Predicting the Equity Premium with Implied 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 1 / 32
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 Dividend yield, P/E, Book-to-market ratio, term spread, etc Question What is the predictive ability of forward-looking information of options? 2 / 32
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? 3 / 32
Motivation and Research Questions Many reasons to investigate predictive ability of CPIVS Theory Chowdhry and Nanda (1991), Easley, O Hara, and Srinivas (1998): Informed traders chose option market first An, Ang, Bali, and Cakici (2014): Noisy rational expectations model of informed trading in both markets option volatilities can predict stock returns Empirical work Option market information: price, volume and volatility Information Content of Option Implied Volatility Spread Nonlinear risks Cross sectional predictability Time-series prediction 4 / 32
Literature Review Information Content of Option Implied Volatility Spread Doran, Fodor, and Jiang (2013), Christoffersen, Jacobs, and Chang (2013), Cao, Gempeshaw, and Simin (2018) Nonlinear risks Bollerslev and Todorov (2011), Kelly and Jiang (2014) Cross sectional evidence Bali and Hovakimian (2009), Cremers and Weinbaum (2010), Xing, Zhang and Zhao (2010) and An, Ang, Bali and Cakici (2014) Time-series prediction Atilgan, Bali and Demirtas (2015), Cao, Gempeshaw, and Simin (2018) 5 / 32
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 6 / 32
Main results CPIVS predicts Quarterly aggregate market returns in-sample and out-of-sample In-sample R 2 : 14.7%! Out-of-sample R 2 : 8.5% (29% during recessions!) Long-run in-sample prediction up to three years CPIVS improves the conditional factor models 50% less pricing errors Prediction power comes from Forward-looking information orthogonal to other predictors Net innovation between call option and put option implied volatility Economic significance of our results Ability to forecast macroeconomic uncertainty 7 / 32
Data and Methodology Mkt risk premium = CRSP value-weighted excess market return CPIVS: difference between call and put option implied volatility CPIVS t = CVOL t PVOL t OptionMetrics (1996-2016) At-the-Market (ATM) Option Implied volatility Delta: 0.5 Days-to-expiration: 30 days Quarterly average of daily spread 8 / 32
Data and Methodology Other predictors: Goyal and Welch (2008) Focus on Dividend Yield and Cay Fundamental valuations: Logarithm of dividend-yield ratio (log(dy )) Macroeconomic indicators Consumption-to-wealth ratio (Cay) Kitchen Sink: stack all variables 9 / 32
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 10 / 32
Equity Premium CPIVS Time Series of CPIVS and Equity Premium 0.3 0.02 0.2 0 0.1 0-0.02-0.1-0.04-0.2-0.3-0.06 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 2016 Equity Premium CPIVS 11 / 32
Log Dividend Yield CPIVS Time Series of CPIVS and Log(DY) -3.4 0.02-3.6 0-3.8-4 -0.02-4.2-0.04-4.4-4.6-0.06 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 2016 log(dy) CPIVS 12 / 32
Methodology In-sample Prediction OLS prediction for one-quarter, semiannual, and one-year ahead aggregate market returns where r t+h = α i,h + β i,h X i,t + ε i,t+h h = 1 (quarterly), 2 (semiannually), and 4 (annually) X represents individual predictors Newey-West and Hodrick standard errors 13 / 32
Methodology Out-of-sample Prediction 1 Compare predictor with the historical average 2 Mean Square Forecast Error (MSFE) Is one-step ahead forecast error using our predictors smaller than forecast using historical average? 3 Utility Gain Do investors see any utility gains using the predictors? 14 / 32
Methodology Out-of-sample Prediction: MSFE and R 2 OS Predictors (X i ) Historical Average (X 0 ) One-step Forecast r i,t+s r 0,t+s Forecast error ê i,t+s = r t+s r i,t+s e 0,t+s = r t+s r 0,t+s MSFE MSFE 2 i = 1 S S s=1 ê2 i,t+s MSFE 2 0 = 1 S S s=1 ê2 0,t+s Statistics Evaluation R 2 OS = 1 MSFE i MSFE 0 If R 2 OS > 0, then MSFE i < MSFE 0 Predictor beats historical average 15 / 32
Out-of-sample Prediction: Utility Gains For a quadratic utility investor, the optimal weight in the market is ( ) ( ) w = 1 E(rm) γ Setting γ = 5, compute utility gains from using CPIVS as follows: At each period t, σ 2 rm σ 2 = trailing sample variance of the market, w0 uses E(r m ) = sample average, w 1 uses E(r m ) = E(r m CPIVS). Keep the returns from rc = (1 w)r f + wr m using the two w s At time T Calculate utility using mean and variance of the two portfolios Utility gain = U(r c CPIVS) U(r c ) 16 / 32
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) R 2 (%) 14.7 5.7-1.0 7.7 11.8 0.2 3.1 22.3 2.4 17 / 32
Empirical Results: Out-of-sample Prediction Overall Expansion Recession ROS 2 U-Gain ROS 2 U-Gain ROS 2 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) 18 / 32
Empirical Results: Out-of-sample Prediction Robustness Test the predictability of CPIVS on the following portfolios Size, operating profitability, and investment-to-asset up to 90% out-of-sample significance (29/32) Industry portfolios up to 90% out-of-sample significance (15/17) 19 / 32
Empirical Results: Conditional Asset Pricing Models Incorporate the information from CPIVS, log(dy) and Cay into conditional versions 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 20 / 32
Empirical Results: Conditional Asset Pricing Models The generic conditional asset pricing is E t (r t+1 Z t ) = α(z t ) + β(z t )E t (F t+1 Z t ) where Z t = lagged instruments = {log(dy ) t, Cay t, CPIVS t } Three versions: α fixed, β = b 0 + b 1 Z t ; α = a0 + a 1 Z t, β = b 0 + b 1 Z t ; α fixed, β fixed, Et (F t+1 Z t ) = d 0 + d 1 Z t 21 / 32
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 D2-3.44-4.30-3.72-2.41 D3-2.45-1.86-0.80-0.96 D4 0.26 0.22 0.26 0.60 D5-1.70-0.82-0.86-2.88 D6 0.11 0.69 0.99-0.36 D7-0.51-0.45-0.04-1.36 D8 3.00 1.76 2.87 2.24 D9 2.51 1.77 1.44 1.44 HIGH 2.24 0.59-0.16 2.96 22 / 32
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 23 / 32
Empirical Results: Two-step Orthogonality Method: Step 1 Predictor i: obtain the residual ε i,t+1 from r t+1 = α i + β i X i,t + ε i,t+1 Step 2 Predictor j: Regress the residual ε i,t+1 on other predictors X j,t, j i, ε i,t+1 = δ j + γ j X j,t + µ j,t+1, j i Evaluation: If γ j is significant, then the predictor j contains further information than predictor i. 24 / 32
Empirical Evidence: Two-step Orthogonality Standardize the predictors: comparable coefficients i = CPIVS i = log(dy) β log(dy ) R 2 β (CPIVS) R 2 0.22 3.5% 0.37 12.5% (1.81) (3.20) i = CPIVS i = Cay β Cay R 2 β (CPIVS) R 2 0.16 1.1% 0.41 15.8% (1.82) (4.34) 25 / 32
Empirical Evidence: Net Innovation Intuition Innovation predicts returns Innovation in both options CVOL: capture innovation in calls PVOL: capture innovation in puts CPIVS: approximately the difference between calls and puts Call-put parity: the difference between calls and puts 26 / 32
Empirical Evidence: Net Innovation Information from Call and Put Options Overall Recession ROS 2 U-Gain ROS 2 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) 27 / 32
Empirical Results: Campbell and Shiller Decomposition Decompose market returns into three components: 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 28 / 32
Empirical Results: Decomposition Standardize the predictors: β CPIVS Panel A: Predictive Regression: r 0.034 (4.118) Panel B: VAR residual using {log(dp)} Expected Return Cash Flow Discounted Rate β CPIVS 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 β CPIVS 0.003 0.020-0.012 (0.80) (4.89) (-1.07) 29 / 32
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 Uncertainty t+h = α i + β i X i,t + ε i,t+h where h = 1 (one-quarter ahead), (h = 2) (two quarters ahean) 30 / 32
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) R 2 (%) 14.4 0.8 0.1 14.5 0.5 0.1 31 / 32
Conclusion Call-put option implied volatility spread predicts quarterly returns Significant in-sample and out-of-sample CPIVS improves conditional asset pricing model Forward-looking information within CPIVS contributes: through cash flow and discounted rate channels predicts lower overall uncertainty 32 / 32