Correlation Trading

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  • Topic: Variance swap, Correlation trading, Credit risk
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Equity Correlation Trading
Silverio Foresi and Adrien Vesval Goldman Sachs NYU, April 2006

Outline
• • • Equity Correlation: Definitions, Products and Trade Structures Rationale: Evidence and Models Opportunities: an Historical Perspective

Correlation Products

Building Blocks: Vol Products
• Realized variance:

RV


1 = n



T

t =1

St (ln( )) S t −1

2

OTC products to trade realized variance: – Delta-hedged options (straddles) – Volatility swap – Variance swap Listed Products – Futures on realized variance



Implied Correlation
• From index and single-stock implied vols, one can extract the average pairwise Implied Correlation (= IC) embedded in option prices by the market. Let FVV = Fair Value of Variance, then IC is



IC =

(∑i =1 wi FVVi ) − ∑i =1 wi FVVi
n 2 n 2

FVVIndex − ∑i =1 wi FVVi
n 2

Basic Trade Idea
• Mechanics: a dispersion trade consists of – selling vol on the index, while simultaneously – buying vols on the component Appeal: – historically index volatility has traded rich, while – individual stock volatility has been fairly priced – implied correlation has historically been above realized



Correlation Market “Anomaly”
Index = Eurostoxx
80% 70% 60% 50% 40% 30% 20% 10% 0%
/9 8 /0 0 /9 6 /9 3 /9 4 /0 2 /0 4 12 /1 /9 9 /9 2 /0 1 /9 7 /9 5 /0 3 12 /1 12 /1 12 /1 12 /1 12 /1 12 /1 12 /1 12 /1 12 /1 12 /1 12 /1 12 /1 12 /1 /0 5

Rolling 3-month realized correlation (forward looking) 1YR implied correlation Rolling 1-year realized correlation (forward looking)

Correlation Market “Anomaly”
Index = Dow Jones
140% 120% 100% 80% 60% 40% 20% 0%
10 /6 /9 2/ 7 6/ 9 6/ 8 6/ 1 0 98 /6 /9 2/ 8 6/ 9 6/ 9 6/ 1 0 99 /6 /9 2/ 9 6/ 0 6/ 0 6/ 1 0 00 /6 /0 2/ 0 6/ 0 6/ 1 6/ 10 01 /6 /0 2/ 1 6/ 0 6/ 2 6/ 10 02 /6 /0 2/ 2 6/ 0 6/ 3 6/ 03

Rolling 1-year realized correlation (frwd looking) 1-YR implied correlation

Correlation Trading: Products
• Correlation swaps: pay the difference between an implied correlation strike and the average pairwise correlation in a basket of stocks. Correl-swaps are not a natural hedge for dealers’ or structurers’ books, as theses books are mostly exposed to covariance risk. Delta-hedged straddles: sell index straddles, buy single-stock straddles. Delta-hedging a book of 50-100 options is expensive and complicated for a hedge fund. Index var-swaps against single-stock var-swaps: it is the most popular way to structure the trade over the last 2/3 years has been to trade. This structure fits broker-dealer books relatively well and is manageable from a hedge fund point of view as no delta-hedging is necessary.





Dispersion Trading: Var-swaps
• Sell a var-swap on an index, buy variance swaps on the individual components of the index. On the single stock side, vega notionals are typically proportional to index weights. By adjusting the ratio of index vega notional to stock vega notional, one can modify the return distribution profile of the portfolio. Most people like the trade “vega neutral” (sum of single stock vega notional = - index vega) or “premium neutral” (sum of variance notional * variance strikes on the index side = index variance notional * index variance strike). As the next 2 slides will show, a “premium neutral” trade is a good way to replicate a covariance exposure.







Vega-Neutral trade
Payoff Matrix (in $M, for a $1M index vega dispersion trade on DJIA,43% implied correlation) VOL RATIO Correlation
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 0.1 (4.09) (4.10) (4.10) (4.11) (4.12) (4.13) (4.14) (4.15) (4.16) (4.17) (4.18) (4.19) (4.19) (4.20) (4.21) (4.22) (4.23) (4.24) (4.25) (4.26) (4.27) 0.2 (3.74) (3.77) (3.81) (3.84) (3.88) (3.92) (3.95) (3.99) (4.02) (4.06) (4.10) (4.13) (4.17) (4.20) (4.24) (4.28) (4.31) (4.35) (4.39) (4.42) (4.46) 0.3 (3.15) (3.23) (3.31) (3.39) (3.48) (3.56) (3.64) (3.72) (3.80) (3.88) (3.96) (4.04)...
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