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Time-Varying Margin Requirements and Optimal Portfolio Choice

Published online by Cambridge University Press:  10 June 2016

Oleg Rytchkov
Oleg Rytchkov*
Affiliation:
[email protected], Temple University, Fox School of Business, Philadelphia, PA 19122.
*
*Corresponding author: [email protected]
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Abstract

This paper studies the optimal consumption and portfolio problem of an investor with recursive preferences who is subject to time-varying margin requirements. The level of the requirements at each moment is determined by contemporaneous volatility of returns, which is stochastic and may have jumps. I show that the nonstandard hedging demand produced by margin requirements increases with their persistence and volatility. However, for realistic values of parameters, the hedging demand is small even in the presence of jumps, and contemporaneous jumps in prices have a much stronger effect on optimal portfolio than jumps in constraints.

Type
Research Articles
Information
Journal of Financial and Quantitative Analysis , Volume 51 , Issue 2 , April 2016 , pp. 655 - 683
Copyright
Copyright © Michael G. Foster School of Business, University of Washington 2016 

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References

Aït-Sahalia, Y., and Kimmel, R.. “Maximum Likelihood Estimation of Stochastic Volatility Models.” Journal of Financial Economics, 83 (2007), 413–452.Google Scholar
Andersen, T. G.; Benzoni, L.; and Lund, J.. “An Empirical Investigation of Continuous-Time Equity Return Models.” Journal of Finance, 57 (2002), 1239–1284.Google Scholar
Ang, A., and Bekaert, G.. “International Asset Allocation with Regime Shifts.” Review of Financial Studies, 15 (2002), 1137–1187.CrossRefGoogle Scholar
Ang, A.; Papanikolaou, D.; and Westerfield, M. M.. “Portfolio Choice with Illiquid Assets.” Management Science, 60 (2014), 2737–2761.Google Scholar
Attanasio, O. P., and Weber, G.. “Intertemporal Substitution, Risk Aversion and the Euler Equation for Consumption.” Economic Journal, 99 (1989), 59–73.Google Scholar
Bansal, R., and Yaron, A.. “Risks for the Long Run: A Potential Resolution of Asset Pricing Puzzles.” Journal of Finance, 59 (2004), 1481–1509.CrossRefGoogle Scholar
Barberis, N. “Investing for the Long Run When Returns Are Predictable.” Journal of Finance, 55 (2000), 225–264.Google Scholar
Basak, S., and Croitoru, B.. “Equilibrium Mispricing in a Capital Market with Portfolio Constraints.” Review of Financial Studies, 13 (2000), 715–748.Google Scholar
Basak, S., and Cuoco, D.. “An Equilibrium Model with Restricted Stock Market Participation.” Review of Financial Studies, 11 (1998), 309–341.Google Scholar
Bhamra, H. S., and Uppal, R.. “The Role of Risk Aversion and Intertemporal Substitution in Dynamic Consumption-Portfolio Choice with Recursive Utility.” Journal of Economic Dynamics and Control, 30 (2006), 967–991.CrossRefGoogle Scholar
Brandt, M. W. “Portfolio Choice Problems.” In Handbook of Financial Econometrics, Vol. 1, Aït-Sahalia, Y. and Hansen, L. P., eds. Amsterdam, The Netherlands: North-Holland (2010).Google Scholar
Brennan, M. J.; Schwartz, E. S.; and Lagnado, R.. “Strategic Asset Allocation.” Journal of Economic Dynamics and Control, 21 (1997), 1377–1403.CrossRefGoogle Scholar
Broadie, M.; Chernov, M.; and Johannes, M.. “Model Specification and Risk Premia: Evidence from Futures Options.” Journal of Finance, 62 (2007), 1453–1490.CrossRefGoogle Scholar
Buraschi, A.; Porchia, P.; and Trojani, F.. “Correlation Risk and Optimal Portfolio Choice.” Journal of Finance, 65 (2010), 393–420.CrossRefGoogle Scholar
Campbell, J. Y.; Chan, Y. L.; and Viceira, L. M.. “A Multivariate Model of Strategic Asset Allocation.” Journal of Financial Economics, 67 (2003), 41–80.CrossRefGoogle Scholar
Campbell, J. Y., and Viceira, L. M.. “Consumption and Portfolio Decisions When Expected Returns Are Time Varying.” Quarterly Journal of Economics, 114 (1999), 433–495.Google Scholar
Campbell, J. Y., and Viceira, L. M.. “Who Should Buy Long-Term Bonds?” American Economic Review, 91 (2001), 99–127.CrossRefGoogle Scholar
Campbell, J. Y., and Viceira, L. M.. Strategic Asset Allocation: Portfolio Choice for Long-Term Investors. Oxford, UK: Oxford University Press (2002).CrossRefGoogle Scholar
Chabakauri, G. “Dynamic Equilibrium with Two Stocks, Heterogeneous Investors, and Portfolio Constraints.” Review of Financial Studies, 26 (2013), 3104–3141.CrossRefGoogle Scholar
Chacko, G., and Viceira, L. M.. “Dynamic Consumption and Portfolio Choice with Stochastic Volatility in Incomplete Markets.” Review of Financial Studies, 18 (2005), 1369–1402.Google Scholar
Chen, X.; Favilukis, J.; and Ludvigson, S. C.. “An Estimation of Economic Models with Recursive Preferences.” Quantitative Economics, 4 (2013), 39–83.Google Scholar
Chernov, M.; Gallant, A. R.; Ghysels, E.; and Tauchen, G.. “Alternative Models for Stock Price Dynamics.” Journal of Econometrics, 116 (2003), 225–257.Google Scholar
Chernov, M., and Ghysels, E.. “A Study towards a Unified Approach to the Joint Estimation of Objective and Risk Neutral Measures for the Purpose of Options Valuation.” Journal of Financial Economics, 56 (2000), 407–458.CrossRefGoogle Scholar
Cox, J. C.; Ingersoll, J. E.; and Ross, S. A.. “A Theory of the Term Structure of Interest Rates.” Econometrica, 53 (1985), 385–407.CrossRefGoogle Scholar
Cuoco, D. “Optimal Consumption and Equilibrium Prices with Portfolio Constraints and Stochastic Income.” Journal of Economic Theory, 72 (1997), 33–73.Google Scholar
Cuoco, D., and Liu, H.. “A Martingale Characterization of Consumption Choices and Hedging Costs with Margin Requirements.” Mathematical Finance, 10 (2000), 355–385.Google Scholar
Cvitanić, J., and Karatzas, I.. “Convex Duality in Constrained Portfolio Optimization.” Annals of Applied Probability, 2 (1992), 767–818.CrossRefGoogle Scholar
Danielsson, J.; Shin, H. S.; and Zigrand, J.-P.. “The Impact of Risk Regulation on Price Dynamics.” Journal of Banking and Finance, 28 (2004), 1069–1087.Google Scholar
Detemple, J., and Murthy, S.. “Equilibrium Asset Prices and No-Arbitrage with Portfolio Constraints.” Review of Financial Studies, 10 (1997), 1133–1174.Google Scholar
Detemple, J. B.; Garcia, R.; and Rindisbacher, M.. “A Monte Carlo Method for Optimal Portfolios.” Journal of Finance, 58 (2003), 401–446.CrossRefGoogle Scholar
Detemple, J. B., and Rindisbacher, M.. “Closed-Form Solutions for Optimal Portfolio Selection with Stochastic Interest Rate and Investment Constraints.” Mathematical Finance, 15 (2005), 539–568.Google Scholar
Dudley, E., and Nimalendran, M.. “Margins and Hedge Fund Contagion.” Journal of Financial and Quantitative Analysis, 46 (2011), 1227–1257.CrossRefGoogle Scholar
Duffie, D., and Epstein, L. G.. “Asset Pricing with Stochastic Differential Utility.” Review of Financial Studies, 5 (1992), 411–436.CrossRefGoogle Scholar
Egloff, D.; Leippold, M.; and Wu, L.. “The Term Structure of Variance Swap Rates and Optimal Variance Swap Investments.” Journal of Financial and Quantitative Analysis, 45 (2010), 1279–1310.CrossRefGoogle Scholar
Epstein, L., and Zin, S.. “Substitution, Risk Aversion, and the Temporal Behavior of Consumption and Asset Returns: A Theoretical Framework.” Econometrica, 57 (1989), 937–969.Google Scholar
Eraker, B. “Do Stock Prices and Volatility Jump? Reconciling Evidence from Spot and Option Prices.” Journal of Finance, 59 (2004), 1367–1404.CrossRefGoogle Scholar
Eraker, B.; Johannes, M.; and Polson, N.. “The Impact of Jumps in Volatility and Returns.” Journal of Finance, 58 (2003), 1269–1300.Google Scholar
Fleming, W. H., and Soner, H. M.. Controlled Markov Processes and Viscosity Solutions. New York, NY: Springer (2006).Google Scholar
Gârleanu, N. “Portfolio Choice and Pricing in Illiquid Markets.” Journal of Economic Theory, 144 (2009), 532–564.CrossRefGoogle Scholar
Gârleanu, N., and Pedersen, L. H.. “Margin-Based Asset Pricing and Deviations from the Law of One Price.” Review of Financial Studies, 24 (2011), 1980–2022.Google Scholar
Gorton, G. B., and Metrick, A.. “Haircuts.” Federal Reserve Bank of St. Louis Review, 92 (2010), 507–519.Google Scholar
Grossman, S. J., and Vila, J.-L.. “Optimal Investment Strategies with Leverage Constraints.” Journal of Financial and Quantitative Analysis, 27 (1992), 151–168.Google Scholar
Guvenen, F. “Reconciling Conflicting Evidence on the Elasticity of Intertemporal Substitution: A Macroeconomic Perspective.” Journal of Monetary Economics, 53 (2006), 1451–1472.CrossRefGoogle Scholar
Hall, R. E. “Intertemporal Substitution in Consumption.” Journal of Political Economy, 96 (1988), 339–357.Google Scholar
Hedegaard, E. “How Margins Are Set and How They Affect Commodity Futures Prices.” Working Paper, Arizona State University (2011).Google Scholar
Jones, C. S. “The Dynamics of Stochastic Volatility: Evidence from Underlying and Options Markets.” Journal of Econometrics, 116 (2003), 181–224.Google Scholar
Judd, K. L. Numerical Methods in Economics. Cambridge, MA: MIT Press (1998).Google Scholar
Karlin, S., and Taylor, H. M.. A Second Course in Stochastic Processes. San Diego, CA: Academic Press (1981).Google Scholar
Kim, T. S., and Omberg, E.. “Dynamic Nonmyopic Portfolio Behavior.” Review of Financial Studies, 9 (1996), 141–161.Google Scholar
Liu, J. “Portfolio Selection in Stochastic Environments.” Review of Financial Studies, 20 (2007), 1–39.Google Scholar
Liu, J., and Longstaff, F. A.. “Losing Money on Arbitrage: Optimal Dynamic Portfolio Choice in Markets with Arbitrage Opportunities.” Review of Financial Studies, 17 (2004), 611–641.Google Scholar
Liu, J.; Longstaff, F. A.; and Pan, J.. “Dynamic Asset Allocation with Event Risk.” Journal of Finance, 58 (2003), 231–259.CrossRefGoogle Scholar
Liu, J., and Pan, J.. “Dynamic Derivative Strategies.” Journal of Financial Economics, 69 (2003), 401–430.Google Scholar
Longstaff, F. A. “Portfolio Claustrophobia: Asset Pricing in Markets with Illiquid Assets.” American Economic Review, 99 (2009), 1119–1144.Google Scholar
Lynch, A. W. “Portfolio Choice and Equity Characteristics: Characterizing the Hedging Demands Induced by Return Predictability.” Journal of Financial Economics, 62 (2001), 67–130.Google Scholar
Merton, R. C. “Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case.” Review of Economics and Statistics, 51 (1969), 247–257.Google Scholar
Merton, R. C. “Optimum Consumption and Portfolio Rules in a Continuous-Time Model.” Journal of Economic Theory, 3 (1971), 373–413.Google Scholar
Obstfeld, M. “Risk-Taking, Global Diversification, and Growth.” American Economic Review, 84 (1994), 1310–1329.Google Scholar
Ogaki, M., and Reinhart, C. M.. “Measuring Intertemporal Substitution: The Role of Durable Goods.” Journal of Political Economy, 106 (1998), 1078–1098.Google Scholar
Pan, J. “The Jump-Risk Premia Implicit in Options: Evidence from an Integrated Time-Series Study.” Journal of Financial Economics, 63 (2002), 3–50.Google Scholar
Rytchkov, O. “Asset Pricing with Dynamic Margin Constraints.” Journal of Finance, 69 (2014), 405–452.CrossRefGoogle Scholar
Sangvinatsos, A., and Wachter, J. A.. “Does the Failure of the Expectations Hypothesis Matter for Long-Term Investors?” Journal of Finance, 60 (2005), 179–230.CrossRefGoogle Scholar
Schroder, M., and Skiadas, C.. “Optimal Consumption and Portfolio Selection with Stochastic Differential Utility.” Journal of Economic Theory, 89 (1999), 68–126.CrossRefGoogle Scholar
Schroder, M., and Skiadas, C.. “Optimal Lifetime Consumption-Portfolio Strategies under Trading Constraints and Generalized Recursive Preferences.” Stochastic Processes and Their Applications, 108 (2003), 155–202.Google Scholar
Schroder, M., and Skiadas, C.. “Lifetime Consumption-Portfolio Choice under Trading Constraints, Recursive Preferences, and Nontradeable Income.” Stochastic Processes and Their Applications, 115 (2005), 1–30.Google Scholar
Skiadas, C. “Dynamic Portfolio Choice and Risk Aversion.” In Handbooks in Operations Research and Management Science: Financial Engineering, Vol. 15, Birge, J. R. and Linetsky, V., eds. Amsterdam, The Netherlands: North-Holland (2008).Google Scholar
Svensson, L. E. “Portfolio Choice with Non-Expected Utility in Continuous Time.” Economics Letters, 30 (1989), 313–317.Google Scholar
Tepla, L. “Optimal Portfolio Policies with Borrowing and Shortsale Constraints.” Journal of Economic Dynamics and Control, 24 (2000), 1623–1639.CrossRefGoogle Scholar
Vila, J.-L., and Zariphopoulou, T.. “Optimal Consumption and Portfolio Choice with Borrowing Constraints.” Journal of Economic Theory, 77 (1997), 402–431.Google Scholar
Wachter, J. “Portfolio and Consumption Decisions under Mean-Reverting Returns: An Exact Solution for Complete Markets.” Journal of Financial and Quantitative Analysis, 37 (2002), 63–91.Google Scholar
Weil, P. “The Equity Premium Puzzle and the Risk-Free Rate Puzzle.” Journal of Monetary Economics, 24 (1989), 401–421.Google Scholar
Wu, L. “Jumps and Dynamic Asset Allocation.” Review of Quantitative Finance and Accounting, 20 (2003), 207–243.Google Scholar
Yogo, M. “Estimating the Elasticity of Intertemporal Substitution When Instruments Are Weak.” Review of Economics and Statistics, 86 (2004), 797–810.CrossRefGoogle Scholar
Zhou, G., and Zhu, Y.. “Volatility Trading: What Is the Role of the Long-Run Volatility Component?” Journal of Financial and Quantitative Analysis, 47 (2012), 273–307.Google Scholar
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