Morgan Stanley proves Value at Risk models still sketchy

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The big news from Morgan Stanley's latest quarterly earnings isn't profits or revenues. It's the investment bank's wonky calculation of Value at Risk, or VaR.

On most days VaR is barely mentioned outside of risk management reports, but it's important because financial institutions use it to measure their chances of losing money when the market moves against them.

A simple example: if a portfolio has a one-day 10 per cent VaR of $10-million, there is a 10 per cent chance the portfolio will lose $10-million in one day. Pretty straightforward.

But Morgan Stanley ruffled feathers this morning because its Value at Risk suddenly dropped this quarter. Asked about it, chief financial officer Ruth Porat said the bank changed its models from a four-year time horizon to a one-year look-back period. Alphaville has a good summary of how drastically that changed the results.

However, Morgan Stanley's changes are only part of a much bigger problem: the methods for measuring Value at Risk have always been flawed.

For an extensive explanation – and I mean extensive – there's a detailed paper from NYU's Stern School of Business. Here's the short version:

VaR can be calculated three ways: using variances and covariances, relying on historical simulations and running Monte Carlo simulations. Without getting into details how each works, just know that they all have flaws.

In the variance and covariance method, the models rely on normal distributions, which means their data must be normalized. (Remember that from stats?) And once it is, the models can underestimate the effect of outliers within the data set.

When running historical simulations, the models rely on past data to predict the future. As any portfolio manager knows, past performance rarely predicts future success. Plus, when looking backward, each data point is viewed independently, so the model doesn't pick up on trends and their resulting volatility.

As for Monte Carlo simulations, they can be helpful because they don't rely on normal distributions, and the person running the model can add in as many risk factors as he or she likes, but doing so makes the models bulky. The NYU study notes that "a yield curve model with 15 key rates and four possible values for each will require 1,073,741,824 simulations (4 to 15th) to be complete."

Plus, "with Monte Carlo simulations, we get more freedom to specify different types of return distributions, but we can still be wrong when we make those judgments," the paper noted.

So what does his all mean in the end? The models make it easy to underestimate risk. And perhaps even worse, people who understand how Value at Risk calculations really work can tweak their models to make it look as though everything is A-okay, even if it isn't.