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Dynamic Asset Allocation Techniques

Published online by Cambridge University Press:  12 March 2012

S. Jarvis ,
A. Lawrence  and
S. Miao
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Abstract

Investment strategy is often static, punctuated by infrequent reviews. For most long-term investors, this practice results in large risks being taken that could otherwise be managed with a more dynamic investment policy. The bulk of this paper is aimed at analysing and describing two multi-period investment strategy problems — in order to derive potential dynamic strategies. Along the way, we show how static investment strategies can fail to deliver an investor's long-term objectives and describe the relationship of our work to other areas of the finance literature. This paper does not cover trading strategies such as Tactical Asset Allocation.

This paper sets out two main approaches to the multi-period problem. The first approach optimises a utility function. The second approach uses partial differential equation (PDE) technology to optimise a target statistic (in this case, TailVaR) subject to return and long-only constraints.

Keywords

Investment StrategyStochastic ModellingDynamic ProgrammingMulti-Period OptimisationTail VaRUtility
Type
Sessional meetings: papers and abstracts of discussions
Information
British Actuarial Journal , Volume 15 , Issue 3 , September 2009 , pp. 573 - 655
Copyright
Copyright © Institute and Faculty of Actuaries 2009

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References

Acerbi, C. & Tasche, D. (2002). On the coherence of expected shortfall. Journal of Banking and Finance, 26, 1487–1503.CrossRefGoogle Scholar
Artzner, P., Delbaen, F., Eber, J.M. & Heath, D. (1997). Thinking coherently. Risk, 10, November, 68–71.Google Scholar
Artzner, P., Delbaen, F., Eber, J.M. & Heath, D. (1999). Coherent measures of risk. Mathematical Finance, 9(3), 203–228.Google Scholar
Artzner, P. (2002). Conditional value at risk: is it good in the multiperiod case? IIR Conference on volatility and risk, London, February 2002.Google Scholar
Artzner, P., Delbaen, F., Eber, J.M., Heath, D. & Ku, H. (2007). Coherent multiperiod risk adjusted values and Bellman' principle. Annals of Operations Research, 152, 5–22.CrossRefGoogle Scholar
Barnes, M., Chambers, A., Earnshaw, A., Jarvis, S.J., McMahon, R. & Ridges, P. (2008). Controlling the growth of your hedge. Presented to the Finance Investment and Risk Management Conference, Manchester, June 2008.Google Scholar
Bellman, R. (1957). Dynamic programming. Princeton University Press.Google Scholar
Black, F. & Perold, A. (1992). Theory of constant proportion portfolio insurance. Journal of Economic Dynamics and Control, 16, 403–426.CrossRefGoogle Scholar
Box, G.E.P. & Draper, N.R. (1987). Empirical model-building and response surfaces. Wiley. ISBN 0471810339Google Scholar
Boyle, P., Hardy, M. & Vorst, T. (2005). Life after VaR. Journal of Derivatives, 13, 48–55.CrossRefGoogle Scholar
Cairns, A.J.G. (2000). Some notes on the dynamics and optimal control of stochastic pension fund models in continuous time ASTIN Bulletin 30: 19–55. Available, with erratum, at http://www.ma.hw.ac.uk/~andrewc/papers/Google Scholar
Chapman, R.J., Gordon, T.J. & Speed, C.A. (1999). Pensions, funding and risk. British Actuarial Journal, 7(4), 605–662.CrossRefGoogle Scholar
Cheridito, P., Delbaen, F. & Kupper, M. (2006). Dynamic monetary risk measures for bounded discrete-time processes. Electronic Journal of Probability, 11, 57–106.CrossRefGoogle Scholar
Clewlow, L. & Strickland, C. (1998). Implementing derivatives models. Wiley.Google Scholar
Cox, J. & Huang, C.F. (1989). Optimal consumption and portfolio policies when asset prices follow a diffusion process. Journal of Economic Theory, 49, 33–83.CrossRefGoogle Scholar
Cox, J.C., Ross, S.A. & Rubinstein, M. (1979). Option pricing: a simplified approach. Journal of Financial Economics, 7, 229–263.CrossRefGoogle Scholar
Crank, J. & Nicolson, P. (1947). A practical method for numerical evaluation of solutions of partial differential equations of the heat conduction type. Proceedings of the Cambridge Philosophical Society, 43, 50–67.CrossRefGoogle Scholar
Dempster, M.A.H., Germano, M., Medova, E.A. & Villaverde, M. (2003). Global assetliability management. British Actuarial Journal, 9, 137–216.CrossRefGoogle Scholar
Derman, E. & Kani, I. (1994). The volatility smile and its implied tree. Goldman Sachs, January 1994.Google Scholar
Duffie, D. (2001). Dynamic asset pricing theory, 3rd edition. Princeton University Press.Google Scholar
Duffy, D.J. (2006). Finite difference methods in financial engineering. Wiley.Google Scholar
Dupire, B. (1994). Pricing with a smile. Risk, January 1994.Google Scholar
Exley, C.J., Mehta, S.J.B. & Smith, A.D. (1997). The financial theory of defined benefit pension schemes. British Actuarial Journal, 3, 835–966.CrossRefGoogle Scholar
Gabih, A. & Wunderlich, R. (2004). Optimal portfolios with bounded shortfall risks. In vom Scheidt, J. & Richter, M. (eds). Tagungsband zum Workshop ‘Stochastische Analysis’ (21–42). TU Chemnitz, Fakultät für Mathematik.Google Scholar
Gandy, R. (2005). Portfolio optimization with risk constraints. PhD-Dissertation, Universität Ulm.Google Scholar
Goetzmann, W., Ingersoll, J., Spiegel, M. & Welch, I. (2002). Sharpening Sharpe ratios. NBER Working Paper No. 9116.Google Scholar
Henderson, V. & Hobson, D. (2007). Horizon-unbiased utility functions. Stochastic processes and their applications, 117, 1621–1641.Google Scholar
Jarvis, S.J., Southhall, F. & Varnell, E. (2001). Modern valuation techniques. Presented to Staple Inn Actuarial Society.Google Scholar
Karatzas, I., Lehoczky, J. & Shreve, S. (1987). Optimal portfolio and consumption decisions for a ‘small investor’ on a finite horizon. SIAM Journal of Control and Optimisation, 25, 1157–1186.Google Scholar
Karatzas, I. & Shreve, S.E. (1998). Methods of mathematical finance, Springer, New York.Google Scholar
Kemp, M.H.D. (1996). Asset/liability modelling for pension funds. Staple Inn Actuarial Society.Google Scholar
Kupper, M. & Schachermeyer, W. (2009). Representation results for law-invariant time consistent functions. Mathematics and Financial Economics, 2, 189–210.CrossRefGoogle Scholar
Leland, H.E. (1980). Who should buy portfolio insurance? Journal of Finance, 35(2), 581–594.CrossRefGoogle Scholar
Martellini, L. & Milhau, V. (2009). Measuring the benefits of dynamic asset allocation strategies in the presence of liability constraints. EDHEC, March 2009.Google Scholar
Merton, R. (1969). Lifetime portfolio selection under uncertainty: the continuous-time case. Review of Economics and Statistics, 51(3), 247–257.CrossRefGoogle Scholar
Merton, R. (1971). Optimum consumption and portfolio rules in a continuous-time model. Journal of Economic Theory, 3, 373–413.CrossRefGoogle Scholar
Nielsen, P.H. (2006). Optimal investment strategies: a short survey of classical and recent results. Presented to the International Congress of Actuaries.Google Scholar
Pflug, G.Ch. (2000). Some remarks on the Value-at-Risk and the conditional Value-at-Risk. In Uryasev, S. (ed.). Probabilistic constrained optimization: methodology and applications. Kluwer Academic Publishers, 2000.Google Scholar
Rockafellar, R.T. (2001). Optimisation under uncertainty. University of Washington lecture notes. Available at http://www.math.washington.edu/~rtr/uncertainty.pdfGoogle Scholar
Rockafellar, R.T. & Uryasev, S. (2000). Optimization of conditional Value-At-Risk. The Journal of Risk, 2(3), 21–41.CrossRefGoogle Scholar
Rogers, L.C.G. (2003). Duality in constrained optimal investment and consumption problems: a synthesis. Paris-Princeton Lectures on Mathematical Finance 2002, (Springer Lecture Notes in Mathematics 1814), 95–131.Google Scholar
Rom, B.M. & Ferguson, K. (1994). Post-modern portfolio theory comes of age. 4th AFIR International Colloquium, 349–364.Google Scholar
Roorda, B. & Schumacher, J.M. (2007). Time consistency conditions for acceptability measures, with an application to tail value at risk. Insurance: Mathematics and Economics, 40, 209–230.Google Scholar
Roorda, B., Schumacher, J.M. (2010). When can a risk measure be updated consistently? Preprint.Google Scholar
Ross, S. (1976). The arbitrage theory of capital asset pricing. Journal of Economic Theory, 13(3), 341–360.CrossRefGoogle Scholar
Samuelson, P.A. (1969). Lifetime portfolio selection by dynamic stochastic programming. Review of Economics and Statistics, 51, 239–246.CrossRefGoogle Scholar
Seydel, R. (2009). Tools for Computational Finance (4th edition). Springer.Google Scholar
Sharpe, W.F. (1964). Capital asset prices: a theory of market equilibrium under conditions of risk, Journal of Finance, 19(3), 425–442.Google Scholar
Smith, A.D. (1996). How actuaries can use financial economics. British Actuarial Journal, 2, 1057–1193.CrossRefGoogle Scholar
Uryasev, S. (2000). Conditional Value-at-Risk: optimization algorithms and applications. Financial Engineering News, 14 (February), 1–5.Google Scholar