Sparse Signals in the Cross-Section of Returns Alex Chinco, Adam D. - - PowerPoint PPT Presentation

Sparse Signals in the Cross-Section of Returns

Alex Chinco, Adam D. Clark-Joseph, and Mao Ye

University of Illinois at Urbana-Champaign January 5th, 2016

Canonical Problem: Find an x that forecasts returns.

Canonical Problem: Find an x that forecasts returns.

Canonical Problem: Find an x that forecasts returns.

Canonical Problem: Find an x that forecasts returns.

Step 1: Use intuition to identify x. Step 2: Use statistics to estimate x’s quality rn,t = ˆ θ0 + ˆ θ1 · xt−1 + ǫn,t x is a good predictor if |ˆ θ1| or R2 is big.

Lagged returns of Family Dollar were a significant predictor for more than 20% of all NYSE-listed oil and gas stocks during 20-minute stretch on October 6th, 2010.

Lagged returns of Family Dollar were a significant predictor for more than 20% of all NYSE-listed oil and gas stocks during 20-minute stretch on October 6th, 2010. Goal: Use statistics

(the LASSO) to both identify and estimate x.

Slogan: LASSO to identify and estimate x.

• 1. Out-of-sample predictability
• 2. Trading-strategy returns
• 3. Evidence of sparsity
• 4. More than just news
• 5. Economic implications

how does it work?

Want: Tool to identify and estimate largest coefficients. LASSO is OLS holding hands with a penalty function: min

ϑ

   1 2 · T ·

T

• t=1
• rn,t − ϑ0 −

N

• n′=1

ϑn′ · rn′,t−1

• 2

+ λ ·

N

• n′=1

|ϑn′|   

ˆ θn′ ˆ ϑn′ λ

To identify means to ignore small OLS coefs ˆ ϑn′ = sgn[ˆ θn′] · (|ˆ θn′| − λ)+

• ut-of-sample

predictability

Benchmark: Fit AR model using OLS in 30-min windows. Make out-of-sample forecast in 31st min, f OLS

n,t .

Run 1 reg. per (stock, month) to assess out-of-sample fit: rn,t+1 = ˜ an + ˜ bn · fOLS

n,t −µOLS n

σOLS

n

• + en,t+1

Benchmark: Fit AR model using OLS in 30-min windows. Make out-of-sample forecast in 31st min, f OLS

n,t .

Run 1 reg. per (stock, month) to assess out-of-sample fit: rn,t+1 = ˜ an + ˜ bn · fOLS

n,t −µOLS n

σOLS

n

• + en,t+1

Out-of-Sample Return Predictability Const ˜ an 0.01×10−4

(19.42)

0.01×10−4

(19.42)

0.01×10−4

(19.42)

OLS ˜ bn 3.57×10−4

(140.59)

3.00×10−4

(136.06)

LASSO ˜ cn 3.17×10−4

(166.77)

2.40×10−4

(175.02)

• Adj. R2

5.43% 4.56% 8.08%

The LASSO: Fit the LASSO using same 30-min windows. Make out-of-sample forecast in 31st min, f LASSO

n,t

. Run 1 reg. per (stock, month) to assess out-of-sample fit: rn,t+1 = ˜ an + ˜ cn · fLASSO

n,t

−µLASSO

n

σLASSO

n

• + en,t+1

The LASSO: Fit the LASSO using same 30-min windows. Make out-of-sample forecast in 31st min, f LASSO

n,t

. Run 1 reg. per (stock, month) to assess out-of-sample fit: rn,t+1 = ˜ an + ˜ cn · fLASSO

n,t

−µLASSO

n

σLASSO

n

• + en,t+1

Out-of-Sample Return Predictability Const ˜ an 0.01×10−4

(19.42)

0.01×10−4

(19.42)

0.01×10−4

(19.42)

OLS ˜ bn 3.57×10−4

(140.59)

3.00×10−4

(136.06)

LASSO ˜ cn 3.17×10−4

(166.77)

2.40×10−4

(175.02)

• Adj. R2

5.43% 4.56% 8.08%

Result: Using the LASSO increases out-of-sample return predictability by factor of 8.08/

5.43 = 1.5!

rn,t+1 = ˜ an + ˜ bn · fOLS

n,t −µOLS n

σOLS

n

• + ˜

cn · fLASSO

n,t

−µLASSO

n

σLASSO

n

• + en,t+1

Out-of-Sample Return Predictability Const ˜ an 0.01×10−4

(19.42)

0.01×10−4

(19.42)

0.01×10−4

(19.42)

OLS ˜ bn 3.57×10−4

(140.59)

3.00×10−4

(136.06)

LASSO ˜ cn 3.17×10−4

(166.77)

2.40×10−4

(175.02)

• Adj. R2

5.43% 4.56% 8.08%

trading-strategy returns

Out-of-Sample Return Predictability Const ˜ an 0.01×10−4

(19.42)

0.01×10−4

(19.42)

0.01×10−4

(19.42)

OLS ˜ bn 3.57×10−4

(140.59)

3.00×10−4

(136.06)

LASSO ˜ cn 3.17×10−4

(166.77)

2.40×10−4

(175.02)

• Adj. R2

5.43% 4.56% 8.08%

TS Momentum: Ignoring look-ahead bias and trading costs, the LASSO generates monthly excess returns of (390 · 21) · 3.17×10−4 = 2.60% where ˜ cn is the return to a time-series momentum strategy ˜ cn = 1

T · T t=1

fLASSO

n,t

−µLASSO

n

σLASSO

n

• · rn,t+1

Out-of-Sample Return Predictability Const ˜ an 0.01×10−4

(19.42)

0.01×10−4

(19.42)

0.01×10−4

(19.42)

OLS ˜ bn 3.57×10−4

(140.59)

3.00×10−4

(136.06)

LASSO ˜ cn 3.17×10−4

(166.77)

2.40×10−4

(175.02)

• Adj. R2

5.43% 4.56% 8.08%

Result: LASSO-based strategy generates returns of 0.30% per month net of trading costs. Predictability matters. Trading-Strategy Returns No Spread NBBO rLASSO

n,t

• 2.82%

(128.47)

0.30%

(23.58)

evidence of sparsity

1 11 24 Oct 5th Oct 12th Oct 19th Oct 26th

Significant Predictors per Stock in October 2009

Result: LASSO typically uses only 11 predictors.

more than just news

Result: News announcements don’t reveal how information is going to propagate through the market. Use data from RavenPack.

#UsedByn,t isUsed n→m,t hasNewsn,t 0.65

(8.84)

0.01

(0.21)

hasNewsn,t × newsRelevancen,t 0.88

(10.69)

hasNewsn,t × newsImpactn,t 2.01

(13.20)

• Adj. R2

93.2% 94.1% 94.5% 14.2% Time FE

• Group FE

economic implications

1 s t 2 , 1 9 1 s t Oct 1st 4th5th 6 7 8 11 12 13 14 15 18 19 20 21 22 25 26 27 28 29Nov 1st ←− −→

Significant Predictors in October 2010

Implication: There is structure between factors and noise.

Slogan: LASSO to identify and estimate x.

• 1. Out-of-sample predictability
• 2. Trading-strategy returns
• 3. Evidence of sparsity
• 4. More than just news
• 5. Economic implications