BSE launches Realised Volatility Index

BSE has launched India's first Realised Volatility Index today in a bid to increase its (abysmal) equity derivatives volumes. You can download the PDF to view more about this here. BSE will lauch 1, 2 and 3 month futures and options contracts to trade in this RealVol Index.

First, let's understand what this is and how it can be used, followed by goof-ups:

What is Realized Volatility? How does it compare with VIX, which is already launched?

Realized Volatility is calculated from actual volatility of BSE Sensex. In contrast, Voltility Index (VIX), which is a measure of implied volatility in the market (as the market views it - it may incorporate the "fear factor" in the market, or swerve drastically with spikes / drops in call-money rates, which are referenced as borrowing rates for short term (1-2 days)). So unlike VIX, if market is very volatile, but closes near its previous close, the RealVol will either not be affected much or it'll go down to a certain extent.

How do Realized Volatility Futures / options help?

Realized Volatility provides traders with a tool to hedge their option values against volatility movements. As some of you might be knowing already, an Option price varies primarily with 3 parameters - Price of underlying, Volatility, and Time to expiry. So let's say if you've bought a Call option on Nifty (can't imagine anyone buying an option on Sensex due to poor liquidity), you should make profits if Nifty moves up. BUT, if the volatility of Nifty drops, or its taking too long to move up, (which it does finally), your option will still end up losing its value. So, higher volatilities / time add to option values and vice-versa.

Thus, for options traders, even if their view goes right, but volatility drops, they still end-up making losses. To avoid this, they can sell volatility futures / call option / buy put option and thus hedge their long call option position against volatility.

Goof-ups:

This idea is probably borrowed from CBOE, which is ok...but there are major issues in implementation. To understand this, first lets have a quick look at the comparison of similar products from BSE and CBOE.

(click on the image for a larger view)

• BSE is taking the average standard deviation formula into account, without doing (n-1) in the denominator ! Statistically speaking, you should average with 'n' if and only if, you are taking the entire data set (or population) into consideration for calculation. But if you are taking only a sample data from the bigger data set, you should take 'n-1' to account for degrees of freedom. This is an unacceptable error ! [Besides, taking average standard deviation is not a very good measure, its always better to use conditional volatility (EWMA, GARCH, etc.) for better accuracy...but more on this sometime later].
• A little digging reveals the reason why they are doing so...this is because they are resetting the value of n after every interval. It means that for calculating 1-month RealVol, lets say today is the first day of RealVol futures / options contract, they will take only 1 day volatility into account. On the 2nd day, they take the average of the last 2 days (including today's EOD Sensex value), on the 3rd day, average of last 3 days, and so on...till the 22nd day (last trading day, unlike calendar days which will be 30 at this stage), when they'll take average of last 22 days. And then bang ! Again the next 1 month starts with 1 day average !!! See example below to understand this better. 
  
  

  

  
  In this example, I've calculated 1 month RealVol (annualized) based on CBOE method and BSE method...and see the difference on the first couple of days...What this means is, if  day1 (second last row) is, say extremely volatile, (lets say Sensex tanked by 5%), then the first day RealVol value will be high, then if sensex closes at the same level next day, the RealVol will be nearly half of yesterday's value...! Such a drastic drop (30%) in value of RealVol in just 1 day, whereas if you actually see using the correct methodology (CBOE's), its not so drastic. People long on volatility futures / options on day 2 will most likely get stopped out...despite the fact that volatility did not really fall by that much...! CBOE, on the other hand, calculates RealVol on 22-day rolling window basis (for 1 month series), and so does not see large fluctuations at the beginning of the series.
  BSE's method of NOT taking rolling window is also the reason (perhaps) behind ignoring degrees of freedom (not taking 'n-1') in the denominator, as otherwise, on the first day the real vol figure will be undefined !

I hope you've got the picture...the intention is good, but as usual, the execution is poor. Even in nifty options, the volume are extremely poor for the 2nd and 3rd month series, so for BSE (with really poor liquidity in derivatives overall) RealVol series of 2nd and 3rd months most definitely will not be traded in near future. It just the 1st month which will see some action...but as soon as market realizes that the RealVol is not actually helping them in hedging their options, they'll forsake this instrument...and then BSE guys will wonder why the heck is their derivatives section not taking off...[By the way, futures and options are not fungible across exchanges, so if you buy Nifty options, and hedge using RealVol option on Sensex, though there is good correlation, its not a very good hedge anyways]

I hope someone in BSE is taking a note of this...and also in NSE...so that they'll not make the same mistake. Expect something similar from NSE soon.