Re: What about 30-day 99% VaR...

From: Glyn Holton
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Date: 10 Nov 2006
Time: 05:20:38

Comments

Hi Andreas: Thanks for your interesting post. Based on your explanation of what the regulators are doing, I think their goals are admirable, but we may take issue with some of the details of implementation. These days, it is hard to define exactly what constitutes an "investment," but I know that a derivative isn't one. Any fund that purports to "invest" in derivatives could use a healthy dose of regulatory oversight, and it sounds like that is what European regulators intend. By limiting these "sophisticated" funds to 200% leverage, the regulators are ensuring they don't go out and do anything too "sophisticated" with investors' money. Bravo! I also like their thinking in terms of leverage. For investors (as opposed to, say, traders) leverage is a better way to describe their risk than is value-at-risk. Tell a pension fund that their 30-day 95% VaR is $20 million, and they won't quite know what to make of the number. They will wonder "how does this compare to other pension funds that are similar to us ... ?" If you tell them that their portfolio has leverage such that it is 120% as risky as the S&P 500, then that speaks to them. Now "leverage" is one of those words that, like "investment" is becoming increasingly difficult to define. It used to be that leverage was about borrowing money and placing it at risk. Suppose two investors both have $1000. One invests it in the S&P 500. The other borrows $2000 and invests the full $3000 in the S&P 500. We say the second investor has 300% the leverage of the first. The leverage was achieved through borrowing. But today, the investor could have achieved similar exposure through a whole variety of mans -- repo, derivatives, securities lending, a structured note, etc. Since we can no longer define leverage in terms of borrowing, how can we define it and encompass all these different forms of leverage? What the European regulators have done is come up with a wonderful operational definition: "leverage" is the ratio of a portfolio's VaR to the VaR of some reference portfolio. I like that! Of course, they are using a questionable VaR metric to implement their definition. I won't recount all that is wrong with 30-day 99% VaR, having done so already for ten-day 99% VaR. The absolute magnitude of the numbers that will be produced will be utterly meaningless. However, there is some good news. Those numbers may still have some relative significance. Let me explain. Suppose we construct to different VaR measures that purport to calculate 30-day 99% VaR. We apply them both to some portfolio, call it Portfolio A. One VaR measure comes up with a VaR of $400,000. The other one comes up with a VaR of $900,000. No surprises in the discrepancy -- with 30-day 99% VaR, the absolute magnitudes are meaningless. Suppose, however, we apply both VaR measures to another portfolio, say Portfolio B. For this portfolio, the VaR measures come up with respective VaRs of $1,200,000 and $2,600,000. Again, the VaR measures disagree on the absolute level of the risk, but THEY DO AGREE ON THE RELATIVE LEVEL OF THE RISK. The two VaR measures both indicate that Portfolio B is approximately three times as risky as Portfolio A. The reason is that, if a VaR measure uses, say, very high standard deviations for key factors, this will inflate the VaR numbers it calculates for all portfolios. Such a VaR measure will still be good at saying "this portfolio is more risky than that one." The bad news is that this nice property of VaR measures tend to manifest itself more with reasonable VaR metrics, such as one-day 95% VaR, than with unreasonable VaR metrics, such as 30-day 99% VaR. Many people think it is somehow conservative to calculate VaR with extreme VaR metrics that produce large numbers. It isn't. A VAR metric is just a measurement convention. It doesn't make any difference whether we calculate distances in inches or meters. People should think of VaR metrics the same way. The choice should be driven by which VaR metric can be most conveniently and meaningfully calculated. I would strongly encourage the European regulators to forget about 30-Day 99% VaR and go with one-day 95% VaR. Also, it is absolutly essential that the "sophisticated" funds use the same VaR measure to calculate the VaR of their investment portfolio and reference portfolio.

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