Statistical Arbitrage, Enhanced Indexing and 130/30 Marco Avellaneda & Stanley J. Zhang Courant Institute, New York University Finance Concepts LLC Summary -- Overview of Statistical Arbitrage as an investment strategy -- Using ETFs as relative-value indicators -- Mean-reversion & the Ornstein-Uhlenbeck process -- Examples of trades -- Portfolio construction: the PLATA fund -- Synthetic 130/30 funds constructed from PLATA and Indices -- Comparison of PLATA+SP with 130/30 Mutual Funds and a 130/30 ETF -- Conclusions Statistical Arbitrage Trading strategy consisting of investing in long-short stocks (or another asset class) with a mean-reversion theme -- Pairs trading: practiced since the 1990s, invented by Morgan Stanley’s prop team -- ``Factor neutral’’ trading: generalizes pairs trading -- ETF relative-value trading: the subject of this presentation Idea: measure statistically a time-series of spread between two or more correlated stocks or indices and invest in overbought/undersold spreads. Trading Universe: Stocks of more than 1BB cap Market Cap unit: 1M/usd Sector ETF Num of Stocks Average Max Min Internet HHH 22 10,350 104,500 1,047 Real Estate IYR 87 4,789 47,030 1,059 Transportation IYT 46 4,575 49,910 1,089 Oil Exploration OIH 42 7,059 71,660 1,010 Regional Banks RKH 69 23,080 271,500 1,037 Retail RTH 60 13,290 198,200 1,022 Semiconductors SMH 55 7,303 117,300 1,033 Utilities UTH 75 7,320 41,890 1,049 Energy XLE 75 17,800 432,200 1,035 Financial XLF 210 9,960 187,600 1,000 Industrial XLI 141 10,770 391,400 1,034 Technology XLK 158 12,750 293,500 1,008 Consumer Staples XLP 61 17,730 204,500 1,016 Healthcare XLV 109 14,390 192,500 1,025 Consumer discretionary XLY 207 8,204 104,500 1,007 Total 1417 11,291 432,200 1,000 January, 2007 Using ETFs as relative value indicators: e.g. EBAY versus QQQQ Idea: rather than considering all stock pairs, which requires handling two specific risks per trade and a huge number of pairs, consider a stock and the sector ETF corresponding to its industry Pro: the relative analysis of a stock compared to its peers is done comparing with an index. We deal with one stock-specific risk at a time, not 2. Pro: the complexity of the signal generation is significantly reduced and the origin of excess returns is simple to explain Con: some large cap stocks track too closely the industry, so no signals are available. Equivalently, the strategy can be viewed as somewhat biased to small caps Con: Some stocks do not fit well the ETF identikit. We leave those to fundamental analysts. Modeling the Evolution of Stock Residuals ( ) ( ) dS t dI t ( ) Stock returns a sum of a multiple = β + ε i t ( ) ( ) of an ETF return and a residual process i i S t I t i Residual= drift component (expected ( ) ( ) ε = α + t dt dX t excess return above mkt.) + increment i i i of a stationary process ( ) ( ( )) ( ) Ornstein-Ulembeck = κ − +σ dX t m X t dt dW t AR-1 process i i i i i i Statistical Estimation Window=3 months (~ 60 business days) to include at least one earnings announcement Statistics on the Estimated OU Parameters ETF Abs(Alpha) Beta Kappa Reversion days EquiVol Abs(m) HHH 0.20% 0.69 38 7 4% 3.3% IYR 0.11% 0.90 39 6 2% 1.8% IYT 0.18% 0.97 41 6 4% 3.0% RKH 0.10% 0.98 39 6 2% 1.7% RTH 0.17% 1.02 39 6 3% 2.7% SMH 0.19% 1.01 40 6 4% 3.2% UTH 0.09% 0.81 42 6 2% 1.4% XLF 0.11% 0.83 42 6 2% 1.8% XLI 0.15% 1.15 42 6 3% 2.4% XLK 0.17% 1.03 42 6 3% 2.7% XLP 0.12% 1.01 42 6 2% 2.0% XLV 0.14% 1.05 38 7 3% 2.5% XLY 0.16% 1.03 39 6 3% 2.5% Total 0.15% 0.96 40 6 3% 2.4% Average over 2006-2007 Trading Signals We introduce an s-score for each stock: ( ) − X t m = s (t) i i i σ eq,i < − Open long position if s 1.25 i > + Open short position if s 1.25 i > − Close long position if s 0.50 i < + Close short position if s 0.50 i Schematic view of mean-reversion trading Sell stock here & hedge S_i Open short 1.25 0.50 Buy stock here & hedge t -0.50 -1.25 Open long S-score of JPM ( vs. XLF ) 3 2 1 0 -1 -2 -3