KOSPI Derivatives - A Recipe for Disaster?
May 05, 2005
Today it was reported in the Financial Times that Aman Capital Management, a hedge fund, has lost around $48 million since the beginning of this year. What is disturbing is that this represents almost 20% of the fund's assets under management and further, around $43 million of the above loss has been incurred in the month of April alone. The bulk of the losses, it seems, has come from the fund managers bet in derivatives based on the Korea Composite Stock Price Index (KOSPI).
We don't know what the exact derivative instruments were or how they were structured by the broker-dealer. They could be anything from simple call and put options or straddles and strangles to more sophisticated barrier options or volatility swaps. It is also unclear whether the fund managers were long or short these instruments.
But one thing is clear: the fund managers were victim to the volatility of the KOSPI index. Therefore, the million dollar question is, regardless of the derivative instruments that they were trading and regardless of their long and short positions on these instruments, overall were the fund managers long or short volatility? No matter how you dabble in the derivatives market in the end it all boils down to whether you are long (buy) or short (sell) volatility. No matter how big or how sophisticated your portfolio of derivatives (options, swaps, whatever) in the final analysis you are either long volatility or short volatility.
Let us then look at the volatility - or more accurately, the implied volatility - of the KOSPI (options). We analyse the implied volatility of KOSPI using our own proprietary volatility index for KOSPI.
KOSPI options, over the past one and half year have shown very high implied volatility, at least relative to other major equity indices in the world. This seems strange given the low volatility milieu that we are living in. What is even stranger is the volatility of this (implied) volatility of KOSPI is also high; in fact it is abnormally high.
Below is an analysis of our proprietary volatility index for the underlying KOSPI equity index. Our volatility index for KOSPI is called KIXX™ and we have plotted the KIXX™ for a 14 month period from 4th March 2004 to 4th May 2005.
Just to remind you that KIXX™ is an index of implied volatility of the underlying KOSPI equity index and it is calculated by us in a way that is very similar to the way the old VIX was calculated on S & P 100 index. KIXX™ is an end of the day measure of the 30 day implied volatility of an at the money (ATM) KOSPI option.
As the graph shows the KIXX™ itself has been quite volatile. The historical daily volatility of KIXX™ for the above time period is 7.46% an astronomically high number. This translates into 118.42% annualized volatility for the KIXX™. This daily volatility of KIXX™ is in a way the measure of volatility of volatility (what the option traders call VVOL) of the underlying KOSPI index; it is actually the volatility of the implied volatility of KOSPI because the KIXX™ is a measure of the implied volatility of KOSPI.
The distinguishing feature of the above graph - implied volatility index of KOSPI - is not that it has spiked up at times to close to the level of 50.00 but rather that even when the volatility index has been below 25, it has been displaying rapidly changing peaks and troughs.
The above number shows how volatile KOSPI has been and how rapidly the implied volatility of KOSPI has fluctuated. Is it then any surprise that anyone dabbling in KOSPI derivatives has to contend with such turbulence?
Traders associate fat tails with changing volatility. KOSPI has been displaying fat tails for a long time now. A changing volatility is a scary thing and vvol (volatility) measures the change in volatility (normally, vvol is calculated for historical volatility). If an asset displays very high volatility of volatility on a very small volatility then we get what is called a Pareto-Levy distribution. In the case of KOSPI we are getting a very high volatility of volatility on a very high volatility. Isn't this even scarier?
Well, in such a scenario what would an ace trader or a fund manager do? Would he ultimately buy or sell volatility? And to do so what derivative instruments (or products) he would use? Having bought (or sold) volatility how does he go about hedging his trades?
These questions, we leave it to the readers and some of you may be interested in discussing them on our online forum. But in the end one thing is clear. A high value of implied volatility of KOSPI (or for that matter any asset) is scary, but what is even scarier is a (very) high volatility of volatility of the index.
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