Sunday, February 3, 2008

Hit by a fat tail...


It’s 10am, your rottweiler has just chewed your Italian leather boots, your wife has burnt your pancakes and your mistress is on the phone proclaiming that “it’s over because, really, you’re pretty lousy in bed.” Oh yeah, and while you’re at it, your broker is leaving you a message that the stock market is crashing and you’ve lost a third of your savings. A bad hair day? No, my friend. You’re likely living in a fat tail!...

…In a manner of speaking! Economists talk about fat tails when they want to refer to the probability that extreme events such as the above occur in a much higher frequency than you would regard as "normal."

So why tails? And why fat?!

It all began with what we call a probability distribution. Think of each day of your life as a dot under a bell-shaped curve: Most of the dots are concentrated around the middle, in the bulge of the bell: Days of medium pain and medium pleasure; boots are shiny, pancakes edible and mistress satisfied (at least that’s what you think!)

But then you get those few days of tremendous joy or extreme misery. These will be situated within the small little corners at the right and left of the bell—the “tails”. The fewer the extreme days, the thinner the tails. Now, if you are an extreme type, your life bell will look somewhat different: A thinner bulge in the middle (with fewer average days) and, yes, you guessed it, “fat tails!”

Roaming around the various salons these days, you’ll notice much of the party chatter being about tails; tails behaving badly. In fact, it’s not just party chatter. Some economists are losing sleep over this, and first and foremost Ben Bernanke. And given the bashing and teasing he has received for his recent emergency cut by numerous commentators, myself included, I though we owe it to Ben to at least present his side of the story.. out of respect for his lack of sleep as well as his remarkable contribution to the body of academic literature in the field.

So there it goes: “I’m having a nightmare here!…” Ben is pleading. “I am dreaming I’m inside a bell-shaped universe and the tails are suddenly fat! Wait.. it gets worse: One of them, that nasty left one, is much fatter than the right one. Yes, not only are things more likely to get extreme, but it’s not going to be that you’ll win the lottery. Instead, you’re going to lose your job, your shares will crumple, the value of your home will collapse and you might even get a run on your bank that will see your deposits evaporate.”

“So I feel I should take action. No, it’s not because I care about the stock markets. It’s about that thing I am allowed to care about: GROWTH!

“You know, back in the ‘80s I wrote a paper where I suggested that sharp declines in the prices of shares, houses, etc can amplify and prolong a downturn in economic growth. This is how it works: For banks to lend you money, they need to feel comfortable they will get paid back. So they will ask you for a collateral—your home, say. But if the value of your home drops below the amount you borrowed, banks will feel uneasy: If you were to default, they could take your home and sell it but they would not get all their money back. And uneasy translates in lower lending.”

“So see what happens: The economy slows, jobs are lost, home prices go down, banks cut back their lending, new business ideas cannot get financed, the economy slows further, more jobs are lost, etc etc. Combine that with a drop in share prices, and it gets even worse. A downward spiral to misery. I called that the ”financial accelerator” at the time. Pretty scientific, huh?"

“So as I was saying before, I’m taking action. Timely, decisive and flexible action. I’m cutting rates in a drastic fashion, and pampering the markets I’ll be there for them.. and pray for the best! Better safe than sorry.”

Hmmm.. “safe”? Not exactly, there are always risks. First, you have the risk of perpetuating complacency in the markets by fomenting moral hazard. Second, you have the risk of undermining that second objective that Ben cares about: Inflation.

And then, you also have the question of symmertry in the line of reasoning itself: Surely, the financial accelerator works to amplify the impact of market upturns too in ways that can be undesirable: Bank lending becomes excessive, the price of risk-taking drops to absurd levels, markets become “irrationally exuberant.” All that breeding ground for a big fat crash. (Sounds familiar?) Isn’t there scope, therefore, for timely, decisive and flexible action in such cases?

Well, I’ll chew my Italian leather boots the day Bernanke’s Fed comes out and says: “Following days of market euphoria and loose credit conditions, the Federal Open Market Committee decided today to raise its target for the federal funds rate by 75bps […] and stands ready to take further action if such conditions continue.”


Glossary: fat tails, well-behaved tails, probability distribution, collateral, financial accelerator, rottweiler.

And if you want to read further:
Fed’s rate cut marks an end to gradualism (Financial Times)

Bernanke’s Bounty

Federal Reserve Bank of New York Governor Frederic Mishkin on Monetary Policy Flexibility, Risk Management, and Financial Disruptions



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