Wednesday, June 6, 2012

Black Swans and multivariate time series analysis

Chart: UniWIBID performance 1 year, 2012-05-04; source:

Turkey doesn't expect Thanksgiving is coming. Therefore its existence is nice and smooth. Until the harsh reality suddenly and painfully hits it.

This analogy can be applied to the UniWIBID fund which invests in fixed income equities. It's value has been very steadily, even a little scarily, growing for the previous eight years. Until it has been hit by the bankruptcy of the Polish Building Group (PBG).

As a result, the fund lost 2.71% in a single day. That moved its value back to November 30th, 2011 or by some 6 months. The fund management predicts that despite this event, the fund should work up the loss before the end of the year. And it seems possible judging on the previous performance. Unless another Black Swan hits...

Black Swans are defined as unpredictable events with serious consequences. This definition implies that you can't foresee such events using historical data for the relevant information is simply not present in the time series being analyzed.

However, it is sometimes possible to infer such possibility from different but connected times series, i.e. by using multivariate time series analysis.

In the case of UniWIBID, you may have potentially used the previous performance of IDEA Premium - another fixed income fund that recently lost 3.26%

Chart: IDEA Premium performance 1 year, 2012-06-05; source:

Therefore, even if Black Swans are not predictable, it is sometimes possible to get some warnings when the analysis is expanded outside the single time series.

This is quite important, since many financial models are based on the assumptions that the future can be predicted based on the past asset performance and they are limited to a single time series.

Take the standard Black-Scholes option pricing model - it assumes the changes in price of the underlying asset can be completely modeled using the past prices and normally distributed random changes of them. Since the Black Swan events are always connected with non-normal jumps, the Black-Scholes model cannot cope with them. And since the model is limited to a single time series, it is also unable to factor in potential shocks propagation that may be already visible in other time series.

PS: I have mentioned above that the sudden drop in value of the UniWIBID fund was caused by the bankruptcy of the PBG.

The shares of the company itself felt by nearly 50% in a single day:

Chart: PBG price, 5 days, 2012-06-05; source:

But that was just a culmination of the long process of decline of this stock:

Chart: PBG price vs WIG20 and mWIG40 (log), 3 years, 2012-06-05; source:

There was a clear downward trend present in the price of the stock that could be interpreted as a warning sign. Especially when the trajectory of the PBG price was compared against the market.

That is not always the case, though...

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