Abstract
A lockup period for investment in a hedge-fund is a time period after making the investment during which an investor cannot freely redeem his investment. Since long lockup periods have recently been imposed, it is important to estimate the premium an investor should expect from extended lockups. For this, Derman et al. (Wilmott J. 1(5–6):263–293, 2009) proposed a parsimonious three-state discrete-time Markov Chain (DTMC) to model the state of a hedge fund, allowing the state to change randomly among the states “good,” “sick” and “dead” every year. In this paper, we propose an alternative three-state absorbing continuous-time Markov Chain (CTMC) model, which allows state changes continuously in time instead of yearly. Allowing more dynamic state changes is more realistic, but the CTMC model requires new techniques for parameter fitting. We employ nonlinear programming to solve the new calibration equations. We show that the more realistic CTMC model is a viable alternative to the previous DTMC model for estimating the premium for extended hedge fund lockups.
Similar content being viewed by others
References
Agarwal, V., & Naik, N. Y. (2000). Multi-period performance persistence analysis of hedge funds. Journal of Financial and Quantitative Analysis, 35(3), 327–342.
Ahmed, A. (2011). Many hedge funds still smarting from the financial crisis. The New York Times, April 6.
Aigner, P., Beyschlag, G., Frederich, T., Kalepky, M., & Zagst, R. (2012). Modeling and managing portfolios including listed private equity. Computers & Operations Research, 39(4), 753–764.
Al Janabi, M. A. M. (2013). Optimal and coherent economic-capital structures: evidence from long and short-sales trading positions under illiquid market perspectives. Annals of Operations Research, 205(1), 109–139.
Anderson, E., Bai, Z., Bischof, C., Blackford, S., Demmel, J., Dongarra, J., Du Croz, J., Greenbaum, A., Hammarling, S., McKenney, A., & Sorensen, D. (1999). LAPACK user’s guide (3rd ed.). Philadelphia: SIAM.
Ang, A., & Bollen, N. P. B. (2009). Lockup up by a lockup: valuing liquidity as a real option. Financial Management, 39(3), 1069–1095.
Aragon, G. (2007). Share restrictions and asset pricing: evidence from the hedge fund industry. Journal of Financial Economics, 83(1), 33–58.
Ben-David, I., Franzoni, F., & Moussawi, R. (2012). Hedge fund stock trading in the financial crisis of 2007–2008. The Review of Financial Studies, 25(1), 1–54.
Boyle, P., Li, S., & Zhu, Y. (2010). Hedge fund redemption restrictions, financial crisis, and fund performance (Working paper). Wilfrid Laurier University.
Boyson, N., Stulz, R., & Stahel, C. (2010). Hedge fund contagion and liquidity shocks. The Journal of Finance, 65(5), 1789–1816.
Browne, S. J., Milevsky, M. A., & Salisbury, T. S. (2003). Asset allocation and the liquidity premium for illiquid annuities. The Journal of Risk and Insurance, 70(3), 509–526.
De Roon, F. A., Guo, J., & ter Horst, J. R. (2009). Being locked up hurts (SSRN Working paper).
Derman, E., Park, K. S., & Whitt, W. (2009). Markov chain models to estimate the premium for the extended hedge fund lockup. Wilmott Journal, 1(5–6), 263–293. Available at http://www.columbia.edu/~ww2040/allpapers.html.
Derman, E., Park, K. S., & Whitt, W. (2010). A stochastic-difference-equation model for hedge-fund relative returns. Quantitative Finance, 10(7), 701–733.
Edwards, F. R., & Caglayan, M. O. (2001). Hedge fund performance and manager skill. The Journal of Futures Markets, 21(11), 1003–1028.
Golts, M., & Kritzman, M. (2010). Liquidity options. The Journal of Derivatives, 18(1), 80–89.
Hull, J. C. (2003). Options, futures, and other derivatives (5th ed.). New York: Prentice-Hall.
Jagannathan, R., Malakhov, A., & Nonikov, D. (2010). Do hot hands persist among hedge fund managers? An empirical evaluation. The Journal of Finance, 65(1), 217–255.
Karlin, S., & Taylor, H. M. (1975). A first course in stochastic processes. San Diego: Academic Press.
Kazemi, H. (2010). Asset allocation and illiquidity risk. CAIA Association.
Koh, F., Koh, W. T. H., & Teo, M. (2003). Asian hedge funds: return persistence style and fund characteristics (Working Paper). Singapore Management University.
Longstaff, F. A. (1995). How much can marketability affect security values? The Journal of Finance, 50(5), 1767–1774.
Longstaff, F. A. (2001). Optimal portfolio choice and the valuation of illiquid securities. The Review of Financial Studies, 14(2), 407–431.
Park, H. (2007). Risk measures for hedge funds and a survival analysis. Ph.D thesis, University of Massachusetts.
Ross, S. M. (2003). Introduction to probability models (8th ed.). San Diego: Academic Press.
Rouah, F. (2006). Competing risks in hedge fund survival. Ph.D thesis, McGill University.
Schittkowski, K. (1986). Nlqpl: a Fortran-subroutine solving constrained nonlinear programming problems. Annals of Operations Research, 5(2), 485–500.
Stoyanov, S. V., Rachev, S. T., & Fabozzi, F. J. (2013). Sensitivity of portfolio VaR and CVaR to portfolio return characteristics. Annals of Operations Research, 205(1), 169–187.
Wahab, M. I. M., & Lee, C.-G. (2011). Pricing swing options with regime switching. Annals of Operations Research, 185(1), 139–160.
Wu, D., & Olson, D. L. (2010a). Enterprise risk management: coping with model risk in a large bank. Journal of the Operational Research Society, 61(2), 179–190.
Wu, D. D., & Olson, D. (2010b). Enterprise risk management: a DEA VaR approach in vendor selection. International Journal of Production Research, 48(16), 4919–4932.
Acknowledgements
The authors thank Emanuel Derman for suggesting the lockup premium problem and for his helpful comments on this paper. The second author acknowledges support from NSF grants DMI-0457095 and CMMI-0948190.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Park, K.S., Whitt, W. Continuous-time Markov chain models to estimate the premium for extended hedge fund lockups. Ann Oper Res 211, 357–379 (2013). https://doi.org/10.1007/s10479-013-1496-z
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10479-013-1496-z