Friday, January 16, 2009

Valuation and Risk Measurement Models under Heavy Criticism – What Went Wrong?

Are valuation and risk measurement models as the root of all evil?

In this crisis we witnessed a broken market. Financial institutions relaying on complex financial models for both valuation and risk management suffered heavy losses and saw their methodologies break before their eyes.

Many valuation models and risk models literally stopped functioning and started spewing out numbers that seem to have no real connection with reality and stock market prices.

Many investors and financiers alike are losing faith in what was once held high as the hope of objective decision making based on mathematical calculations. Math and numbers provided a sense of security and scientific aura to many managers who only recently learned of their limitations, the hard way.

It is natural for us to assume complex equations and finance theory applied to the markets is much better than any subjective human judgment made. The model does over-estimate risk or influenced by market psychology. The model is no eager to sell on profit and is essentially not biased by any psychological human weakness.

So what went wrong?

Understanding models

Reality is far too complex to model. At least for us simple minded humans. As a result all models have to make assumptions which simplify reality and enable to model it while still providing powerful insights into the subject matter.

Many simple models are very powerful such as simple economic supply and demand, game-theory prisoner’s dilemma and many many others. The most important thing, then, is to be aware of the assumptions made in the model and draw the model’s limitations as a result.

In order to understand how far these limitations may go I’ll examine too very commonly used financial models: VaR, which is a commonly used risk measurement model and Black and Scholes which is a commonly used valuation model.

VAR and black swans

I’ve recently discussed the question of whether the western financial markets are just a huge Ponzi Scam. Nassim Taleb, author of the Black Swan theory suggests so (read more here: Is the Stock Market a Big Ponzi (Madoff) Scheme?).

So what do black swans have to do with value at risk? Let’s have a look at VaR and its purpose.

Value at Risk is a widely used measure of the risk of loss on a specific portfolio of financial assets. All the financial institutions in the world use VaR in their risk management efforts. For a given portfolio, probability and time horizon, VaR is defined as a threshold value such that the probability that the mark-to-market loss on the portfolio over the given time horizon exceeds this value (Wikipedia)

To put it simply VaR is the amount a certain portfolio might lose on a given probability and length of time.

For example, if a portfolio of stocks has a one-day 5% VaR of $1 million, there is a 5% probability that the portfolio will fall in value by more than $1 million over a one day period (Wikipedia).

When VaR is applied a probability has to be assumed. This is one of the main weaknesses of VaR and is crucial for understanding its limitations. When VaR is calculated a given timeframe and confidence level are assumed. For example I’d like to have a 95% confidence that in a 10 day period I will not lose over $1,000 on my portfolio.

What VaR does is take either historical or expected values for the assets and uses a statistical distribution to calculate the maximum loss on a 95% confidence level.

The problem lies with the remaining 5% which are not modeled and that’s where the black swans come into play. A black swan refers to a large-impact, hard-to-predict, and rare event beyond the realm of normal expectations. That is exactly what that remaining 5% (or 1%) represent. The chances are slim but the impact will be destructive (see sub-prime and credit crisis).

This limitation cannot be avoided. Had one modeled for 100% of occurrences than the Value at Risk would simply be the entire portfolio as there’s always a chance to lose everything.

Black and Scholes Model and non standard times

Another very commonly used model is the Black and Scholes model for option pricing. This model, sometimes under certain adjustments, is considered the gold standard for option pricing.

The model is quite complex and relays on relatively advanced mathematics but as always the model needs to make assumptions on reality which in turn limits it.

The Black and Scholes model is very powerful for option pricing and provides very interesting data on the impact of time, base asset price movements and standard deviation on the price of options.

However, the mighty Black and Scholes model assumes that the stock prices, which are the basic asset for the option, distribute normally (Normal Distribution) and that continues trading exists.

Obviously when the market is broken and trading is slim Black and Scholes simply doesn’t work. Option pricing according to Black and Scholes will usually be ridiculously high.

More complex financial instruments call for more complex valuation models along with more difficult to understand assumptions and limitations. No wonder we got lost in all the numbers.

It’s not that everyone wasn’t aware. There aren’t any better tools out there

I wouldn’t hurry to disparage financiers everywhere. Most of these individuals understand very well the limitations of models and modeling for financial assets. The problem is there aren’t any better tools out there.

Financial institutions have to quantify risk and valuate assets somehow. As such these models are the best solution available next to selling the assets altogether.

The problem stated when models weren’t accompanied with adequate skepticism, conservatism and a good infrastructure that calls for experience and judgment. It’s really not my intention to offer wisdom in hindsight. I’d make the same mistakes myself. That’s just human nature. Let’s make sure we implement these lessons in the future.

As always the industry will overshoot to access conservatism of valuations and extreme risk assessment. The ones that will make money are the ones that will be brave enough to remain calm and sound and apply the common sense we all know to be right but too afraid to apply.

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Image by: scottwills


Praveen Puri said...

I think that a major issue is that these models give a slight edge, and then Wall Street works the edges with leverage.

In other words, let's say an arbitrage strategy gives a 99.8% chance to make a 1/10 % return (using 1:1 leverage).

Then, they might use 50:1 leverage to make a 5% return.

The problem is what happens if the 0.2% circumstances happen?

They need to play defense against these outlier conditions by using less leverage.

Bad Credit - Easy said...

Anyone say LTCM? Its just dangerous to rely on equations when the root of the trading markets is human greed and fear. There is no equation that can count for these factors.