Statistical Arbitrage on US ETFs - Stanford University · 2020. 6. 3. · Statistical Arbitrage on...

Statistical Arbitrage on US ETFsMS&E 448 Final Presentation

Shane Barratt Russell Clarida Mert Esencan Francesco InsullaCole Kiersznowski Andrew Perry1

Stanford University

May 5, 2020

1Authors listed in alphabetical orderShane Barratt, Russell Clarida, Mert Esencan, Francesco Insulla, Cole Kiersznowski, Andrew Perry (Stanford University)Statistical Arbitrage May 5, 2020 1 / 24

Overview

1 Review of Project

2 Data

3 Trading Strategy

4 Results

5 Conclusion

6 Appendix

Shane Barratt, Russell Clarida, Mert Esencan, Francesco Insulla, Cole Kiersznowski, Andrew Perry (Stanford University)Statistical Arbitrage May 5, 2020 2 / 24

Review of Project

Background

Statistical arbitrage = short-term trading strategy that bets onmean-reversion of asset baskets (more later)

The intuition of statistical arbitrage is based on the idea that thedifference between what an equities’ price is and what it should be isdriven by idiosyncratic shocks

Statistical arbitrage requires 3 steps:1 Finding asset baskets2 Prediction based on mean-reversion3 Portfolio construction


Review of Project

Market–Neutral Investments

n assets, with prices pt ∈ Rn+ at time period t = 1, . . . ,T

Assume assets are hedged w.r.t. market, i.e., each asset is actually 1unit of the asset and −β units of the market, where β is thecorrelation of the market returns with the asset returns

Observation: Investing (long or short) in any of these assets ismarket-neutral


Data

TAQ data

21 ETFs: SPY, MDY, DIA, XLK, XLV, XLF, XLP, XLY, XLU, XLE,XLI, XLB, QQQ, IVV, IWB, IWF, IJH, IJR, IWN, IWD, IVW, IVE

Minute-level price data from NYSE TAQ WRDS for 2003-2020

1 million+ price points

Used Yahoo Finance API to get corporate actions and adjusted forsplits (ETFs do split!)


Data

TAQ data

20042006

20082010

20122014

20162018

2020

Date

0

50

100

150

200

250

300

350

400

price

Figure: Index Prices Over Time


Trading Strategy

Hedging each ETF

Each day, construct window of last 5 days

Compute correlation of each ETF’s returns with respect to SPY inwindow

Construct market-neutral basket for each ETF


Trading Strategy

Finding Pairs

Create asset basket for each of the 190 pairs via regression on window

0 250 500 750 1000 1250 1500 1750

0.3

0.2

0.1

0.0

0.1

0.2

0.3(1)IJH -(.63)IWD -(0.33)SPY

Figure: Example basket.

Hope that some of the 190 asset baskets are mean-reverting


Trading Strategy

Modeling Residual Returns

The residual returns are modeled with a Ornstein–Uhlenbeck (OU)process

The OU process is mean-reverting which satisfies the assumption thatprices return to basket means:

dXt = ρ(µ− Xt)dt + σdBt , ρ, σ > 0 (1)

where ρ is the speed of mean reversion, µ is the long run average, σis the instantaneous volatility, and Bt is a standard Brownian motion

We allow for the assumption that over a short trading period that ρ,µ, and σ stay constant


Trading Strategy

AR(1) Process

Constants ρ, µ, and σ in the OU model are calculated with a AR(1)process (Auto-Regressive with lag one).

An AR(1) process is given by

Xt+1 = λ+ φXt + εt (2)

The interpretation of λ, φ, and ε as it relates to the OU process is

λ = µ(1− e−ρδt)φ = e−ρδt

εt ∼ N(

0, σ2

2ρ (1− e−2ρδt)) (3)

We fit an AR(1) to all possible baskets.


Trading Strategy

Trading Signal

Now that we are able to model stocks as an OU process we need adimensionless trading signal

We will use the distance that Xt is from the mean µ. Giving us thesignal

st = Xt − µ (4)

We use a linear bet size on the strength of the signal to invest in eachbasket. This allows us to make returns as the signal returns to zero.


Trading Strategy

Trading

After we find the weights of each basket we can back out the weightson each of the ETFs

Go long low baskets

Go short high baskets

Leverage around 2-3

No TCs (major limitation)

Implemented in numpy w/ vectorized operations. Takes about 10minutes for full backtest


Results

Results

Sharpe 1.244

20082010

20122014

20162018

2020

1

2

3

4

5

6

7

Figure: Daily Returns of Statistical Arbitrage Strategy with NBER Recession BarsShane Barratt, Russell Clarida, Mert Esencan, Francesco Insulla, Cole Kiersznowski, Andrew Perry (Stanford University)Statistical Arbitrage May 5, 2020 13 / 24

Results

Drawdown

Max Drawdown 20%

20082010

20122014

20162018

2020

0.20

0.15

0.10

0.05

0.00

Figure: DrawdownShane Barratt, Russell Clarida, Mert Esencan, Francesco Insulla, Cole Kiersznowski, Andrew Perry (Stanford University)Statistical Arbitrage May 5, 2020 14 / 24

Results

Daily Returns Regressed on the VIX

10 20 30 40 50 60 70 80VIX

0.10

0.05

0.00

0.05

0.10

0.15

0.20

daily

retu

rn

Figure: Daily Returns Regressed on the VIX


Results

Daily Returns Regressed on the VVIX

60 80 100 120 140 160 180 200VVIX

0.10

0.05

0.00

0.05

0.10

0.15

0.20

daily

retu

rn

Figure: Daily Returns Regressed on the VVIX


Results

Daily Returns Regressed on SPY

0.10 0.05 0.00 0.05 0.10 0.15SPY return

0.10

0.05

0.00

0.05

0.10

0.15

0.20

stra

tegy

retu

rn

Figure: Daily Returns Regressed on SPY


Results

Daily Returns on Shuffled Data

0 200000 400000 600000 800000 1000000 1200000

0.8

0.9

1.0

1.1

1.2

Figure: Daily Returns on Shuffled Data


Conclusion

Conclusion

Much of the struggle in this process is data acquisition and pipelines.While we believe the result to be compelling, we also know thatstructuring strong back-testing frameworks, acquiring and storing newdata, and testing an array of signals is the minimum requirement for a statarb strategy to even begin to hope to be competitive.


Conclusion

Questions?


Conclusion

Thank You


Appendix

Appendix: A more complete approach

Given a subset of returns, to find the optimal weights, we canmaximize the “AR-ness”, instead of using residuals or regression.

Let Z = Xα

Assume Z ∼ AR(1)

Then Z = ρBZ + ε, ε ∼ N (0, σ20)

Regress ∆Z = δ︸︷︷︸ρ−1

BZ + ε

Get δ̂, σ2, σ20, se2(δ̂), t0 =δ̂

se(δ̂)

ADFuller: H0 ≡ δ = 0, p ≈ 2(1− Φ(t0))

α∗ = argmin1Tα=1

−t0


Appendix

Appendix: Comparison to naive approach

Figure: −t0 contour plot Figure: −t0 vs iteration


Appendix

Appendix: Across all pairs

Figure: −t0 for all pairs


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Statistical Arbitrage on US ETFs - Stanford University · 2020. 6. 3. · Statistical Arbitrage on...

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