**Amid increased volatility and broader market uncertainty, investors are looking for strategies with a track record for generating strong risk-adjusted returns. What if there were strategies that could mostly generate risk free and hedged returns through the year of between 15% to 30% per annum?**

Well, there is one! Called Dispersion Trading or Volatility Arbitrage, the derivatives desk at Prabhudas Lilladher has introduced a strategy that can remove the risk out of equity volatility for us common folk!

**Introduction**

Existing since the early 2000s, driven by the demand of hedge funds and coupled with the emergence of OTC volatility trading products such as “volatility” , “variance” swaps and “corridor variance” swaps, volatility spreading and **dispersion strategy** have become increasingly popular over the years and now trade in significant size between investment banks and their clients (e.g. a 10M USD ticket is common in the US).

One knows that Option prices contain important information regarding the market’s perception of future risks. The implied probability calculated using option prices across strikes and maturities – referred to as the volatility surface – for a given stock or index, provides relevant insight about the **aggregate expectation** of market participants about its future volatility. Interestingly, options on equity indices enclose **even more valuable information.**

Using market prices on index options **in combination with** option prices of the constituent stocks of the index, one can gain insights into implied correlation, a measure of how the market sees the relative movement of stocks versus each other and then trade it- referred to as **dispersion trading**.

**Basics First**

Lets start with a common man example first- arbitrage. Since we all know what this is , we must also know that arbitrage in essence is risk free – and that it can consistently generate profits. However, plain arbitrage is no longer attractive enough and therefore, fund managers and derivatives desks have continually evolved to look at new ways of arbitrage!

Thats where volatility arbitrage comes in! Since its a more complex arbitrage, there are opportunities – as not many may do this. Plus it requires some complex jugglery in timing the trade – so not all can make easy money either.

**Introducing Dispersion Trading**

Dispersion trading is a volatility based strategy seeking to profit from difference in implied volatility between similar instruments. Dispersion trading is built on an idea that the index options are one type of instrument and single stock options are the other- and that their volatility should ideally be similar – (*but normally isnt)* till expiry.

Since the index is constructed using a portfolio of underlying instruments , it could be viewed as a collection of stock options and can be replicated as such with options on all stocks in the **weights** corresponding to the index. In an efficient market the price of the index option and the portfolio of single stock options *should then be the same.* Interestingly it has been observed that this is not so.

And thats where the arbitrage comes in!

This give rise to a trading opportunity since it is possible to sell / buy expensive index options and then buy/sell a cheaper portfolio of single stock options, which is what dispersion trading is all about.

Remember however that the dispersion of an index is a measure of the collective behaviour of its components’ returns around their mean- This concept is strongly related to correlation: for given volatilities of components, the lower the overall correlation between them, the higher the dispersion of the index (and lower the index volatility).

**Cheap?**

In our context, expensive means in *relation to implied volatility* – deciding which IVs are diverging from their fair value and then taking a call on which to sell and which to buy.

Unfortunately dispersion trading is not as easy as this sound. Several conditions complicate and limit the possibility to trade on the mispricing.

The most important of these is the difference between expected and realised correlation on the index – which could result in losses and reduce the returns.

Naturally, correlation and dispersion are at opposite ends: the **higher the correlation between the index components the lower the dispersion and vice versa.**

**Typical Trade**

The two most popular types of dispersion trades are *vanilla dispersions*, based on vanilla options (typically straddles), and *variance dispersions*, based on variance swaps. **Dont worry about the terms** – but you of course need to know what a straddle is – basically the buying and selling of a call and put option at the same strike and at the money (ATM).

Since the underlying trade needs to be **market neutral,** we would do a straddle on the underlying index (example Short Bank Nifty Straddle July 2019) as well as the opposite straddle on the individual stock options (LongHDFC Bank Straddle July 2019, Long ICICI Bank Straddle July 2019 etc) in the weightages that they have on the index so that the overall trades on both long and short side have the same size.

Since both sides are similar in nature, the main way in which there can be arbitrage is if one of them is mispriced or gives sudden opportunities due to large market moves.

Now in the above Bank Nifty example, two scenarios may unfold:

**Case 1: High dispersion**

Let’s take a case where over a 1-month period stock A drops 10% and stock B rallies 10%. What happens to the index during this period? Answer: it ends up unchanged.

Now let us consider the following sample trade. At the beginning of the period, the trader: • Buys 0.5 notional units of at-the-money straddle on stock A for 5%, and • Buys 0.5 notional units of at-the-money straddle on stock B for 12%, and • Sells 1 notional unit of at-the-money straddle on the index for 6%

What is the P&L of this trade at the end of the period?

0.5 * (Stock A move of 10% – cost of 5% of the straddle A) + 0.5 * (Stock B move of 10% – cost of 12% cost of straddle B) – (Index move of 0% – cost of 6% straddle IDX) =** +7.5%**

What happened? The fact that the stocks returns are dispersed allows the trader to collect the premium of the short straddle position on the index (which does not move due to stock dispersion), while the stocks having moved (up and down) during the period pay part or the entirety of the premium spent on the straddles he/she purchased.

Now let us take a case where the price of the straddles on the stock and index are the same, but both stock A and B rally by 10% during the period. What happens to the index during this period? Answer: it rallies by 10% , the same amount of the stocks.

We will do the same trade, sell the index straddle to buy ½ unit each of straddles on stock A and B. The only thing that has changed compared to the previous example is the return on stock A – now fully correlated with stock B – and as a result the return on the index, is now 10% instead of 0%.

What is the P&L of this trade at the end of the period? 0.5 * (Stock A move of 10% – cost of 5% of the straddle A) + 0.5 * (Stock B move of 10% – cost of 12% cost of straddle B) – (Index move of 10% – cost of 6% straddle IDX) = –**3.5%**

What happened? The fact that the stocks returns are correlated results in an equally important move in the index. The loss on the short straddle position in the index superseded the overall gains on long straddle positions on stocks.

**Impact of Correlation**

Since correlation has a major impact on profitability, our desks continually look at potential scenarios to decide potential returns from the strategy before entering a trade.

The correlation among the securities are used as a factor to determine the entry of a trade. Depending on the value of correlation between individual stocks, the dispersion can be traded by selling the index options and buying options on index components or by buying index options and selling options on index components.

**In Conclusion**

Dispersion trading is complex strategy however this is rewarded with the strategy being a profitable one which offers high rewards in response to a low risk. Trading at times where volatility is high (viz. quarterly results, individual stock news etc) when the correlation would not be strong may result in more profit.

**PL Derivatives : Dispersion Strategies**

PL Desk advises its clients on such strategies and initiates these around expiry time each month. The Bank Nifty is typically preferred due to its lower number of stocks as well as correlations inherent in the index and has proven to generate substantially attractive risk adjusted returns over the past 18 years and 2019 has proven to be extremely profitable (*performance can be shared in person*).

The only limitation however is that the creation of a market neutral strategy for a client would require a margin of about Rs 1.5 cr or so at the minimum as only that can one buy the entire portfolio of stock options in the same proportion as the index.The returns however are substantial and therefore such a commitment would be justifiable especially as the product also has fairly low number of trades and thus transaction costs.

The ideal time horizon for a client is advised at between 12 to 18 months to let the laws of probability play out on the capital.

One also has the opportunity to talk to our desks to customise indices or straddles in line with personal views on expected correlation.

So if you are interested in creating this strategy for your portfolio, email us at **tea@plindia.com** or call us at **022-66322479** for a personal meeting with our derivatives team so we can Show You The Money!