This post was originally published on September 10th, 2007.  It has been republished from a previous version of the site.  Note that since this post was published, a number of VIX exchange-traded assets have hit the market.

As this past summer has seen a long-term regime change in the systemic market volatility, discussion of the VIX and other volatility indices has picked up dramatically.  Though volatility has been an issue many times in the past, however, one thing has changed since the last period of high volatility – more and more investors expect more and more complicated products to be tradeable in easier and easier ways.  For example, the ETF market has provided a large number of products specializing in commodities, bonds, and even inverses.  None of these are assets that are impossible or sometimes even difficult to trade, but in sum, there are hundreds of ETFs and CEFs new in the past 10 years that provide nothing but access to these holdings.

As we discuss volatility, though, there are a number of problems.  First, although the VIX is the most understood volatility proxy, its products are by no means the most liquid.  Secondly, the VIX is designed as an theoretical price, not an asset – this is advantageous in that it is quoted in units of the underlying asset, but volatility is much more expensive and difficult to hedge than variance.   This is obvious when one compares the liquidity of the variance swap market to any VIX-related derivatives, though somewhat confusing to the an outside investor who is told that they are merely related by squaring or square-rooting.

Having admitted that the variance swap market is very liquid, and that the two are related by such a simple mathematical operation, why then is a volatility ETF still so far away?  The problem is likely due to the fact that the reason outside investors want a volatility proxy is diametrically opposed to the safety of the ETF issuer.  When ETF investors discuss the VIX and their desire for such a product, they are not thinking of realizing the arbitrage profit between implied and future realized volatility – they’re thinking of realizing a hedge against the Poisson jump part of the Merton market model.  The problem is that these larger shocks are nearly impossible to hedge against without high expenses, and given the volatility of volatility in the market presently, such losses would likely sum to a figure that would have the ETF holders even more upset than various oil commodity ETF holders earlier this year.  Add to this the fact that nearly all products are OTC markets and the asymmetry of risk for buyer and seller in any risk market and you probably have those insurance and risk analysts putting up roadblocks left and right.

Don’t get me wrong, I am all for a volatility proxy ETF myself, and have even seen hits on this site originating from various ETF issuers on the very topic of replicating the VIX, but I’m not too optimistic in the short term for a product with a safe and sustainable structure.  While I’m out on the line making predictions though, let me add this last one as a hedge – if we do see a volatility-tracking ETF in the next 2 years, expect it to come with one of the top 5 expense ratios in the market.

This post was originally published on September 10, 2007. It was imported from a previous version of the site.

As this past summer has seen a long-term regime change in the systemic market volatility, discussion of the VIX and other volatility indices has picked up dramatically.  Though volatility has been an issue many times in the past, however, one thing has changed since the last period of high volatility – more and more investors expect more and more complicated products to be tradeable in easier and easier ways.  For example, the ETF market has provided a large number of products specializing in commodities, bonds, and even inverses.  None of these are assets that are impossible or sometimes even difficult to trade, but in sum, there are hundreds of ETFs and CEFs new in the past 10 years that provide nothing but access to these holdings.

As we discuss volatility, though, there are a number of problems.  First, although the VIX is the most understood volatility proxy, its products are by no means the most liquid.  Secondly, the VIX is designed as an theoretical price, not an asset – this is advantageous in that it is quoted in units of the underlying asset, but volatility is much more expensive and difficult to hedge than variance.   This is obvious when one compares the liquidity of the variance swap market to any VIX-related derivatives, though somewhat confusing to the an outside investor who is told that they are merely related by squaring or square-rooting.

Having admitted that the variance swap market is very liquid, and that the two are related by such a simple mathematical operation, why then is a volatility ETF still so far away?  The problem is likely due to the fact that the reason outside investors want a volatility proxy is diametrically opposed to the safety of the ETF issuer.  When ETF investors discuss the VIX and their desire for such a product, they are not thinking of realizing the arbitrage profit between implied and future realized volatility – they’re thinking of realizing a hedge against the Poisson jump part of the Merton market model.  The problem is that these larger shocks are nearly impossible to hedge against without high expenses, and given the volatility of volatility in the market presently, such losses would likely sum to a figure that would have the ETF holders even more upset than various oil commodity ETF holders earlier this year.  Add to this the fact that nearly all products are OTC markets and the asymmetry of risk for buyer and seller in any risk market and you probably have those insurance and risk analysts putting up roadblocks left and right.

Don’t get me wrong, I am all for a volatility proxy ETF myself, and have even seen hits on this site originating from various ETF issuers on the very topic of replicating the VIX, but I’m not too optimistic in the short term for a product with a safe and sustainable structure.  While I’m out on the line making predictions though, let me add this last one as a hedge – if we do see a volatility-tracking ETF in the next 2 years, expect it to come with one of the top 5 expense ratios in the market.

This post was originally published on September 3rd, 2007. It has been slightly modified from a previous version of the site.  N.B.: This code has been tested in Matlab R2009b and R2010a and still works fine.

Kaplan and Knowles, extending the original work of Shadwick and Keating as well as that of Kazemi, Schneeweis, and Gupta, describe a generalized downside risk-adjusted measure Kappa.  By design, the Omega and Sortino measures are special cases of the Kappa measure, and, as such, the Kappa function is capable of calculating both easily.

So that this very helpful function can be used by those in the community who are having difficulty with the original works, I am publishing a single-line Kappa function for Matlab.

% D : return series vector
% r : return threshold
% n : Kappa order
function k = kappa(D, r, n)
k = (mean(D) - r) ./ nthroot(mean((D < r) .* (r-D).^n), n);

To calculate the Omega measure, put n=1 and add 1 to the result, i.e. kappa(D, r, 1) + 1.

To calculate the Sortino ratio, put n=2, i.e. kappa(D,r,2).