Dispersion Trading on the Dow Jones Industrial Average

OutlineI- Dispersion strategy is based on implied vs realized correlation

II- A study of a ‘naïve’ strategy on the DJI from 2000 to 2005

III- Two other improvements

IV- An improvement of the naïve strategy: Component selection

V- Implementing a timing strategy

I – What is dispersion trading ?

What is Dispersion Trading?

Dispersion trading involves trading the volatility of an index against that of the index’s components

It involves making a bet on whether the components will move together as a unit or ‘disperse’ and move separately

We can replicate the index IV with its components IV

• Use each component IV:

Correlation Weighted Component Vol matches actual DJX Implied Vols

Implied Correlation

• We can use the implied volatilities of the index and it’s components to derive a measure of average correlation

More Implied Correlations

• As expected, the implied correlation is less volatile when longer lookback periods are used

We observe that the realized correlation of the index is less than its implied correlation.The index straddles might therefore seem overpriced

Correlation on the DOW seems overestimated

How can we earn profits from this observation ?

II – A ‘naïve’ strategy on the DOW

Naïve Strategy

• Each month, sell index volatility, buy component volatility: Short Correlation• Executed using ATM front month straddles

– Professionals sometimes use variance swaps instead• Take a gross exposure of $100 at the beginning of each month• Studied using (1) the MBBO price and (2) the bid-ask spread

A Naïve dispersion strategy seems profitable

Naive Strategy Cumulative Returns, MBBO

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What happens when we take Bid/Ask into account ?

Bid/Ask spread lowers profit

Naive Strategy Cumulative Return

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Bid Ask Spread MBBO

• It is possible that, after the stock market crash following 9/11, the market players learned to better price index volatility and to better forecast the correlation amongst component stocks.

Profitability is reduced after the volatility surge following 9/11

1/2000-10/11 10/11-6/2005StdDev of Returns 1.1680275 1.145478Avg Returns 23.884% 4.762%Sharp Ratio 4.0895931 1.774507

Before and After the Volatility Spike of 9/11

Naive Strategy Cumulative Return

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Bid Ask Spread MBBO

III – Two possible strategy improvements

We tested the enhancement of following a delta-neutral strategy

• The dispersion position's delta exposure to stock ‘i’ …

• The return of the daily delta-hedged dispersion strategy (VT: Payoff Vt: Cost of the straddle) …

Refinement: Delta-Neutral Strategy

Delta Hedge the delta positions of straddles daily (assuming no Transaction Costs)

• With delta hedging, the average monthly return decreases while the Sharpe ratio goes up slightly.

• Performance Comparison Against Base Case

No Transc. CostsStdDev of Returns 2.2415 1.7878Avg Returns 7.918% 10.940%Sharp Ratio 3.921145 3.780734

With Delta Hedging Without Delta Hedging

Refinement: Delta-Neutral Strategy

• Buy cheapest individual options and write most expensive index options.

• i.e. Buy ATM individual straddles and sell OTM index strangles

Selling pricey strangles increases the average monthly return slightly, while the Sharpe ratio goes down a bit.

• Performance Comparison Against Base Case

Refinement: OTM Index Strangles

StdDev of Returns 2.8833 1.7878Avg Returns 11.318% 10.940%Sharp Ratio 3.5801 3.7807

With ATM StraddlesWith OTM Index Strangles

IV- Selecting a subset of the components with PCA

How do we reduce the number of components in the strategy?

30 components in the Dow Jones: High trading costs

PCA can determine the components that explain most of the index variance

• Principal Components Analysis is a 3 step method (Su, 2005):– Step 1 : Write the weighted covariance matrix over the previous 1 year data

– Step 2: Find the Principal Components: Eigenvectors of the diagonalized matrix

– Step 3: Run a multiple correlation to find how many original components to keep at each trading date

Each month we choose a subset of 10-13 stocks of the DOW that best explains 80% of the variance

On average 10 DJI components explain more than 80% of the variance

PCA vs Naive - MBBO prices

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Naive PCA

Without trading costs, PCA strategy is less effective than Naïve strategy

With trading costs, PCA selection has better results than Naive

PCA vs Naive - $0.15/contract

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PCA vs Naive - $0.45/contract

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Still, profits stop increasing after 2002:A timing strategy is needed

• The higher the transaction cost, the better the relative performance of the PCA selection strategy:

V- Implementing a conditioning strategy

The Timing of the Dispersion Trade

Potential indicators :• Realized Values: Calculated on the basis of historical market data,

e.g. values of historical volatility, observed correlations between stock prices .

• Implied Values: Values implied by the option prices observed on the current day in the market.

• Theoretical Values: Calculated on the basis of portfolio theory.

Conditioning Strategy

• Goal: Find a signal to go long/short correlation that provides better results than the naïve strategy.

• Idea: Compare 30 day implied correlation to its 3 month moving average.

– Short correlation when significantly above 3 month MA: We expect correlation to go down

– Long correlation when significantly below We expect correlation to go up

30 Day Implied Correl. vs. 3 Month Moving Average

Short correlation

Long correlation

Strategy Details

• Initiate short correlation Position (short index vol, long component vol) when correlation/MA > 1.4

• Initiate long correlation position when correlation/MA < 0.8

• Always have a position on

The ratio of implied correlation to its 3 month MA seems to mean revert

Strategy ResultsCumulative Returns for Trading Strategy vs Naive Strategy

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Strategy Naive

The strategy makes some good calls,some bad ones. Total returns are

about the same

Strategy ResultsCumulative Returns for Trading Strategy with PCA vs. Naive PCA

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PCA Trading Strategy PCA Naive

Success! Using PCA, the strategy outperforms the Naïve PCA

Conclusions

• Dispersion trading on the DOW seemed a very easy and profitable strategy until 9/11

• After 9/11, a clever conditional strategy is needed to keep making profits

• Delta Hedging reduces the variance and increases the Sharpe ratio

• Selling index strangles rather than straddles increases returns but reduces the Sharpe ratio

• We can use PCA to replicate the returns with lower trading costs

• Our timing idea produced mediocre results, but when combined with PCA, was surprisingly effective