Journal of Applied Probability

Optimal closing of a momentum trade

Erik Ekström and Carl Lindberg

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

There is an extensive academic literature that documents that stocks which have performed well in the past often continue to perform well over some holding period - so-called momentum. We study the optimal timing for an asset sale for an agent with a long position in a momentum trade. The asset price is modelled as a geometric Brownian motion with a drift that initially exceeds the discount rate, but with the opposite relation after an unobservable and exponentially distributed time. The problem of optimal selling of the asset is then formulated as an optimal stopping problem under incomplete information. Based on the observations of the asset, the agent wants to detect the unobservable change point as accurately as possible. Using filtering techniques and stochastic analysis, we reduce the problem to a one-dimensional optimal stopping problem, which we solve explicitly. We also show that the optimal boundary at which the investor should liquidate the trade depends monotonically on the model parameters.

Article information

Source
J. Appl. Probab. Volume 50, Number 2 (2013), 374-387.

Dates
First available in Project Euclid: 19 June 2013

Permanent link to this document
https://projecteuclid.org/euclid.jap/1371648947

Digital Object Identifier
doi:10.1239/jap/1371648947

Mathematical Reviews number (MathSciNet)
MR3102486

Zentralblatt MATH identifier
1266.91095

Subjects
Primary: 91G10: Portfolio theory
Secondary: 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60]

Keywords
Optimal stopping momentum trading quickest detection problem for Brownian motion

Citation

Ekström, Erik; Lindberg, Carl. Optimal closing of a momentum trade. J. Appl. Probab. 50 (2013), no. 2, 374--387. doi:10.1239/jap/1371648947. https://projecteuclid.org/euclid.jap/1371648947


Export citation

References

  • Beibel, M. and Lerche, H. R. (1997). A new look at optimal stopping problems related to mathematical finance. Statistica Sinica 7, 93–108.
  • Blitz, D. C. and Vliet, P. (2008). Global tactical cross-asset allocation: applying value and momentum across asset classes. J. Portfolio Manag. 35, 23–38.
  • Borodin, A. N. and Salminen, P. (2002). Handbook of Brownian Motion–-Facts and Formulae, 2nd edn. Birkhäuser, Basel.
  • Connolly, R. and Stivers, C. (2003). Momentum and reversals in equity-index returns during periods of abnormal turnover and return dispersion. J. Finance 58, 1521–1556.
  • Cooper, M. J., Gutierrez, R. C., Jr. and Hameed, A. (2004). Market states and momentum. J. Finance 59, 1345–1365.
  • Du Toit, J. and Peskir, G. (2009). Selling a stock at the ultimate maximum. Ann. Appl. Prob. 19, 983–1014.
  • Ekström, E. and Lu, B. (2011). Optimal selling of an asset under incomplete information. Internat. J. Stoch. Anal. 2011, 17pp.
  • Figelman, I. (2007). Stock return momentum and reversal. J. Portfolio Manag. 34, 51–67.
  • Gebhardt, W. R., Hvidkjaer, S. and Swaminathan, B. (2005). Stock and bond market interaction: does momentum spill over? J. Financial Econom. 75, 651–690.
  • George T. J. and Hwang, C.-Y. (2004). The 52-week high and momentum investing. J. Finance 59, 2145–2176.
  • Graversen, S. E., Peskir, G. and Shiryaev, A. N. (2001). Stopping Brownian motion without anticipation as close as possible to its ultimate maximum. Theory Prob. Appl. 45, 41–50.
  • Griffin, J. M., Ji, X. and Martin, J. S. (2003). Momentum investing and business cycle risk: evidence from pole to pole. J. Finance 58, 2515–2547.
  • Grundy, B. D. and Martin, J. S. (2001). Understanding the nature of the risks and the source of the rewards to momentum investing. Rev. Financial Studies 14, 29–78.
  • Gutierrez, R. C., Jr. and Kelley, E. K. (2008). The long-lasting momentum in weekly returns. J. Finance 63, 415-447.
  • Hogan, S., Jarrow, R., Melvyn, T. and Warachka, M. (2003). Testing market efficiency using statistical arbitrage with applications to momentum and value strategies. J. Financial Econom. 73, 525–565.
  • Jegadeesh, N. and Titman, S. (1993). Returns to buying winners and selling losers: implications for stock market efficiency. J. Finance 48, 65–91.
  • Jegadeesh, N. and Titman, S. (1995). Overreaction, delayed reaction, and contrarian profits. Rev. Financial Studies 8, 973–993.
  • Jegadeesh, N. and Titman, S. (2001). Profitability of momentum strategies: an evaluation of alternative explanations. J. Finance 56, 699–720.
  • Jegadeesh, N. and Titman, S. (2002). Cross-sectional and time-series determinants of momentum returns. Rev. Financial Studies 15, 143–157.
  • Karatzas, I. and Shreve, S. E. (1998). Methods of Mathematical Finance (Appl. Math. 39). Springer, New York.
  • Karatzas, I. and Shreve, S. E. (2000). Brownian Motion and Stochastic Calculus, 2nd edn. Springer, New York.
  • Klein, M. (2009). Comment on "Investment timing under incomplete information". Math. Operat. Res. 34, 249–254.
  • Korajczyk, R. A. and Sadka, R. (2004). Are momentum profits robust to trading costs? J. Finance 59, 1039–1082.
  • Lee, C. M. C. and Swaminathan, B. (2000). Price momentum and trading volume. J. Finance 55, 2017–2069.
  • Lewellen, J. (2002). Momentum and autocorrelation in stock returns. Rev. Financial Studies 15, 533–564.
  • Liptser, R. S. and Shiryaev, A. N. (1977). Statistics of Random Processes. I. Springer, New York.
  • Liu, L. X. and Zhang, L. (2009). Momentum profits, factor pricing, and macroeconomic risk. Rev. Financial Studies 21, 2417–2448.
  • Moskowitz, T. J. and Grinblatt, M. (1999). Do industries explain momentum? J. Finance 54, 1249–1290.
  • Oksendal, B. (2003). Stochastic Differential Equations, 6th edn. Springer, Berlin.
  • Peskir, G. and Shiryaev, A. (2006). Optimal Stopping and Free-Boundary Problems. Birkhäuser, Basel.
  • Rouwenhorst, K. G. (1998). International momentum strategies. J. Finance 53, 267–284.
  • Shiryaev, A. N. (1978). Optimal Stopping Rules. Springer, New York.
  • Shiryaev, A. N. (2002). Quickest detection problems in the technical analysis of the financial data. In Mathematical Finance–-Bachelier Congress (Paris, 2000), Springer, Berlin, pp. 487–521.
  • Shiryaev, A. N. and Novikov, A. A. (2008). On a stochastic version of the trading rule "Buy and Hold". Statist. Decisions 26, 289–302.
  • Shiryaev, A., Xu, Z. and Zhou, X. Y. (2008). Thou shalt buy and hold. Quant. Finance 8, 765–776.
  • Stojanovic, S. (2004/05). Optimal momentum hedging via hypoelliptic reduced Mone-Ampère PDEs. SIAM J. Control Optimization 43, 1151–1173.
  • Villeneuve, S. (2007). On threshold strategies and the smooth-fit principle for optimal stopping problems. J. Appl. Prob. 44, 181–198.