backed products were a crate of eggs, but some of them were rotten, maybe 5%. The bank repackages the eggs into cartons of six, keeping one egg and selling the rest. The price of the other eggs “reflects the risk of who gets the rotten eggs” (148). Under the assumption that the rotten eggs do not cluster, like the original assumption about the double-yolk eggs, the chance that at least one egg in the six will be rotten is 27%. If the first egg is rotten, the bank that sold the egg takes the hit, but they are willing to take the risk because they sold the other five at a profit. The second egg is bought by a “junior investor” who takes on the second-highest risk. That risk of getting a rotten egg, however, is just 3% according to the bank’s calculations. The junior investor gets a discount to reflect that risk. Senior investors buy the remaining eggs, and the chance of any remaining rotten eggs is very low, about 0.2%, so they pay more money.

However, if the banks calculated incorrectly at the beginning—about how many rotten eggs there were or if they were truly distributed randomly and not in clusters—then “each level of repackaging dramatically amplified the effect of that mistake” (149). If the risk of getting a rotten egg is only 5%, then the chance of a second rotten egg is 3%, and the chance of a third is exceedingly small. However, if the chance is actually 10% rather than 5%, then the chance that the second egg is rotten hasn’t fallen from 5% to 3% but has actually risen to between 10% and 11.5%. The second egg in the second repackaging now has a 15% risk of being bad, not a 1.5% chance. The second egg in the third repackaging likewise becomes 2,500 times riskier.

The same analysis works to show what happens if the eggs come in clusters. The banks’ mathematicians believed that the rotten eggs wouldn’t cluster because mortgage defaults are often caused by individual problems like illness or divorce and there would be no reason for those factors to cluster. However, they missed another factor that could cause clustering: a national housing price slump. Subprime mortgages depended completely on the value of houses continuing to rise. They were offered with very low interest rates for a period of time, after which they were expected to be canceled and replaced with a new mortgage. But if the value of the house went down, no lender would want to take the risk of offering a new mortgage. The borrower would be stuck with the original mortgage, which now had higher repayments after the introductory period. They would then default, leaving the lender with a house worth less than what they’d loaned for it. This scenario happened repeatedly, not just rarely and individually. Since the math was wrong, and clusters were likely, the repackaging that was meant to minimize the risk of getting a rotten egg actually exacerbated it.

Soon, the Lehman Brothers bank went under, and many other banks were about to collapse from their own bad math. The government “couldn’t afford to let their financial system collapse” (153), so they used taxpayer money to bail them out. This caused crushing debts that people still suffer from today, having to endure tax hikes and severe cuts in public services. This happened in many countries, and it created crippling debt for various nations.

This crisis led to a sea change in “faith in the investment world” (159). The first casualty was the Greenspan doctrine, the regulatory mistake that allowed the crisis to occur. Basically, the doctrine held that “self interest was the best guardian of banks’ balance sheets” (159). No one thought banks would make decisions so bad that they would bankrupt themselves. The doctrine is named after Alan Greenspan, the chairman of the Federal Reserve for the 20 years leading up to the crisis. Though the banks’ self-interest was healthy, Greenspan ended up “overestimating the quality of their management” (159).

The second casualty was the “efficient-markets hypothesis,” a theory that “anything that can be predicted by rational, well-informed investors will already be reflected in the price of assets” (160). However, the behavior of rational, well-informed investors leads to “completely random” behavior of asset prices; when all the predictable elements are accounted for, the only things left that drive the market are unpredictable factors. The efficient-markets hypothesis argues that there are “no obvious bargains, no easy forecasts, no get-rich-quick schemes” because if they were truly obvious, they would have been snapped up already (161). The author holds that while the banking crisis of 2007 gave the efficient-markets hypothesis a beating, it still holds mostly true. It simply has well-recorded limitations.