There is a consolidated opinion in the financial risk management arena that giving more weight to most recent observation is a good thing, improving the forecasting power of risk measures such as VaR.
The front office professionals have a consolidated view that the risk measures must reflect the current "dimension" of risk. For this reason they are measured with a short historical period of observation and/or exponentially weighted (or GARCH) measures. The Risk Managers like to weigh the most recent events as there is a consolidated opinion that this process improves the back-testing statistics.
However, giving more weight to the most recent history increases the pro-cyclicality of the risk measure. Pro-cyclicality means that the risk measure moves in the opposite direction of the market, it increases when markets fall, it decreases when market thrive. This behavior generates a perverse consequence: money managers and traders are encouraged to take on bigger positions when risk goes down, buying more risk when the price is high and the market quotations are topping. On the other side, market falls increase risk, making it more likely that VaR limits are triggered and then causing stop losses and a "selling" of risk positions when the quotations are low.
In other words the pro-cyclicality of risk measures determines what George Cooper calls in his book "The Origin of Financial Crises" a positive feed-back process. The existence of pro-cyclical measures creates in the financial market a mechanism where the reduction of price generates an increase of the offer side of the market rather than of the demand side. Cooper explains that the financial markets differ from other goods markets, where a reduction of price always results into an increase of demand, generating a self-stabilizing effect. Differently from markets of goods, in the financial markets a reduction of price does not necessarily generate an increase in demand. Symmetrically, increase in price is often a catalyst for new demand. This innate nature of financial markets contains the seeds of instability and the intrinsic presence of periodic boom and bust cycles.
It is out of the scope of the article to discuss if the theories of Cooper are right or wrong, but what is certain is that a pro-cyclical risk measure increases the instability of financial markets, adding to the offer during market falls and powering demand during boom cycles. This is a perverse effect and what exponential weighting does is to amplify the positive feed-back process, contributing to the instability of the markets. The paradox is that VaR and risk management was originally introduced to mitigate systemic risks and strengthen market stability.
Our article presents a new risk measure, called Hybrid VaR, with two objectives in mind:
- improve the statistical reliability of VaR measures, achieving good back-testing results in moments of stress.
- introduce an anti-cyclical component, designed to invert pro-cyclicality in good market times.
Hybrid VaR blends traditional VaR measures with the worst P&L from a selection of historical stress test scenarios. The VaR measure remains anchored to a rolling window of time, always reflecting the market conditions in the most recent n observations used by the measure.
In contrast, the stress tests scenarios always look at fixed time windows of stressed financial conditions.
The two measures, VaR and worst historical stress test, are assigned with weights calibrated in an anti-cyclical way: the more the markets thrive, the more the memory of the worst periods of stress increases, introducing a disincentive to take on more risk when market quotations are topping.
We have back-tested the Hybrid VaR measure during the turbulent 5 years comprised between 1st of January 2004 and 31st of December 2008. Both the daily and bi-weekly back-testing exercises yield the best results among a selection of different methodologies and the bi-weekly tests return a number of violations almost identical to the ones expected.
We conclude the article recommending the use of Hybrid VaR: it introduces a relevant anti-cyclical component in the risk measure and seems to work well and better than many other measures in back-testing terms.
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