Super Models With Fat Tails - Cook`s Kitchen


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Everybody it seems wants to break up the big commercial banks who use customer deposits to play fast and loose in derivatives markets. But we hear few good arguments other than "they tend to lose a lot of money" and "they pose risk to the financial system."

I am going to give you a nearly irrefutable argument: Once a bank reaches a certain size of assets, its business becomes too complex to manage, and it is therefore bound to get caught up in occasional failures of risk management.

The complexity comes in two major forms that I will call behavioral and mathematical. First, let's look at the actual size of some big banks and see where the idea of "too big to manage" might become relevant...

Total Deposits of 5 Largest US Banks at End of 2011

JPMorgan Chase ( JPM ) $1.093 Trillion

Bank of America ( BAC ) $1.047 Trillion

Wells Fargo ( WFC ) $843 Billion

Citigroup ( C ) $799 Billion

US Bank ( USB ) $215 Billion

(source: Bloomberg )

Behavioral Complexity

This one is simple to understand. Combine lots of variables concerning the inflow and outflow of cash and other investments with the tendency of people to do dumb things and you have a recipe for money to get lost -- especially where the temptation of leverage is involved in complicated derivatives.

The extreme example is the rogue trader. Sure you can have controls to prevent theft, excessive risk, and mere stupidity, but it gets a lot harder when you have tens of thousands of employees responsible for the movement and accounting of hundreds of billions of dollars.

There is also the pressure to please Wall Street with an investment return on those mega billions. JPM's Jaime Dimon trusted Ina Drew in their London Chief Investment Office to create outsized returns (even if they called it "just hedging"). And she obviously trusted the "London Whale" to make it happen.

The losses of big banks over the recent decades are in some ways a never-ending tale of one trading pal saying to another, "You know what you're doing... don't you?"

Mathematical Complexity

As if trying to tame big assets and lots of staff wasn't enough, how about trying to tame "wild randomness?" This is the phrase that Nassim Taleb introduced to us in 2007 in his seminal book The Black Swan .

Taleb taught us that the bell curve of standard deviation was invented to measure the variation among physical phenomena. It is also very useful for creating statistical representations of expected outcomes in some forms of human behavior, like athletics, academics, election results, and surveys. The normal distribution gives us useful information to make fairly reliable predictions.

But standard deviation becomes extremely fragile when measuring the fluctuations in asset prices, especially where derivatives and leverage are involved . This is because markets are social beasts unto themselves and the crowd behavior of 100 or 1 million investors and traders can create randomness that makes bell curves much more flat and wide... and with very fat tails.

The "tails" are the outlier regions of the distribution. Think of the event that happens very infrequently, like the 100-year flood, or the asteroid in your back yard, or winning the PowerBall.

Super Models: Beautiful, But Rarely Real

Ever since the Black-Scholes option pricing model ushered the dawn of the derivatives era, quantitative types have been busy creating models of markets to gauge probability and risk.

The primary problem with most models built on standard deviation is that they don't account for geometric complexity. If a trader or risk manager assumes that the ten-year volatility of a particular security will prevail for the next year or month, then he or she is making a very risky assumption -- again, especially if the leverage of the positions can create losses that multiply very quickly.

Why? Because markets are built on all sorts of social, political, economic, even geological and meteorological variables. Combine one variable each of the preceding and the complexity gets awfully open to random outcomes outside the bounds of a "normal" distribution. The standard bank VAR (value at risk) model can't account for this complexity.

We deride the weather man when his 7-day forecast doesn't pan out, and we forget when he gets it right most of the time. Statistical modeling of weather is extremely advanced these days and it can still miss when you get out past a week. Now imagine how accurate its predictions would be if it had to deal with political and economic variables too.

Stress Testing the Models

What was wrong with JPMorgan's risk model for its London interest rate desk? Besides the fact I just described where it could not account for many variables of market behavior -- possibly one like a Greece exit the eurozone -- the model probably had the wrong assumptions fed into it about all kinds of other variables, such as the volatility and direction of interest rates.

One thing I started asking last week was this: "How did this get past the Fed and Treasury earlier this year during the so-called bank stress tests?" My instinct was simply what I've been talking about: the models and the math are so complex, that if one flashes enough numbers and graphs across a screen, a regulator might say just nod and feign comprehension, saying "Oh, that looks good."

And, I found another part of my answer today. I saw an interview with Sheila Bair, former chair of the FDIC. She heard that JPM had actually tweaked their VAR model in and around the time of the stress tests. She said she'd be asking a lot of questions about that if she were still involved in protecting and guaranteeing consumer deposits.

Size Matters

So this brings us back to the original question, what is an appropriate and manageable size for a bank? Zacks Chief Equity Strategist John Blank recently shared with us the "3% of GDP Rule:"

"In that rule, no bank can have asset/liabilities over 3% of GDP, which in U.S. terms, is around $50B.

The logic: Lock down the bank's size. From 10 massive banks we get 60 mid-size banks. So 50 new managements in smaller, more-focused banks, which, to me, is better risk management.

The new managers can only seek to raise cash flow returns through a better business mix and loans; which ultimately forces them back into high-dividend paying defensive stocks; which stabilizes our now volatile high-beta banking stock sector.

So why haven't you heard of it? Because we went for 2,600 pages of Dodd-Frank regulation instead. If we are a pro-competitive country, it mystifies me as to why throwing the 3%-of-GDP-Rule under the carpet continues to be tolerated."

Over-Confidence Replaces Probability Knowledge

Derivatives models have given Wall Street a magic genie to create more leverage and elaborate stories about how things should work. Unfortunately, even the PhDs in mathematics get seduced by the beauty of their models and forget it's only pretend.

When the risk managers can simply use a "plug n play" formula to value the firm's risk and leave it at that... well, we know how that worked for Bear Stearns, Merrill Lynch, and Lehman.

Whether it's the rogue trader hiding bad bets on a separate ledger or the giant bank that is "too big to manage" over-confidence, hubris, and plain old mathematical ignorance can burn money fast. Often, the trader and the risk manager most responsible have a weak knowledge of probability and the gearing of leverage which can get geometric pretty quick. (For the record, I am not a mathematician.)

Even if one does understand the bell curve, as Taleb showed us standard deviation is often not robust enough for multi-dimensional financial markets. This is because markets are full of "wild randomness." When anything can happen, there is no standard for deviation.

In closing, a word about "too big to manage." I worked for a currency trading desk where I could trade $1-$2 million unhedged positions. My loss limit for the day was $10,000 (I never hit it thank goodness), our operation was small and focused, and our internal risk controls were fantastic, with checks, double-checks, and triple-checks by risk management staff. I couldn't dream of hiding a bad trade or open position because it would have been impossible.

The JPM debacle is further proof that these giant banks cannot manage all the wings of all the derivatives beasts they attempt to tame.

Kevin Cook is a Senior Stock Strategist with
BANK OF AMER CP (BAC): Free Stock Analysis Report
CITIGROUP INC (C): Free Stock Analysis Report
JPMORGAN CHASE (JPM): Free Stock Analysis Report
US BANCORP (USB): Free Stock Analysis Report
WELLS FARGO-NEW (WFC): Free Stock Analysis Report
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The views and opinions expressed herein are the views and opinions of the author and do not necessarily reflect those of Nasdaq, Inc.

This article appears in: Investing , Stocks
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