Correlation Trading
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
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