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Recovery with Applications to Forecasting Equity Disaster Probability and Testing the Spanning Hypothesis in the Treasury Market

Published online by Cambridge University Press:  18 July 2022

Gurdip Bakshi Open the ORCID record for Gurdip Bakshi [Opens in a new window] ,
Xiaohui Gao  and
Jinming Xue
Gurdip Bakshi*
Affiliation:
Temple University Fox School of Business
Xiaohui Gao
Affiliation:
Temple University Fox School of Business [email protected]
Jinming Xue
Affiliation:
Southern Methodist University Cox School of Business [email protected]
*
[email protected] (corresponding author)
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Abstract

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We investigate the implications of recovering real-world conditional expectation of return functions using options on the S&P 500 index and Treasury bond futures. First, we construct estimates of the probability of disasters, defined as higher than 6%, 5%, or 4% equity market declines over option expiration cycles. This measure of disaster probability forecasts realized disasters. Second, we employ options on the futures of the 10- and 30-year Treasury bonds to construct estimates for the expected return of bond futures. These measures display forecasting ability for subsequent futures returns beyond the level, slope, and curvature variables extracted from the yield curve.

Type
Research Article
Information
Journal of Financial and Quantitative Analysis , Volume 58 , Issue 4 , June 2023 , pp. 1808 - 1842
Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of the Michael G. Foster School of Business, University of Washington

Footnotes

We are extremely grateful for the feedback of the referee and Jennifer Conrad (the editor). Earlier versions were presented at the Chinese University of Hong Kong, the University of Massachusetts–Amherst, the University of Maryland, the University of North Carolina–Chapel Hill, Temple University, the University of Wisconsin–Madison, and the Midwest Finance Association meetings (San Antonio). It was a pleasure to address the comments of John Campbell, Fousseni Chabi-Yo, Yannick Dillschneider, Jens Jackwerth, Chris Jones (a discussant), Johnathan Loudis, Raimond Maurer, and Ngoc-Khanh Tran. We sincerely appreciate the comments of David Brown, Vincent Campasano, Jay Cao, Peter Carr, Ric Colacito, Robert Connolly, John Crosby, Ian Dew-Becker, Robert Engle, Bjorn Eraker, Steve Heston, Nikunj Kapadia, Hossein Kazemi, Matthew Linn, Mark Loewenstein, Dilip Madan, Sanjay Nawalkha, Daniela Osterrieder, Erwan Quintin, Alberto Rossi, Oleg Rytchkov, Shrihari Santosh, Pavel Savor, Sang Byung Seo, Ivan Shaliastovich, Xiaoxiao Tang, and Liuren Wu. Wei Zhou suggested improvements to the proofs. All computer codes are available from any of the authors.

References

Aït-Sahalia, Y.; Wang, Y.; and Yared, F.. “Do Options Markets Correctly Price the Probabilities of Movement of the Underlying Asset?” Journal of Econometrics, 102 (2001), 67–110.CrossRefGoogle Scholar
Almeida, C., and Garcia, R.. “Robust Economic Implications of Nonlinear Pricing Kernels.” Management Science, 63 (2017), 3361–3380.CrossRefGoogle Scholar
Amihud, Y.; Hurvich, C.; and Wang, Y.. “Multiple-Predictor Regressions: Hypothesis Testing.” Review of Financial Studies, 22 (2009), 413–434.CrossRefGoogle Scholar
Andersen, T.; Fusari, N.; and Todorov, V.. “The Risk Premia Embedded in Index Options.” Journal of Financial Economics, 117 (2015), 558–584.CrossRefGoogle Scholar
Audrino, F.; Huitema, R.; and Ludwig, M.. “An Empirical Implementation of the Ross Recovery Theorem as a Prediction Device.” Journal of Financial Econometrics, 19 (2021), 291–312.CrossRefGoogle Scholar
Bakshi, G.; Chabi-Yo, F.; and Gao, X.. “A Recovery That We Can Trust? Deducing and Testing the Restrictions of the Recovery Theorem.” Review of Financial Studies, 31 (2018), 532–555.CrossRefGoogle Scholar
Bakshi, G.; Crosby, J.; and Gao, X.. “The Puzzle of Treasury Option Returns and the Consistent Pricing of Options and the Yield Curve.” Working Paper, Temple University and University of Maryland (2020).Google Scholar
Bakshi, G.; Kapadia, N.; and Madan, D.. “Stock Return Characteristics, Skew Laws, and the Differential Pricing of Individual Equity Options.” Review of Financial Studies, 16 (2003), 101–143.CrossRefGoogle Scholar
Bauer, M., and Hamilton, J.. “Robust Bond Risk Premia.” Review of Financial Studies, 31 (2018), 399–448.CrossRefGoogle Scholar
Bianchi, D.; Buchner, M.; and Tamoni, A.. “Bond Risk Premiums with Machine Learning.” Review of Financial Studies, 34 (2020), 1046–1089.CrossRefGoogle Scholar
Bollerslev, T., and Todorov, V.. “Tails, Fears, and Risk Premia.” Journal of Finance, 66 (2011), 2165–2211.CrossRefGoogle Scholar
Borovička, J.; Hansen, L.; and Scheinkman, J.. “Misspecified Recovery.” Journal of Finance, 71 (2016), 2493–2544.CrossRefGoogle Scholar
Carr, P., and Wu, L.. “A Simple Robust Link Between American Puts and Credit Protection.” Review of Financial Studies, 24 (2011), 473–505.CrossRefGoogle Scholar
Chabi-Yo, F., and Loudis, J.. “The Conditional Expected Market Return.” Journal of Financial Economics, 137 (2020), 752–786.CrossRefGoogle Scholar
Chen, H.; Joslin, S.; and Tran, N.. “Rare Disasters and Risk Sharing with Heterogeneous Beliefs.” Review of Financial Studies, 25 (2012), 2189–2224.CrossRefGoogle Scholar
Christoffersen, P.; Jacobs, K.; and Heston, S.. “Capturing Option Anomalies with a Variance-Dependent Pricing Kernel.” Review of Financial Studies, 26 (2013), 1963–2006.CrossRefGoogle Scholar
Cieslak, A., and Povala, P.. “Expected Returns in Treasury Bonds.” Review of Financial Studies, 28 (2015), 2859–2901.CrossRefGoogle Scholar
Cochrane, J. Asset Pricing, Princeton, NJ: Princeton University Press (2005).Google Scholar
Cochrane, J., and Piazzesi, M.. “Bond Risk Premia.” American Economic Review, 95 (2005), 138–160.CrossRefGoogle Scholar
Collin-Dufresne, P., and Goldstein, R.. “Do Bonds Span the Fixed-Income Markets?” Journal of Finance, 57 (2002), 1685–1730.CrossRefGoogle Scholar
Dew-Becker, I.; Giglio, S.; and Kelly, B.. “Hedging Macroeconomic and Financial Uncertainty and Volatility.” Journal of Financial Economics, 142 (2021), 23–45.CrossRefGoogle Scholar
Dillschneider, Y., and Maurer, R.. “Functional Ross Recovery: Theoretical Results and Empirical Tests.” Journal of Economic Dynamics and Control, 108 (2019), 103750.CrossRefGoogle Scholar
Drechsler, I., and Yaron, A.. “What’s Vol Got To Do With It.” Review of Financial Studies, 24 (2011), 1–45.CrossRefGoogle Scholar
Du, J., and Kapadia, N.. “The Tail in the Volatility Index.” Working Paper, University of Massachusetts (2013).Google Scholar
Duffee, G. “Term Premia and Interest Rate Forecasts in Affine Models.” Journal of Finance, 57 (2002), 405–443.CrossRefGoogle Scholar
Feunou, B.; Jahan-Parvar, M.; and Tedongap, R.. “Which Parametric Model for Conditional Skewness?” European Journal of Finance, 22 (2016), 1237–1271.CrossRefGoogle Scholar
Feunou, B., and Okou, C.. “Good Volatility, Bad Volatility and Option Pricing.” Journal of Financial and Quantitative Analysis, 54 (2019), 695–727.CrossRefGoogle Scholar
Follmer, H., and Schied, A.. Stochastic Finance. Boston, MA: De Gruyter (2010).Google Scholar
Gabaix, X. “Variable Rare Disasters: An Exactly Solved Framework for Ten Puzzles in Macro-Finance.” Quarterly Journal of Economics, 127 (2012), 645–700.CrossRefGoogle Scholar
Gao, G., and Song, Z.. “Rare Disaster Concerns Everywhere.” Management Science, 65 (2019), 2947–3448.CrossRefGoogle Scholar
Ghosh, A.; Julliard, C.; and Taylor, A.. “What is the Consumption-CAPM Missing? An Information-Theoretic Framework for the Analysis of Asset Pricing Models.” Review of Financial Studies, 30 (2017), 442–504.CrossRefGoogle Scholar
Gormsen, N., and Jensen, C.. “Higher-Moment Risk.” Working Paper, University of Chicago and Bocconi University (2019).Google Scholar
Greenwood, R., and Vayanos, D.. “Bond Supply and Excess Bond Returns.” Review of Financial Studies, 27 (2014), 663–713.CrossRefGoogle Scholar
Hansen, L., and Jagannathan, R.. “Implications of Security Market Data for Dynamic Economies.” Journal of Political Economy, 99 (1991), 225–261.CrossRefGoogle Scholar
Hansen, L., and Jagannathan, R.. “Assessing Specification Errors in Stochastic Discount Factor Models.” Journal of Finance, 52 (1997), 557–590.CrossRefGoogle Scholar
Jackwerth, J., and Menner, M.. “Does the Ross Recovery Theorem Work Empirically?” Journal of Financial Economics, 137 (2020), 723–739.CrossRefGoogle Scholar
Jensen, C.; Lando, D.; and Pedersen, L.. “Generalized Recovery.” Journal of Financial Economics, 133 (2019), 154–174.CrossRefGoogle Scholar
Joslin, S.; Priebsch, M.; and Singleton, K.. “Risk Premiums in Dynamic Term Structure Models with Unspanned Macro Risks.” Journal of Finance, 69 (2014), 1197–1233.CrossRefGoogle Scholar
Kilic, M., and Shaliastovich, I.. “Good and Bad Variance Premia and Expected Returns.” Management Science, 65 (2019), 2445–2945.CrossRefGoogle Scholar
Kozak, S.; Nagel, S.; and Santosh, S.. “Shrinking the Cross-Section.” Journal of Financial Economics, 135 (2020), 271–292.CrossRefGoogle Scholar
Lewellen, J.; Nagel, S.; and Shanken, J.. “A Skeptical Appraisal of Asset Pricing Tests.” Journal of Financial Economics, 96 (2010), 175–194.CrossRefGoogle Scholar
Liu, Y. “Index Option Returns and Generalized Entropy Bounds.” Journal of Financial Economics, 139 (2021), 1015–1036.CrossRefGoogle Scholar
Ludvigson, S., and Ng, S.. “Macro Factors in Bond Risk Premia.” Review of Financial Studies, 22 (2009), 5027–5067.CrossRefGoogle Scholar
Martin, I. “What is the Expected Return on the Market?” Quarterly Journal of Economics, 150 (2017), 367–433.CrossRefGoogle Scholar
McCracken, M., and Ng, S.. “FRED-MD: A Monthly Database for Macroeconomic Research.” Journal of Business & Economic Statistics, 34 (2016), 574–589.CrossRefGoogle Scholar
Newey, W., and West, K.. “A Simple, Positive Semi-Definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix.” Econometrica, 55 (1987), 703–708.CrossRefGoogle Scholar
Newey, W., and West, K.. “Automatic Lag Selection in Covariance Matrix Estimation.” Review of Economic Studies, 61 (1994), 631–653.CrossRefGoogle Scholar
Qin, L., and Linetsky, V.. “Positive Eigenfunctions of Markovian Pricing Operators: Hansen–Scheinkman Factorization and Ross Recovery.” Operations Research, 64 (2016), 99–117.CrossRefGoogle Scholar
Qin, L.; Linetsky, V.; and Nie, Y.. “Long Forward Probabilities, Recovery and the Term Structure of Bond Risk Premiums.” Review of Financial Studies, 31 (2018), 4863–4883.CrossRefGoogle Scholar
Rosenberg, J., and Engle, R.. “Empirical Pricing Kernels.” Journal of Financial Economics, 64 (2002), 341–372.CrossRefGoogle Scholar
Ross, S. “The Recovery Theorem.” Journal of Finance, 70 (2015), 615–648.CrossRefGoogle Scholar
Schneider, P., and Trojani, F.. “(Almost) Model-Free Recovery.” Journal of Finance, 74 (2019), 323–370.CrossRefGoogle Scholar
Siriwardane, E. “The Probability of Rare Disasters: Estimation and Implications.” Working Paper, Harvard University (2015).CrossRefGoogle Scholar
Song, Z., and Xiu, D.. “A Tale of Two Option Markets: Pricing Kernels and Volatility Risk.” Journal of Econometrics, 190 (2016), 176–196.CrossRefGoogle Scholar
Stambaugh, R. “Predictive Regressions.” Journal of Financial Economics, 54 (1999), 375–421.CrossRefGoogle Scholar
Tran, N. “The Functional Stochastic Discount Factor.” Quarterly Journal of Finance, 9 (2019), 1950013.CrossRefGoogle Scholar
Tran, N., and Xia, S.. “Specified Recovery.” Working Paper, Virginia Tech (2019).Google Scholar
Wachter, J. “Can Time-Varying Risk of Rare Disasters Explain Aggregate Stock Market Volatility?” Journal of Finance, 68 (2013), 987–1035.CrossRefGoogle Scholar
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