Wednesday, July 25, 2012

VaR: you cannot estimate the unknown

In previous post I have introduced the concept of Value at Risk (VaR).

I have mentioned that there is (at least) one serious problem with VaR.

This problem stems from the fact, that VaR uses historical data to estimate future risk.

But what if the historical data simply does not contain information allowing predicting the future?

In an earlier post I presented the case of UniWIBID fixed income fund which after 9 years of amazingly stable returns (albeit small - some 2 bps per day), experienced an unprecedented single day 2.7% drop that wiped out six months of gains.
Chart: UniWIBID daily returns from inception (2003-05-22) till the shock (2012-06-04)

As a result of extremely low pre shock volatility, VaR for UniWIBID was totally uninformative till the very last moment.

Based on the probability distribution of historical returns, it seemed not possible UniWIBID could generate loss at either 5% or 1% probability level. A remote chance of an extremely low loss - 0.0064% - was signaled at cumulative 1% level, only.

The probability that the fund will generate return equal to or below 0%, was 0.004403347, or 0.44%.

Chart: VaR and CVaR potential percentage losses based on pre shock historical returns for UniWIBID

Historical UniWIBID returns did not give any way to properly asses the risk of the fund.

UniWIBID returns alone did not tell anything about fund's concentration in particular assets, potential losses on such assets, probability of generating such losses and dependencies (correlations) between assets.

Meanwhile, based on the fund's annual report, close to 6,7% of UniWIBID's assets were invested in bonds of a development group PBG which recently declared insolvency. This means potential losses on PBG debt anywhere between 40% and 100%.

An extremely low probability event, such as bankruptcy of one of the largest companies in Poland which derives much of its revenues from government-financed contracts, that can potentially have a high impact outcome for UniWIBID value is a classic example of a Black Swan. And Black Swan-type risks cannot be properly modeled using VaR.
Chart: UniWIBID daily returns from inception (2003-05-22) till 2012-07-23, including shock on 2012-06-04

Chart: VaR and CVaR potential percentage losses after the shock

Two possible ways of dealing with shortcomings of VaR-type analysis and adjusting for previously absent situations are stress testing and comparative / multivariate analysis.

The first approach depends on proper identification of critical factors affecting the system, their dependencies, scale of possible shocks, as well their potential individual and joint impacts. The key problem here is predicting the unknown.

The second approach assumes similarity in performance of related systems and reversion to the mean (see my previous post "Black Swans and multivariate time series analysis")

[ R source for VaR / CVaR calculations & visualization in R ]

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