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The Value and Risk of VaR, pt. 2

Aug 8, 2012 Marc Odo

In a previous ZephyrCOVE post I discussed what VaR is and isn’t, some of VaR’s key assumptions, and how it has evolved. In this follow-up post I will explore how VaR is being applied to manager and portfolio analysis, which is Zephyr’s core business. That being said, all of the original points surrounding VaR raised in the previous post still apply here.
Originally VaR was designed for worst-case estimation of very short-term trading positions. VaR of this nature is typically forecasted for no more than a week. This is the opposite end of the spectrum of Zephyr’s traditional business, which focuses upon strategic planning and long-term, consistent performance measured in years, not days. Does it make sense to apply VaR to longer-term investing?

I would argue that VaR is much less relevant for longer-term investors. If one is on a trading desk and is highly leveraged, or if one needs to fund their operations using the daily wholesale markets, then yes, something like VaR is important. In these scenarios it is leverage and liquidity that are the true risks, and a tail event could put you out of business. Bear Sterns and Lehman Brothers are obvious examples.

But even though the bear markets we witnessed in the 2000s were gut-wrenching, eventually the long-term investor recovered. The peak-to-trough losses of the S&P 500 were -44.7% from 9/00 to 9/02 and -51.0% from 11/07 to 2/09. However, by 10/09 and 3/12, respectively, the S&P 500 had recovered all of those losses.

This leads to some other big questions regarding VaR. First of all, does it make sense to build an entire long-term strategy around avoiding events that are, by definition, rare? Yes, there are extremes in the 1% tails that have an outsized negative impact on a portfolio. But does it make sense to build an entire, long-term, wealth appreciation strategy avoiding these possibilities? By being too conservative what is the opportunity cost in avoiding the other 99% of the distribution? Perhaps an analogy can be drawn to an agoraphobic shut-in, too frightened to step outside. What are the costs of never leaving the house?

Another issue has to do with the statistical significance of trying to quantify the tails. VaR is calculated by averaging the datapoints that lie in the most extreme tails. But by definition, these tail events are few, so there might only be something like half a dozen observations in that far-left tail of tail. Just how much should one infer from that handful of datapoints?

The final point I’d like to make regarding VaR is this. Some users have gravitated to VaR because they think VaR is easier to understand or explain than the traditional measure of risk, i.e. standard deviation. However, if one is using a normal, Gaussian distribution then from a mathematical perspective Value-at-Risk IS standard deviation. There might be different assumptions for the cut-off points that specify the VaR, but all of those are calculated using the traditional measure of risk, the standard deviation.

Zephyr has always maintained that there is no single measure that tells an analyst everything he or she needs to know. In order for a metric to truly be useful, one must understand how it is calculated, what it tells you, and perhaps most importantly, what are the limitations.

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