Journal of Asset Management

, Volume 11, Issue 2–3, pp 94–112 | Cite as

Backtesting short-term treasury management strategies based on multi-stage stochastic programming

  • Robert Ferstl
  • Alex Weissensteiner
Original Article


We show the practical viability of a short-term treasury management model which is formulated as a multi-stage stochastic linear program. A company minimises the Conditional Value at Risk of final wealth, subject to given future cash flows and the uncertain future development of interest rates and equity returns, choosing an asset allocation among cash, several bonds and an equity investment. The scenario generation procedure includes an estimation of the market price of risk and a change of the underlying probability measure. We provide an out-of-sample backtest for the proposed policy and compare the performance to alternative strategies. Our approach shows a better risk-return trade-off for different aggregated risk measures. Further, we perform several numerical studies based on a real market data set to test for the sensitivity to changes in the input parameters, for example shifts of the yield curve, changes in the equity spread or the cash flows. The resulting portfolios are well-diversified and the impact on the asset allocation follows economic intuition.


dynamic stochastic optimisation treasury management market price of risk change of measure scenario generation 


  1. Ang, A. and Bekaert, G. (2007) Stock return predictability: Is it there? The Review of Financial Studies 20: 651–707.CrossRefGoogle Scholar
  2. Barberis, N.C. (2000) Investing for the long run when returns are predictable. The Journal of Finance 55: 225–264.CrossRefGoogle Scholar
  3. Baumol, W.J. (1952) The transactions demand for cash: An inventory theoretic approach. The Quarterly Journal of Economics 66 (4): 545–556.CrossRefGoogle Scholar
  4. Bernaschi, M., Torosantucci, L. and Uboldi, A. (2007) Empirical evaluation of the market price of risk using the CIR model. Physica A: Statistical and Theoretical Physics 376: 543–554.CrossRefGoogle Scholar
  5. Bertocchi, M., Moriggia, V. and Dupacova, J. (2000) Sensitivity of bond portfolio's behavior with respect to random movements in yield curve: A simulation study. Annals of Operations Research 99 (1–4): 267–286.CrossRefGoogle Scholar
  6. Bertocchi, M., Moriggia, V. and Dupacova, J. (2006) Horizon and stages in applications of stochastic programming in finance. Annals of Operations Research 142 (1): 63–78.CrossRefGoogle Scholar
  7. Black, F. (1976) The pricing of commodity contracts. Journal of Financial Economics 3: 167–179.CrossRefGoogle Scholar
  8. Black, F., Derman, E. and Toy, W. (1990) A one-factor model of interest rates and its applications to treasury bond options. Financial Analysts’ Journal 46: 33–39.CrossRefGoogle Scholar
  9. Bradley, S.P. and Crane, D.B. (1972) A dynamic model for bond portfolio management. Management Science 19 (2): 139–151.CrossRefGoogle Scholar
  10. Brandt, M.W., Goyal, A., Santa-Clara, P. and Stroud, J.R. (2005) A simulation approach to dynamic portfolio choice with an application to learning about return predictability. The Review of Financial Studies 18 (3): 831–873.CrossRefGoogle Scholar
  11. Brigo, D. and Mercurio, F. (2006) Interest Rate Models – Theory and Practice: With Smile, Inflation and Credit, 2nd edn., Springer Finance. New York: Springer.Google Scholar
  12. Castro, J. (2007) A stochastic programming approach to cash management in banking. European Journal of Operational Research 192 (3): 963–974.CrossRefGoogle Scholar
  13. Chambers, D. and Charnes, A. (1961) Inter-temporal analysis and optimization of bank portfolios. Management Science 7 (4): 393–410.CrossRefGoogle Scholar
  14. Charnes, A., Cooper, W.W. and Miller, M.H. (1959) Application of linear programming to financial budgeting and the costing of funds. The Journal of Business 32 (1): 20–46.CrossRefGoogle Scholar
  15. Cochrane, J.H. (2008) The dog that did not bark: A defense of return predictability. The Review of Financial Studies 21: 1533–1575.CrossRefGoogle Scholar
  16. Cohen, K.J. and Hammer, F.S. (1967) Linear programming and optimal bank asset management decisions. The Journal of Finance 22 (2): 147–165.CrossRefGoogle Scholar
  17. Dempster, M., Pflug, G. and Mitra, G. (2009) Quantitative Fund Management, Financial Mathematics Series. Boca Raton, FL: Chapman & Hall/CRC.Google Scholar
  18. Dempster, M.A.H., Germano, M., Medova, E.A., Rietbergen, M.I., Sandrini, F. and Scrowston, M. (2007) Designing minimum guaranteed return funds. Quantitative Finance 7 (2): 245–256.CrossRefGoogle Scholar
  19. Dempster, M.A.H., Germano, M., Medova, E.A. and Villaverde, M. (2003) Global asset liability management. British Actuarial Journal 9 (1): 137–195.CrossRefGoogle Scholar
  20. Dupacova, J. (2000) Stability properties of a bond portfolio management problem. Annals of Operations Research 99 (1–4): 251–265.CrossRefGoogle Scholar
  21. Dupacova, J. and Bertocchi, M. (2001) From data to model and back to data: A bond portfolio management problem. European Journal of Operational Research 134 (2): 261–278.CrossRefGoogle Scholar
  22. Ferstl, R. and Weissensteiner, A. (2010) Cash management using multi-stage stochastic programming. Quantitative Finance 10 (2): 209–219.CrossRefGoogle Scholar
  23. Geyer, A. and Ziemba, W.T. (2008) The innovest Austrian pension fund financial planning model InnoALM. Operations Research 56 (4): 797–810.CrossRefGoogle Scholar
  24. Golub, B., Holmer, M., McKendall, R., Pohlman, L. and Zenios, S.A. (1995) A stochastic programming model for money management. European Journal of Operational Research 85 (2): 282–296.CrossRefGoogle Scholar
  25. Gondzio, J. and Kouwenberg, R. (2001) High-performance computing for asset-liability management. Operations Research 49 (6): 879–891.CrossRefGoogle Scholar
  26. Høyland, K. and Wallace, S.W. (2007) Chapter 13: Stochastic programming models for strategic and tactical asset allocation – A study from Norwegian life insurance. In: S.A. Zenios and W.T. Ziemba (eds.) Handbook of Asset and Liability Management, Volume 2: Applications and Case Studies. Amsterdam, Netherlands: Elsevier, pp. 591–625.Google Scholar
  27. Jobst, N.J., Mitra, G. and Zenios, S.A. (2006) Integrating market and credit risk: A simulation and optimisation perspective. Journal of Banking & Finance 30 (2): 717–742.CrossRefGoogle Scholar
  28. Jobst, N.J. and Zenios, S.A. (2005) On the simulation of portfolios of interest rate and credit risk sensitive securities. European Journal of Operational Research 161 (2): 298–324.CrossRefGoogle Scholar
  29. Klaassen, P. (2002) Comment on ‘generating scenario trees for multistage decision problems’. Management Science 48: 1512–1516.CrossRefGoogle Scholar
  30. Kusy, M.I. and Ziemba, W.T. (1986) A bank asset and liability management model. Operations Research 34 (3): 356–376.CrossRefGoogle Scholar
  31. Michaud, R.O. (2003) A practical framework for portfolio choice. Journal of Investment Management 1 (2): 14–29.Google Scholar
  32. Mulvey, J.M. and Zenios, S.A. (1994) Capturing the correlations of fixed-income instruments. Management Science 40 (10): 1329–1342.CrossRefGoogle Scholar
  33. Pflug, G.C. (2000) Some remarks on the value-at-risk and the conditional value-at-risk. In: S.P. Uryasev (ed.) Probabilistic Constrained Optimization – Methodology and Applications. Dordrecht, Netherlands: Kluwer Academic Publishers, pp. 272–281.CrossRefGoogle Scholar
  34. Poulsen, R. and Rasmussen, K.M. (2008) Financial Giffen goods: Examples and counterexamples. European Journal of Operational Research 191 (2): 572–576.CrossRefGoogle Scholar
  35. Rebonato, R. (2004) Volatility and Correlation in the Pricing of Equity, FX and Interest-Rate Options. West Sussex, England: John Wiley & Sons.Google Scholar
  36. Rockafellar, R.T. and Uryasev, S. (2000) Optimization of conditional value-at-risk. Journal of Risk 2 (3): 21–41.CrossRefGoogle Scholar
  37. Rockafellar, R.T. and Uryasev, S. (2002) Conditional value-at-risk for general loss distributions. Journal of Banking & Finance 26 (7): 1443–1471.CrossRefGoogle Scholar
  38. Stanton, R. (1997) A nonparametric model of term structure dynamics and the market price of interest rate risk. The Journal of Finance 52 (5): 1973–2002.CrossRefGoogle Scholar
  39. Topaloglou, N., Vladimirou, H. and Zenios, S.A. (2008) A dynamic stochastic programming model for international portfolio management. European Journal of Operational Research 185 (3): 1501–1524.CrossRefGoogle Scholar
  40. Volosov, K., Mitra, G., Spagnolo, F. and Lucas, C. (2005) Treasury management model with foreign exchange exposure. Computational Optimization and Applications 32: 179–207.CrossRefGoogle Scholar
  41. Wachter, J. (2002) Portfolio and consumption decisions under mean-reverting returns: An exact solution. Journal of Financial and Quantitative Analysis 37 (1): 63–91.CrossRefGoogle Scholar

Copyright information

© Palgrave Macmillan, a division of Macmillan Publishers Ltd 2010

Authors and Affiliations

  • Robert Ferstl
  • Alex Weissensteiner
    • 1
  1. 1.Free University of Bolzano/Bozen, School of Economics and Management, Universitätsplatz 1Italy

Personalised recommendations