Skip to main content Accessibility help
Hostname: page-component-78dcdb465f-vddjc Total loading time: 0.983 Render date: 2021-04-15T03:01:06.043Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "metricsAbstractViews": false, "figures": false, "newCiteModal": false, "newCitedByModal": true }

Asset Variance Risk Premium and Capital Structure

Published online by Cambridge University Press:  12 May 2020

Babak Lotfaliei
San Diego State University Fowler College of Business
E-mail address:


This article investigates how the asset-return variance risk premium changes leverage. I find that the premium reduces leverage by increasing risk-neutral bankruptcy probability and costs in a model where asset returns have stochastic variance with the risk premium. Empirically, the model calibrations verify a significant reduction in optimal leverage, closer to observed leverage than the model without the premium. In model-free regressions, I document that leverage correlates negatively with the variance premium. The highest negative correlation is among investment-grade firms with low asset beta and historical variance but high variance premiums because their assets have high exposure to the market’s variance premium.

Research Article
© The Author(s), 2020. Published by Cambridge University Press on behalf of Michael G. Foster School of Business, University of Washington

Access options

Get access to the full version of this content by using one of the access options below.


I am indebted to Jan Ericsson and Aytek Malkhozov (my co-supervisors), my PhD thesis defense committee, Jarrad Harford (the editor), and JingZhi Huang (the referee). I thank Amir Akbari, Sebastien Betermier, Tolga Cenesizoglu, Georges Dionne, Christian Dorion, Evan Dudley, Redouane Elkamhi, Barry Feldman, Dirk Hackbarth, Nelson Heintz, Ali Jafari, Januj Juneja, Jaemin Kim, Marie Lachance, Hugues Langlois, Edward Lawrence, Stefan Nagel, Chris Parsons, Mehdi Salehizadeh, Sergei Sarkissian, Nabil Tahani, Timothy Trombley, and Nikhil Varaiya and the participants and discussants in the seminars at McGill University and San Diego State University, the 2014 Mathematical Finance Days, the 2015 Financial Management Association Meeting, the 2015 Midwest Finance Association Meeting, and the 2016 Global Finance Conference for their helpful comments. Part of this research was conducted in CyberLab at Indiana University–Purdue University Indianapolis. Financial support was provided by the Institut de Finance Mathèmatique de Montreal (IFM2). All errors are mine. Codes and data with pseudo IDs to replicate this article’s figures and tables are available at.


Ait-Sahalia, Y.; Fan, J.; and Li, Y.. “The Leverage Effect Puzzle: Disentangling Sources of Bias at High Frequency.” Journal of Financial Economics, 109 (2013), 224249.CrossRefGoogle Scholar
Ait-Sahalia, Y., and Kimmel, R.. “Maximum Likelihood Estimation of Stochastic Volatility Models.” Journal of Financial Economics, 83 (2007), 413452.10.1016/j.jfineco.2005.10.006CrossRefGoogle Scholar
Arellano, M., and Bond, S.. “Some Tests of Specification for Panel Data: Monte Carlo Evidence and an Application to Employment Equations.” Review of Economic Studies, 58 (1991), 277297.10.2307/2297968CrossRefGoogle Scholar
Bae, K.-H.; Kang, J.-K.; and Wang, J.. “Employee Treatment and Firm Leverage: A Test of the Stakeholder Theory of Capital Structure.” Journal of Financial Economics, 100 (2011), 130153.10.1016/j.jfineco.2010.10.019CrossRefGoogle Scholar
Bakshi, G., and Kapadia, N.. “Delta-Hedged Gains and the Negative Market Volatility Risk Premium.” Review of Financial Studies, 16 (2003), 527566.CrossRefGoogle Scholar
Banerjee, S.; Dasgupta, S.; and Kim, Y.. “Buyer–Supplier Relationships and the Stakeholder Theory of Capital Structure.” Journal of Finance, 63 (2008), 25072552.CrossRefGoogle Scholar
Barras, L., and Malkhozov, A.. “Does Variance Risk Have Two Prices? Evidence from the Equity and Option Markets.” Journal of Financial Economics, 121 (2016), 7992.10.1016/j.jfineco.2016.02.014CrossRefGoogle Scholar
Bekaert, G., and Wu, G.. “Asymmetric Volatility and Risk in Equity Markets.” Review of Financial Studies, 13 (2000), 142.CrossRefGoogle Scholar
Bongaerts, D.; De Jong, F.; and Driessen, J.. “Derivative Pricing with Liquidity Risk: Theory and Evidence from the Credit Default Swap Market.” Journal of Finance, 66 (2011), 203240.10.1111/j.1540-6261.2010.01630.xCrossRefGoogle Scholar
Brennan, M. J., and Schwartz, E. S.. “Corporate Income Taxes, Valuation, and the Problem of Optimal Capital Structure.” Journal of Business, 51 (1978), 103114.CrossRefGoogle Scholar
Bris, A.; Welch, I.; and Zhu, N.. “The Costs of Bankruptcy: Chapter 7 Liquidation versus Chapter 11 Reorganization.” Journal of Finance, 61 (2006), 12531303.10.1111/j.1540-6261.2006.00872.xCrossRefGoogle Scholar
Bruno, G. S. F.Estimation and Inference in Dynamic Unbalanced Panel-Data Models with a Small Number of Individuals.” Stata Journal, 5 (2005), 473500.CrossRefGoogle Scholar
Campbell, J. Y.; Giglio, S.; Polk, C.; and Turley, R.. “An Intertemporal CAPM with Stochastic Volatility.” Journal of Financial Economics, 158 (2018), 207233.CrossRefGoogle Scholar
Campbell, J. Y.; Hilscher, J.; and Szilagyi, J.. “In Search of Distress Risk.” Journal of Finance, 63 (2008), 28992939.10.1111/j.1540-6261.2008.01416.xCrossRefGoogle Scholar
Carr, P., and Wu, L.. “Variance Risk Premiums.” Review of Financial Studies, 22 (2009), 13111341.10.1093/rfs/hhn038CrossRefGoogle Scholar
Chen, H.Macroeconomic Conditions and the Puzzles of Credit Spreads and Capital Structure.” Journal of Finance, 65 (2010), 21712212.CrossRefGoogle Scholar
Chen, H.; Wang, H.; and Zhou, H.. “Stock Return Volatility and Capital Structure Decisions.” Paper presented at the American Finance Association Meeting, Boston, Massachusetts, (2015).Google Scholar
Chen, H.; Xu, Y.; and Yang, J.. “Systematic Risk, Debt Maturity, and the Term Structure of Credit Spreads.” Working Paper, available at, (2013).CrossRefGoogle Scholar
Chen, L.; Collin-Dufresne, P.; and Goldstein, R. S.. “On the Relation between the Credit Spread Puzzle and the Equity Premium Puzzle.” Review of Financial Studies, 22 (2008), 33673409.10.1093/rfs/hhn078CrossRefGoogle Scholar
Choi, J., and Richardson, M.. “The Volatility of a Firm’s Assets and the Leverage Effect.” Journal of Financial Economics, 121 (2016), 254277.CrossRefGoogle Scholar
Correia, R., and Población, J.. “A Structural Model with Explicit Distress.” Journal of Banking and Finance, 58 (2015), 112130.CrossRefGoogle Scholar
Cox, J. C.; Ingersoll, J. E.; and Ross, S. A.. “A Theory of the Term Structure of Interest Rates.” Econometrica, 53 (1985), 385407.CrossRefGoogle Scholar
Davydenko, S. A.; Strebulaev, I. A.; and Zhao, X.. “A Market-Based Study of the Cost of Default.” Review of Financial Studies, 25 (2012), 29592999.10.1093/rfs/hhs091CrossRefGoogle Scholar
DeAngelo, H.; DeAngelo, L.; and Whited, T. M.. “Capital Structure Dynamics and Transitory Debt.” Journal of Financial Economics, 99 (2011), 235261.10.1016/j.jfineco.2010.09.005CrossRefGoogle Scholar
DeAngelo, H., and Roll, R.. “How Stable Are Corporate Capital Structures?Journal of Finance, 70 (2015), 373418.CrossRefGoogle Scholar
Denis, D. J.The Persistent Puzzle of Corporate Capital Structure: Current Challenges and New Directions.” Financial Review, 47 (2012), 631643.CrossRefGoogle Scholar
Dixit, A. K., and Pindyck, R. S.. Investment Under Uncertainty. Princeton, NJ: Princeton University Press (2012).CrossRefGoogle Scholar
Dorion, C. Pricing Financial Derivatives: The Impact of Business Conditions and Systematic Risk. PhD thesis, McGill University, Montreal, Canada (2010).Google Scholar
Du, D.; Elkamhi, R.; and Ericsson, J.. “Time-Varying Asset Volatility and the Credit Spread Puzzle.” Journal of Finance, 74 (2019), 18411885.CrossRefGoogle Scholar
Elkamhi, R.; Ericsson, J.; and Parsons, C. A.. “The Cost and Timing of Financial Distress.” Journal of Financial Economics, 105 (2012), 6281.CrossRefGoogle Scholar
Elsas, R., and Florysiak, D.. “Dynamic Capital Structure Adjustment and the Impact of Fractional Dependent Variables.” Journal of Financial and Quantitative Analysis, 50 (2015), 11051133.CrossRefGoogle Scholar
Eom, Y. H.; Helwege, J.; and Huang, J.. “Structural Models of Corporate Bond Pricing: An Empirical Analysis.” Review of Financial Studies, 17 (2004), 499.CrossRefGoogle Scholar
Ericsson, J., and Reneby, J.. “A Framework for Valuing Corporate Securities.” Applied Mathematical Finance, 5 (1998), 143163.10.1080/135048698334619CrossRefGoogle Scholar
Fama, E. F., and French, K. R.. “Testing Trade-Off and Pecking Order Predictions about Dividends and Debt.” Review of Financial Studies, 15 (2002), 133.10.1093/rfs/15.1.1CrossRefGoogle Scholar
Fan, J. P. H.; Titman, S.; and Twite, G.. “An International Comparison of Capital Structure and Debt Maturity Choices.” Journal of Financial and Quantitative Analysis, 47 (2012), 2356.CrossRefGoogle Scholar
Figlewski, S., and Wang, X.. “Is the ‘Leverage Effect’ a Leverage Effect?” Working Paper, available at, (2001).CrossRefGoogle Scholar
Fouque, J.; Sircar, R.; and Solna, K.. “Stochastic Volatility Effects on Defaultable Bonds.” Applied Mathematical Finance, 13 (2006), 215244.CrossRefGoogle Scholar
Frank, M. Z., and Goyal, V. K., “Trade-Off and Pecking Order Theories of Debt.” Eckbo, B.E., ed., “Handbook of Empirical Corporate Finance,” Handbooks in Finance, San Diego: Elsevier (2007), 135202.Google Scholar
Frank, M. Z., and Goyal, V. K.. “Capital Structure Decisions: Which Factors Are Reliably Important?Financial Management, 38 (2009), 137.10.1111/j.1755-053X.2009.01026.xCrossRefGoogle Scholar
Geske, R.The Valuation of Corporate Liabilities as Compound Options.” Journal of Financial and Quantitative Analysis, 12 (1977), 541552.CrossRefGoogle Scholar
Gilson, S. C.Transactions Costs and Capital Structure Choice: Evidence from Financially Distressed Firms.” Journal of Finance, 52 (1997), 161196.CrossRefGoogle Scholar
Glover, B.The Expected Cost of Default.” Journal of Financial Economics, 119 (2016), 284299.CrossRefGoogle Scholar
Goldstein, R.; Ju, N.; and Leland, H.. “An EBIT-Based Model of Dynamic Capital Structure.” Journal of Business, 74 (2001), 483512.10.1086/322893CrossRefGoogle Scholar
Graham, J. R.How Big Are the Tax Benefits of Debt?Journal of Finance, 55 (2000), 19011941.CrossRefGoogle Scholar
Graham, J. R., and Leary, M. T.. “A Review of Empirical Capital Structure Research and Directions for the Future.” Annual Review of Financial Economics, 3 (2011).10.1146/annurev-financial-102710-144821CrossRefGoogle Scholar
Hackbarth, D.; Hennessy, C. A.; and Leland, H. E.. “Can the Trade-Off Theory Explain Debt Structure?Review of Financial Studies, 20 (2007), 13891428.CrossRefGoogle Scholar
Hennessy, C. A., and Whited, T. M.. “How Costly Is External Financing? Evidence from a Structural Estimation.” Journal of Finance, 62 (2007), 17051745.CrossRefGoogle Scholar
Heston, S. L.A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options.” Review of Financial Studies, 6 (1993), 327343.CrossRefGoogle Scholar
Hong, H., and Sraer, D.. “Quiet Bubbles.” Journal of Financial Economics, 110 (2013), 596606.CrossRefGoogle Scholar
Hsu, J.; Saá-Requejo, J.; and Santa-Clara, P.. “A Structural Model of Default Risk.” Journal of Fixed Income, 19 (2010), 7794.CrossRefGoogle Scholar
Huang, J.-Z., and Huang, M.. “How Much of the Corporate-Treasury Yield Spread Is Due to Credit Risk?Review of Asset Pricing Studies, 2 (2012), 153202.10.1093/rapstu/ras011CrossRefGoogle Scholar
Huang, J.-Z., and Zhou, H.. “Specification Analysis of Structural Credit Risk Models.” Review of Finance, 24 (2020), 4598.Google Scholar
Hull, J., and White, A.. “The Pricing of Options on Assets with Stochastic Volatilities.” Journal of Finance, 42 (1987), 281300.CrossRefGoogle Scholar
Jensen, M. C., and Meckling, W. H.. “Theory of the Firm: Managerial Behavior, Agency Costs and Ownership Structure.” Journal of Financial Economics, 3 (1976), 305360.10.1016/0304-405X(76)90026-XCrossRefGoogle Scholar
Jones, E. P.; Mason, S. P.; and Rosenfeld, E.. “Contingent Claims Analysis of Corporate Capital Structures: An Empirical Investigation.” Journal of Finance, 39 (1984), 611625.CrossRefGoogle Scholar
Kisgen, D. J.Credit Ratings and Capital Structure.” Journal of Finance, 61 (2006), 10351072.CrossRefGoogle Scholar
Kisgen, D. J.Do Firms Target Credit Ratings or Leverage Levels?Journal of Financial and Quantitative Analysis, 44 (2009), 13231344.10.1017/S002210900999041XCrossRefGoogle Scholar
Korajczyk, R. A., and Levy, A.. “Capital Structure Choice: Macroeconomic Conditions and Financial Constraints.” Journal of Financial Economics, 68 (2003), 75109.CrossRefGoogle Scholar
Korteweg, A.The Net Benefits to Leverage.” Journal of Finance, 65 (2010), 21372170.CrossRefGoogle Scholar
Leland, H. E.Corporate Debt Value, Bond Covenants, and Optimal Capital Structure.” Journal of Finance, 49 (1994), 12131252.CrossRefGoogle Scholar
Leland, H. E.Agency Costs, Risk Management, and Capital Structure.” Journal of Finance, 53 (1998), 12131243.CrossRefGoogle Scholar
Leland, H. E., and Toft, K. B.. “Optimal Capital Structure, Endogenous Bankruptcy, and the Term Structure of Credit Spreads.” Journal of Finance, 51 (1996), 9871019.CrossRefGoogle Scholar
Lotfaliei, B.Zero Leverage and the Value in Waiting to Issue Debt.” Journal of Banking and Finance, 97 (2018), 335349.CrossRefGoogle Scholar
Luciano, E., and Nicodano, G.. “Guarantees, Leverage, and Taxes.” Review of Financial Studies, 27 (2014), 27362772.10.1093/rfs/hhu010CrossRefGoogle Scholar
McQuade, T.Stochastic Volatility and Asset Pricing Puzzles.” Working Paper, Stanford University (2018).CrossRefGoogle Scholar
Merton, R. C.On the Pricing of Corporate Debt: The Risk Structure of Interest Rates.” Journal of Finance, 29 (1974), 449470.Google Scholar
Modigliani, F., and Miller, M. H.. “The Cost of Capital, Corporation Finance and the Theory of Investment.” American Economic Review, 48 (1958), 261297.Google Scholar
Murfin, J., and Njoroge, K.. “The Implicit Costs of Trade Credit Borrowing by Large Firms.” Review of Financial Studies, 28 (2015), 112145.CrossRefGoogle Scholar
Myers, S. C.Still Searching for Optimal Capital Structure.” Journal of Applied Corporate Finance, 6 (1993), 414.CrossRefGoogle Scholar
Nickell, S.Biases in Dynamic Models with Fixed Effects.” Econometrica, 49 (1981), 14171426.10.2307/1911408CrossRefGoogle Scholar
Öztekin, Ö.Capital Structure Decisions Around the World: Which Factors Are Reliably Important?Journal of Financial and Quantitative Analysis, 50 (2015), 301323.10.1017/S0022109014000660CrossRefGoogle Scholar
Petersen, M. A.Estimating Standard Errors in Finance Panel Data Sets: Comparing Approaches.” Review of Financial Studies, 22 (2009), 435480.10.1093/rfs/hhn053CrossRefGoogle Scholar
Petersen, M. A., and Rajan, R. G.. “Trade Credit: Theories and Evidence.” Review of Financial Studies, 10 (1997), 661691.CrossRefGoogle Scholar
Rajan, R. G., and Zingales, L.. “What Do We Know About Capital Structure? Some Evidence from International Data.” Journal of Finance, 50 (1995), 14211460.CrossRefGoogle Scholar
Romano, M., and Touzi, N.. “Contingent Claims and Market Completeness in a Stochastic Volatility Model.” Mathematical Finance, 7 (1997), 399412.CrossRefGoogle Scholar
Sabanis, S.Stochastic Volatility and the Mean Reverting Process.” Journal of Futures Markets, 23 (2003), 3347.10.1002/fut.10044CrossRefGoogle Scholar
Schaefer, S. M., and Strebulaev, I. A.. “Structural Models of Credit Risk Are Useful: Evidence from Hedge Ratios on Corporate Bonds.” Journal of Financial Economics, 90 (2008), 119.CrossRefGoogle Scholar
Schwert, M., and Strebulaev, I. A.. “Capital Structure and Systematic Risk.” Working Paper #178, Stanford University (2014).CrossRefGoogle Scholar
Stein, E. M., and Stein, J. C.. “Stock Price Distributions with Stochastic Volatility: An Analytic Approach.” Review of Financial Studies, 4 (1991), 727752.10.1093/rfs/4.4.727CrossRefGoogle Scholar
Strebulaev, I. A.Do Tests of Capital Structure Theory Mean What They Say?Journal of Finance, 62 (2007), 17471787.CrossRefGoogle Scholar
Strebulaev, I. A., and Whited, T. M.. “Dynamic Models and Structural Estimation in Corporate Finance.” Foundations and Trends in Finance, 6 (2011).CrossRefGoogle Scholar
Strebulaev, I. A., and Whited, T. M.. “Dynamic Corporate Finance Is Useful: A Comment on Welch (2013).” Critical Finance Review, 2 (2013), 173191.CrossRefGoogle Scholar
Sundaresan, S.A Review of Merton’s Model of the Firm’s Capital Structure with Its Wide Applications.” Annual Review of Financial Economics, 5 (2013), 2141.CrossRefGoogle Scholar
Tahani, N.Exotic Options Pricing under Stochastic Volatility.” Working Paper 05-01, School of Administrative Studies, York University (2005).Google Scholar
Titman, S., and Wessels, R.. “The Determinants of Capital Structure Choice.” Journal of Finance, 43 (1988), 119.CrossRefGoogle Scholar
Welch, I.Capital Structure and Stock Returns.” Journal of Political Economy, 112 (2004), 106132.10.1086/379933CrossRefGoogle Scholar
Welch, I.A Critique of Recent Quantitative and Deep-Structure Modeling in Capital Structure Research and Beyond.” Critical Finance Review, 2 (2013), 131172.CrossRefGoogle Scholar
Wu, G.The Determinants of Asymmetric Volatility.” Review of Financial Studies, 14 (2001), 837859.CrossRefGoogle Scholar
Zhang, B. Y.; Zhou, H.; and Zhu, H.. “Explaining Credit Default Swap Spreads with the Equity Volatility and Jump Risks of Individual Firms.” Review of Financial Studies, 22 (2009), 50995131.CrossRefGoogle Scholar

Lotfaliei supplementary material

Online Appendices

PDF 591 KB

Full text views

Full text views reflects PDF downloads, PDFs sent to Google Drive, Dropbox and Kindle and HTML full text views.

Total number of HTML views: 0
Total number of PDF views: 223 *
View data table for this chart

* Views captured on Cambridge Core between 12th May 2020 - 15th April 2021. This data will be updated every 24 hours.

Send article to Kindle

To send this article to your Kindle, first ensure is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

Note you can select to send to either the or variations. ‘’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Asset Variance Risk Premium and Capital Structure
Available formats

Send article to Dropbox

To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

Asset Variance Risk Premium and Capital Structure
Available formats

Send article to Google Drive

To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

Asset Variance Risk Premium and Capital Structure
Available formats

Reply to: Submit a response

Your details

Conflicting interests

Do you have any conflicting interests? *