In this article, it is explained how the housing market crash in 2008 was predicted by David Einhorn by using mathematics. It is a pretty interesting read and gives a clear explanation on how to use mathematics to predict events that are seemingly unpredictable.
At the end of the article, there are some questions to answer. I will go through them and try to answer them.
Is it a Random Walk?
One of the first things that Einhorn did was look at real estate prices in different decades and how they compared. He found that the biggest increase came in the 90s, after which the increase dropped significantly. The biggest increase came in regions where prices rose higher than their historical average, while regions with lower prices had relatively smaller increases. This suggests that real estate prices are not a random walk, because if they were, one could not use history to predict future outcomes.
When Michael Lewis wrote the book “The Big Short” he described how some people predicted the housing crash based on mathematical models. He also asked a question at the end of the book: Is it a random walk?
This is a great question, because this is what we would like to know about any phenomenon where we can predict a future outcome. We want to know if we can predict anything or if things are totally random. And I think that in the case of predicting whether someone is going to default on their mortgage, there will be those who say that it is indeed possible to predict this, and there will be those who believe that it is not possible and these are all random events.
There are two useful definitions of randomness in mathematics: one mathematical definition, and one from statistics. In mathematics, a random variable (or more specifically in this context, a stochastic process) is one whose value depends on chance (hence the name). It has no value until it happens. A coin toss has no value until it lands heads or tails. A computer algorithm’s next step has no value until you execute it. And likewise, your friend’s next move in chess has no value until she makes it. This type of randomness underpins most statistical models
The recent Academy Award-winning movie “The Big Short” has brought the 2007 housing crash back into the public consciousness, and one of its characters, Mark Baum (played by Steve Carell), has a conversation about the mathematics behind the crash. The scene has two financial analysts explaining to Baum that what had happened was a random walk, with Baum responding that it was not random at all, but rather completely predictable. The movie implies that it was predictable by most people who understood the mathematics involved.
But can we really claim that being able to predict the market is as simple as understanding random walks? After all, many people did understand this concept, and none of them seem to have been able to predict the crash. As one of my professors said in class recently, “Every economist knew we were headed for a crash. They just didn’t know when.”
So if it was predictable, why couldn’t anyone see it coming?
In Michael Lewis’ “The Big Short” he tells a story about Danny Moses, who was tasked with finding out the cause of the 2008 housing crash. He discovered a mathematical theory written by Benoit Mandelbrot that suggested that financial markets tended to be less predictable than they looked, and mostly followed a random walk.
This was important because if true, it would mean that the credit default swap (CDS) market was at risk of crashing. The CDS market was offering insurance via swaps against mortgage default losses, but as the housing bubble burst, more and more homeowners were defaulting on their mortgages, resulting in fewer and fewer people to pay for the insurance.
The CDS market had been driven by models that assumed past trends would continue into the future. But what if they didn’t? What if mortgage defaults weren’t normally distributed? What if they followed a random walk?
It’s an interesting question mathematically, and also economically. If markets follow a random walk then there is no way to predict them. The best you can do is say that there is a 50% chance something will go up or down tomorrow, and therefore there is no way to make money from it in the long run.
If we look at stock prices for example,
I spent two years in the early 2000’s working as a research scientist for a financial trading firm. While I was there I learned about how some traders are able to apply mathematics and statistics to make money. This is not news to anyone, but there is a huge variety of mathematical approaches out there, and they are all based on different assumptions.
One approach that is used quite often is the random walk model. The idea behind this model is that if you want to predict the future price of a stock or bond, then the best prediction is its current price, and each successive prediction will be an exact copy of the previous one. This is similar to the way one might flip a coin and simply copy down heads or tails as you get them. This does not mean that prices will go up or down randomly – it means that you have no reason to suspect that they will move in any particular direction; either up or down are just as likely.
In the years leading up to the financial crisis of 2008, the U.S. housing market was booming. The price for single-family homes had risen for 53 consecutive months, and people were buying properties with little or no money down, confident that prices would continue to rise and make them rich in the process.
The high-risk mortgage market was already beginning to falter in 2006 when some enterprising investors began betting against it. One of them was Michael Burry, a physician turned hedge fund manager who believed subprime mortgages were going to fail on a massive scale. Burry’s bet paid off spectacularly when the housing bubble burst in 2008, but he almost lost everything along the way because few investors understood what he was doing. That’s where “The Big Short” comes in.
Adapted from Michael Lewis’ book by the same name, “The Big Short” tells the story of three principal players who anticipated and took advantage of the crash: Burry (played by Christian Bale), hedge fund manager Mark Baum (Steve Carell), and former bond trader Charlie Geller (John Magaro) and his partner Jamie Shipley (Finn Wittrock). The film follows their journey as they try to convince Wall Street insiders that there is indeed a
{*}Subprime Mortgage Crisis:
The subprime mortgage crisis was a result of too much borrowing and flawed financial modeling, largely based on the assumption that home prices only go up. Subprime mortgages are those made to borrowers with low credit ratings (a FICO score below 660) or who lacked a verifiable income, among other factors. The housing market’s meltdown in 2007 and 2008 was the most serious financial crisis since the Great Depression.
The housing bubble began to deflate in mid-2006, when home prices peaked. By early 2007, mortgage delinquencies had risen and foreclosures were increasing; some lenders began to display concern as they tightened lending standards. By August 2007, an index of U.S. house prices had fallen more than 10 percent from its 2005 peak, and by late 2008 U.S. housing prices had declined 18 percent from their 2006 peak, which precipitated the failure of many subprime lenders and led central banks in several countries to lower interest rates sharply.
In particular, the crisis has caused economists and policymakers to debate the extent to which various toxic financial products such as synthetic collateralized debt obligations (CDOs) should have been regulated more heavily by national governments and their respective financial regulators.*}
