predicting the equity premium with implied volatility spreadspredicting the equity premium with...

Predicting the Equity Premium withImplied Volatility Spreads

Charles Cao†, Timothy Simin†, and Han Xiao‡

† Department of Finance, Smeal College of Business, Penn State University‡ Department of Economics, Penn State University

March 23, 2018

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Motivation and Research Questions

Stock return predictabilty is an important question in asset pricing

literature (uncondtional and conditional)

Conventional predictiors are based on backward-looking information

I Dividend yield, P/E, Book-to-market ratio, term spread, etc

Question

I What is the predictive ability of forward-looking information of options?

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Motivation and Research Questions

Can the call-put option implied volatility spread (CPIVS) predict the

aggregate market risk premium?

Can we improve the performance of conditional factor models by

incorporating CPIVS?

Why does CPIVS have predictive power?

Does CPIVS predict non-equity variables?

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Motivation and Research Questions

Many reasons to investigate predictive ability of CPIVS

Theory

I Chowdhry and Nanda (1991), Easley, O’Hara, and Srinivas (1998):

Informed traders chose option market first

I An, Ang, Bali, and Cakici (2014): Noisy rational expectations model of

informed trading in both markets ⇒ option volatilities can predict

stock returns

Empirical work

I Option market information: price, volume and volatility

I Information Content of Option Implied Volatility Spread

I Nonlinear risks

I Cross sectional predictability

I Time-series prediction

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Literature Review

Information Content of Option Implied Volatility Spread

I Doran, Fodor, and Jiang (2013), Christoffersen, Jacobs, and Chang

(2013), Cao, Gempeshaw, and Simin (2018)

Nonlinear risks

I Bollerslev and Todorov (2011), Kelly and Jiang (2014)

Cross sectional evidence

I Bali and Hovakimian (2009), Cremers and Weinbaum (2010), Xing,

Zhang and Zhao (2010) and An, Ang, Bali and Cakici (2014)

Time-series prediction

I Atilgan, Bali and Demirtas (2015), Cao, Gempeshaw, and Simin (2018)

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Motivation and Research Questions

We consider a quarterly horizon:

Options are 3-month contracts

Longer horizon prediction: market timing, transaction costs, and

bid-ask spread

Lower autocorrelation: less spurious regression bias

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Main results

CPIVS predicts

I Quarterly aggregate market returns in-sample and out-of-sample

F In-sample R2: 14.7%!

F Out-of-sample R2: 8.5% (29% during recessions!)

I Long-run in-sample prediction up to three years

CPIVS improves the conditional factor models

I 50% less pricing errors

Prediction power comes from

I Forward-looking information orthogonal to other predictors

I Net innovation between call option and put option implied volatility

Economic significance of our results

I Ability to forecast macroeconomic uncertainty

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Data and Methodology

Mkt risk premium = CRSP value-weighted excess market return

CPIVS: difference between call and put option implied volatility

CPIVSt = CVOLt − PVOLt

I OptionMetrics (1996 - 2016)

I At-the-Market (ATM) Option Implied volatility

I Delta: 0.5

I Days-to-expiration: 30 days

I Quarterly average of daily spread

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Data and Methodology

Other predictors: Goyal and Welch (2008)

Focus on Dividend Yield and Cay

Fundamental valuations:

I Logarithm of dividend-yield ratio (log(DY ))

Macroeconomic indicators

I Consumption-to-wealth ratio (Cay)

Kitchen Sink: stack all variables

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Data: Descriptive Statistics

Mean Std. Dev. ρ

Equity Premium 0.015 0.085 0.091

Equal Weighted CPIVS -0.008 0.010 0.159

Value Weighted CPIVS -0.006 0.076 0.168

log(DY) -4.008 0.216 0.915

Cay -0.006 0.022 0.882

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Time Series of CPIVS and Equity Premium

-0.06

-0.04

-0.02

0

0.02

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 2016

CP

IVS

Eq

uit

y P

rem

ium

Equity Premium CPIVS

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Time Series of CPIVS and Log(DY)

-0.06

-0.04

-0.02

0

0.02

-4.6

-4.4

-4.2

-4

-3.8

-3.6

-3.4

1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 2016

CP

IVS

Lo

g D

ivid

end

Yie

ld

log(DY) CPIVS

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Methodology

In-sample Prediction

OLS prediction for one-quarter, semiannual, and one-year ahead

aggregate market returns

rt+h = αi ,h + βi ,hXi ,t + εi ,t+h

where

I h = 1 (quarterly), 2 (semiannually), and 4 (annually)

I X represents individual predictors

I Newey-West and Hodrick standard errors

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Methodology

Out-of-sample Prediction

1 Compare predictor with the historical average

2 Mean Square Forecast Error (MSFE)

I Is one-step ahead forecast error using our predictors smaller than

forecast using historical average?

3 Utility Gain

I Do investors see any utility gains using the predictors?

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Methodology

Out-of-sample Prediction: MSFE and R2OS

Predictors (Xi ) Historical Average (X0)

One-step Forecast ri ,t+s r0,t+s

Forecast error ei ,t+s = rt+s − ri ,t+s e0,t+s = rt+s − r0,t+s

MSFE MSFE 2i = 1

S

∑Ss=1 e

2i ,t+s MSFE 2

0 = 1S

∑Ss=1 e

20,t+s

Statistics R2OS = 1− MSFEi

MSFE0

Evaluation If R2OS > 0, then MSFEi < MSFE0 ⇒

Predictor beats historical average

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Out-of-sample Prediction: Utility Gains

For a quadratic utility investor, the optimal weight in the market is

w =(

1γ

)(E(rm)σ2rm

)Setting γ = 5, compute utility gains from using CPIVS as follows:

At each period t,

I σ2 = trailing sample variance of the market,

I w0 uses E (rm) = sample average, w1 uses E (rm) = E (rm|CPIVS).

I Keep the returns from rc = (1− w)rf + wrm using the two w ’s

At time T

I Calculate utility using mean and variance of the two portfolios

I Utility gain = U(rc |CPIVS)− U(rc)

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Empirical Results: In-sample Prediction

h = 1 (quarter) h = 2 (semiannual) h = 4 (annual)CPIVS 3.58 2.00 1.05

(4.12) (3.14) (2.04)

log(DY) 0.10 0.11 0.11(2.18) (2.75) (4.01)

Cay 0.21 0.38 0.48(0.68) (1.22) (1.28)

R2(%) 14.7 5.7 -1.0 7.7 11.8 0.2 3.1 22.3 2.4

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Empirical Results: Out-of-sample Prediction

Overall Expansion Recession

R2OS U-Gain R2

OS U-Gain R2OS U-Gain

CPIVS 8.48∗∗ 6.31 -7.11 2.15 29.02∗∗ 21.67

(0.01) (0.11) (0.01)

log(DY) 3.00 1.13 14.63∗∗∗ 5.16 -12.32 -14.53

(0.10) (0.00) (0.77)

Cay -5.27 2.05 -20.08 -2.21 14.24∗∗∗ 17.92

(0.31) (0.79) (0.00)

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Empirical Results: Out-of-sample Prediction

Robustness

Test the predictability of CPIVS on the following portfolios

Size, operating profitability, and investment-to-asset

I up to 90% out-of-sample significance (29/32)

Industry portfolios

I up to 90% out-of-sample significance (15/17)

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Empirical Results: Conditional Asset Pricing Models

Incorporate the information from CPIVS, log(DY) and Cay into conditionalversions of AP model

Intuition

Log(DY) and CPIVS predict at different segments of business cycle

Cover equity market, option market, and overall economy information

Time-varying moments may help model

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Empirical Results: Conditional Asset Pricing Models

The generic conditional asset pricing is

Et(rt+1|Zt) = α(Zt) + β(Zt)Et(Ft+1|Zt)

where

I Zt = lagged instruments = {log(DY )t , Cayt , CPIVSt}

Three versions:

I α fixed, β = b0 + b1Zt ;

I α = a0 + a1Zt , β = b0 + b1Zt ;

I α fixed, β fixed, Et(Ft+1|Zt) = d0 + d1Zt

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Empirical Results: Conditional Asset Pricing Models

Operating profitability portfolios: Annual abnormal return (%)

U-FF3 β(Z ) α(Z ), β(Z ) F(Z)

LOW -6.69∗∗∗ -3.66∗∗ -5.51∗∗ -6.04∗∗∗

D2 -3.44∗∗∗ -4.30∗∗∗ -3.72∗∗∗ -2.41D3 -2.45∗ -1.86 -0.80 -0.96D4 0.26 0.22 0.26 0.60D5 -1.70 -0.82 -0.86 -2.88∗∗

D6 0.11 0.69 0.99 -0.36D7 -0.51 -0.45 -0.04 -1.36D8 3.00∗∗∗ 1.76∗∗∗ 2.87∗∗∗ 2.24∗∗

D9 2.51∗∗∗ 1.77 1.44 1.44HIGH 2.24∗∗ 0.59 -0.16 2.96∗∗∗

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Empirical Results

The Source of Prediction

1 CPIVS contains forward-looking information not captured by

backward-looking predictors

2 CPIVS captures the net innovation between call and put option

implied volatility

3 CPIVS can predict innovation in discount rate and cash flow

4 CPIVS predicts macroeconomic uncertainty

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Empirical Results: Two-step Orthogonality

Method:

Step 1 Predictor i : obtain the residual εi ,t+1 from

rt+1 = αi + βiXi ,t + εi ,t+1

Step 2 Predictor j : Regress the residual εi ,t+1 on other predictors

Xj ,t , j 6= i ,

εi ,t+1 = δj + γjXj ,t + µj ,t+1, j 6= i

Evaluation: If γj is significant, then the predictor j contains further

information than predictor i .

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Empirical Evidence: Two-step Orthogonality

Standardize the predictors: comparable coefficients

i = CPIVS i = log(DY)

βlog(DY ) R2

β(CPIVS) R2

0.22∗ 3.5% 0.37∗∗∗ 12.5%

(1.81) (3.20)

i = CPIVS i = Cay

βCay R2

β(CPIVS) R2

0.16∗ 1.1% 0.41∗∗∗ 15.8%

(1.82) (4.34)

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Empirical Evidence: Net Innovation

Intuition

Innovation predicts returns

Innovation in both options

I ∆CVOL: capture innovation in calls

I ∆PVOL: capture innovation in puts

I CPIVS : approximately the difference between calls and puts

Call-put parity: the difference between calls and puts

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Empirical Evidence: Net Innovation

Information from Call and Put Options

Overall RecessionR2OS U-Gain R2

OS U-Gain

CPIVS 8.48∗∗∗ 6.31 29.02∗∗∗ 21.67(0.01) (0.01)

∆CVOL 31.93∗∗∗ 6.03 27.89 7.86(0.01) (0.10)

∆PVOL 26.36∗∗∗ 5.64 20.21 6.32(0.01) (0.15)

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Empirical Results: Campbell and Shiller Decomposition

Decompose market returns into three components:

I Expected returns, Cash flow, and Discount rate

Determine which component is being predicted by CPIVS

Method:Campbell(1991) and Campbell and Ammer(1993)

Step 1: Use VAR to estimate innovations representing each

component

Step 2: Regress each innovation on CPIVS and compare coefficients

Evaluation: significance and magnitude

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Empirical Results: Decomposition

Standardize the predictors:

Panel A: Predictive Regression: rβCPIVS 0.034∗∗∗

(4.118)

Panel B: VAR residual using {log(DP)}Expected Return Cash Flow Discounted Rate

βCPIVS 0.004 0.006∗∗ −0.024∗∗∗

(1.35) (2.45) (-2.81)

Panel C: VAR residual using {log(DP), log(DY), Cay}Expected Return inn Cash Flow inn Discounted Rate inn

βCPIVS 0.003 0.020∗∗∗ -0.012(0.80) (4.89) (-1.07)

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Empirical Results: What else does CVIPS predict?

Macro Uncertainty is defined as Jurado, Ludvigson, and Ng (2015)

Macroeconomic uncertainty is related to market returns

CPIVS predicts macroeconomic uncertainty

Regression model:

Macro Uncertaintyt+h = αi + βiXi ,t + εi ,t+h

where h = 1 (one-quarter ahead), (h = 2) (two quarters ahean)

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Empirical Results: Macro Uncertainty

1Q ahead Macro-U 2Q ahead Macro-U

CPIVS -3.40∗∗∗ -3.48∗∗∗

(2.62) (-2.68)

log(DY) 0.04 0.03(0.52) (0.32)

Cay 0.12 0.11(0.25) (0.19)

R2

(%) 14.4 0.8 0.1 14.5 0.5 0.1

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Conclusion

Call-put option implied volatility spread predicts quarterly returns

I Significant in-sample and out-of-sample

CPIVS improves conditional asset pricing model

Forward-looking information within CPIVS contributes:

I through cash flow and discounted rate channels

I predicts lower overall uncertainty

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