Saturday, February 20, 2010

Mathematical Models Used In Finance: Help or Hindrance??

Normally I don't like to use stories from the British based magazine "The Economist" because they have an extremely asinine policy of not giving credit to writers on individual stories.  Indeed this will hurt them because all writers and journalists will hate them in their heart-of-hearts for this misguided and dictatorial way, but I digress about the Hugo Chavez style editorial policy....  The person/persons who wrote the article (who wrote it is something they feel their readers aren't entitled to know) entitled "Number-crunchers Crunched" did a good job.

The article starts off by noting Black-Scholes model was first used by options traders in the mid-1970s.  Initially, when the Black-Scholes model was used it might have seemed emasculating to some in the macho world of options trading (at least as done on the floors of exchanges then).  But as it proved successful it came to be used by most traders.  Derivatives trading got a shot in the arm from Black-Scholes and over time more "quants" entered the finance and trading field.

Over time though (most obvious with the economic crisis of 2008-2009) these models didn't prove to be so dependable, and many people believe that the unregulated derivatives market, collateralised debt obligations (CDOs), and credit default swaps (CDSs) were the root cause of this crisis.  "The Economist" article states (I paraphrase here) that the math models were useful for interest rates and foreign exchange, but were a total failure in debt markets,  where the mathematical models proved to have zero prognosticating function when it came to the collapse of the housing market.

Bankers took low-quality mortgage-backed securities and bundled them together with supposedly higher quality debt securities (combining different classes or "tranches" of debt).  These different classes of
quality debt securities that were packaged together were then labeled CDOs and stamped with a AAA rating.  Credit ratings agencies (such as Moody's) were more than happy to appease the investment banks who paid them.  Financial firms chose to rely on those models, even though they full well knew that the expected rates of return were unrealistically high for the so-called  "AAA" rated securities.  Some risk managers were even fired from their jobs for questioning the realism of the models (Does the name Iris Mack come to mind??).   No matter how wacky the risk vs. expected return the models showed were, Moody's and S&P models were not to be questioned, afterall as "The Economist" article quotes a regulator saying "A lifetime of wealth was only one model away".

Also, the rampant use of these models probably impacted markets in such a way as to create a sort of "feedback loop" where the models detrimentally affected their (the models') own function to predict.  This feedback process is sometimes termed counter-performativity, which usually occurs when a mathematical model used in the markets becomes so popularly used it then has a negative affect on itself.  It's important to note that this counter-performativity was not a root cause of problems, but one of the many smaller factors to consider.

As the article rightly notes, and I quote here directly from the article (referring here to the mathematical models):
"They failed Keynes's test that it is better to be roughly right than exactly wrong."

The banks were trying to "unwind" the same positions (same types of securities) at the same time.  Which of course added an enormous amount of uncertainty/risk during the peak of the crisis.

Models used for stress tests

The article then goes on to discuss different type models used for stress tests. There are 3 types stress tests this article discusses:

1. VAR "value-at-risk"
2. Conditional VAR (CoVAR)
3. "stress" VAR

These tests can be used to judge a portfolio of assets, or by regulators looking at banks' quality of capital reserves (the banks' capital "buffers" in times of calamity). The VAR was invented by some brainiac types at JPMorgan in the late 1980s.  VAR and its descendants have since become very popular at banks.  Bank regulators seem to favor CoVar style tests more because CoVAR accounts more for spillover affects in bad markets and "counterparty risks"---the distress of others you deal directly with.  CoVAR would give a worse picture of the future, but CoVAR is more realistic during times of major trouble. "Stress"VAR which Morgan Stanley uses, factors in liquidity much more (possible scenarios where liquidity is very tight).

Some banks systems seemed to be more dysfunctional than others.  For example Citigroup was using many different "legacy" systems (computers, etc...) because of many past mergers.  Also different units (subsidiaries) of the same large banks may have used different data inputs into the same models, therefor even inside the same bank, units would come up with different measures of risks.

Some Solutions to Finance Models' Downsides

1. More reliance on solid and prudent judgement, less reliance on numbers.
2.  Using stricter stress tests (such as CoVAR) which rely on more capital buffers and more margin of safety.
3. Synchronizing of IT systems between different units (subsidiaries) and making sure the better information spit out by the IT system makes its way to senior management's eyeballs.
4. "Model-uncertainty reserves".  JPMorgan Chase now holds $3 billion of these such reserves.

"The Economist" article (writer unknown) has more details I didn't include here.  I encourage those interested to go there.

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