Financial Theory - Video John Geanakoplos

In this lecture, we use the overlapping generations model from the previous class to see, mathematically, how demographic changes can influence interest rates and asset prices. We evaluate Tobin's statement that a perpetually growing population could solve the Social Security problem, and resolve, in a surprising way, a classical argument about the link between birth rates and the level of the stock market. Lastly, we finish by laying some of the philosophical and statistical groundwork for dealing with uncertainty.

Until now, the models we've used in this course have focused on the case where everyone can perfectly forecast future economic conditions. Clearly, to understand financial markets, we have to incorporate uncertainty into these models. The first half of this lecture continues reviewing the key statistical concepts that we'll need to be able to think seriously about uncertainty, including expectation, variance, and covariance. We apply these concepts to show how diversification can reduce risk exposure. Next we show how expectations can be iterated through time to rapidly compute conditional expectations: if you think the Yankees have a 60% chance of winning any game against the Dodgers, what are the odds the Yankees will win a seven game series once they are up 2 games to 1? Finally we allow the interest rate, the most important variable in the economy according to Irving Fisher, to be uncertain. We ask whether interest rate uncertainty tends to make a dollar in the distant future more valuable or less valuable.

In order for Social Security to work, people have to believe there's some possibility that the world will last forever, so that each old generation will have a young generation to support it. The overlapping generations model, invented by Allais and Samuelson but here augmented with land, represents such a situation. Financial equilibrium can again be reduced to general equilibrium. At first glance it would seem that the model requires a solution of an infinite number of supply equals demand equations, one for each time period. But by assuming stationarity, the whole analysis can be reduced to one equation. In this mathematical framework we reach an even more precise and subtle understanding of Social Security and the real rate of interest. We find that Social Security likely increases the real rate of interest. The presence of land, an infinitely lived asset that pays a perpetual dividend, forces the real rate of interest to be positive, exposing the flaw in Samuelson's contention that Social Security is a giant, yet beneficial, Ponzi scheme where each generation can win by perpetually deferring a growing cost.

This lecture continues the analysis of Social Security started at the end of the last class. We describe the creation of the system in 1938 by Franklin Roosevelt and Frances Perkins and its current financial troubles. For many democrats Social Security is the most successful government program ever devised and for many Republicans Social Security is a bankrupt program that needs to be privatized. Is there any way to reconcile the views of Democrats and Republicans? How did the system get into so much financial trouble? We will see that the mess becomes quite clear when examined with the proper present value approach. Present value analysis reveals the flaws in the three most popular analyses of Social Security, that the financial breakdown is the fault of the baby boomers, that privatization would bring young investors a better return than they anticipate getting from their social security contributions, and that privatization is impossible without compromising today's retired workers.

Standard financial theory left us woefully unprepared for the financial crisis of 2007-09. Something is missing in the theory. In the majority of loans the borrower must agree on an interest rate and also on how much collateral he will put up to guarantee repayment. The standard theory presented in all the textbooks ignores collateral. The next two lectures introduce a theory of the Leverage Cycle, in which default and collateral are endogenously determined. The main implication of the theory is that when collateral requirements get looser and leverage increases, asset prices rise, but then when collateral requirements get tougher and leverage decreases, asset prices fall. This stands in stark contrast to the fundamental value theory of asset pricing we taught so far. We'll look at a number of facts about the subprime mortgage crisis, and see whether the new theory offers convincing explanations.

In order to understand the precise predictions of the Leverage Cycle theory, in this last class we explicitly solve two mathematical examples of leverage cycles. We show how supply and demand determine leverage as well as the interest rate, and how impatience and volatility play crucial roles in setting the interest rate and the leverage. Mathematically, the model helps us identify the three key elements of a crisis. First, scary bad news increases uncertainty. Second, leverage collapses. Lastly, the most optimistic people get crushed, so the new marginal buyers are far less sanguine about the economy. The result is that the drop in asset prices is amplified far beyond what any market participant would expect from the news alone. If we want to mitigate the fallout from a crisis, the place to begin is in controlling those three elements. If we want to prevent leverage cycle crashes, we must monitor leverage and regulate it, the same way we monitor and adjust interest rates.