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Value at Risk for Algorithmic Trading Risk Management – Part I

30 pointsby shogunmikealmost 11 years ago

2 comments

cschmidtalmost 11 years ago
I&#x27;ve always preferred Conditional Value at Risk (CVaR) to regular VaR. While VaR is the 5% (say) value of loss, CVaR is the average of the loss of the bottom 5%. That way it captures the size of the tail risk.<p>The other really big advantage is that you can optimize over CVaR. You can formulate it in a linear program (LP), so you can maximize expected return subject to a limit on CVaR. [1] You can have several CVaR constraints at 1% and 5% say.<p>In contrast, VaR isn&#x27;t convex, and is difficult to optimize over.<p>[1] <a href="http://www.ise.ufl.edu/uryasev/publications/" rel="nofollow">http:&#x2F;&#x2F;www.ise.ufl.edu&#x2F;uryasev&#x2F;publications&#x2F;</a><p>Edit: there is an interesting presentation comparing CVaR and VaR by Stan Uryasev, the main academic that has worked on CVaR formulations here:<p><a href="http://www.ise.ufl.edu/uryasev/files/2011/11/VaR_vs_CVaR_CARISMA_conference_2010.pdf" rel="nofollow">http:&#x2F;&#x2F;www.ise.ufl.edu&#x2F;uryasev&#x2F;files&#x2F;2011&#x2F;11&#x2F;VaR_vs_CVaR_CAR...</a>
josephlordalmost 11 years ago
The article does mention the downsides but doesn&#x27;t really cover how devastating they can be. VaR was the common calculation persuading the banks that everything was nice and safe in 2007 and 2008.<p>From the article<p><i>VaR does not discuss the magnitude of the expected loss beyond the value of VaR, i.e. it will tell us that we are likely to see a loss exceeding a value, but not how much it exceeds it.<p>It does not take into account extreme events, but only typical market conditions.<p>Since it uses historical data (it is rearward-looking) it will not take into account future market regime shifts that can change volatilities and correlations of assets.</i>
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