Phorgy Phynance

80 Years of Daily S&P 500 Value-at-Risk Estimates

with 10 comments

For Felix:

S&P 500 Daily Value at Risk: Jab 1930 - May 2009

And the last 10 years…

SP500VaR_10yr

Update: Felix has updated his post with a link to my charts above, but makes some comments that I thought I should address.

If we use a shorter horizon that better captures what is going on at this moment, we see that risk plateaued in June and has actually ticked up significantly in the past several weeks as measured via the “stable” distribution. On the other hand, volatility has actually decreased during the past several weeks. What this means, i.e. the discrepancy between “stable” and “normal” is that the tails have become fatter recently.

SP500VaR_2009

Also keep in mind that although risk appears to have decreased since the beginning of the year, it is still at extremely high levels. We would have to go back to 1934 to see comparable risk levels, so it is no time to become complacent.

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Written by Eric

August 6, 2009 at 6:32 am

Posted in VaR

10 Responses

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  1. What’s the VaR probability here?

    Mike

    August 6, 2009 at 12:45 pm

  2. […] time now about better risk models (my SSRN paper is here and my blog post on that paper is here). Phorgy Phynance has a fascinating graph about the difference between the normal distribution and a fat tailed […]

  3. For the practitioners in the audience, would you mind showing details of your model? Have you taken a representative portfolio of options on the S&P? How about equity-credit correlation??

    chemist

    August 7, 2009 at 4:49 am

    • Hi chemist,

      Felix asked for a chart of what VaR would look like for a simplified situation where a bank was invested solely in the S&P 500 just to get a feel for things. That is what my chart represents. Most VaR models would amount to simple volatility estimators if the only securities were equities. Options are accommodated via nonlinear relationships, etc, but that is not necessary for this simple exercise. So there is no “model” to speak of. I simply estimate the stable (and normal) parameters and from that, you can determine VaR. In these charts (as someone noted on alphaville), I use an equal weighting, but I could just as easily have used weighted estimates (which is what I do for my own work in asset management). It just takes longer to compute. The results are not that different though. They will simply look slightly less rectangular with the same trends.

      I hope that answers your questions. This exercise was far simpler than your questions suggest, but that is a virtue in my opinion.

      Cheers!

      phorgyphynance

      August 7, 2009 at 5:59 am

  4. […] August 8, 2009 A few people have commented about the methodology used to produce the charts in my last post. Keep in mind, I threw those together quickly for Felix based on charts already put together for a […]

  5. Not sure if you’re aware of this but conditional VaR is a coherent risk measure while VaR is not.

    quantum probability

    November 18, 2010 at 4:57 am

  6. […] 80 Years of Daily S&P 500 Value-at-Risk Estimates […]

  7. A motivating discussion is worth comment.
    I believe that you need to write more about this issue,
    it might not be a taboo matter but generally folks don’t discuss these subjects. To the next! Best wishes!!

  8. Hi Eric,

    I know this post is from years ago, but I was hoping to use an annual index of VAR for an academic project. Do you have a .csv or something similar of the yearly values of your S&P VAR index? If you’d rather not share, I completely understand.

    Best,

    browntown

    September 1, 2013 at 1:10 am


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