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Back-testing the performance of an actively managed option portfolio at the Swedish stock market, 1990-1999. (English) Zbl 1178.91174
Summary: We build an investment model based on stochastic programming. In the model we buy at the ask price and sell at the bid price. We apply the model to a case where we can invest in a Swedish stock index, call options on the index and the risk-free asset. By re-optimizing the portfolio on a daily basis over a ten-year period, it is shown that options can be used to create a portfolio that outperforms the index. With ex post analysis, it is furthermore shown that we can create a portfolio that dominates the index in terms of mean and variance, i.e. at given level of risk we could have achieved a higher return using options.

MSC:
91G10 Portfolio theory
91G20 Derivative securities (option pricing, hedging, etc.)
90C15 Stochastic programming
Software:
RiskMetrics
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[1] Birge, J.R.; Louveaux, F., Introduction to stochastic programming, (1997), Springer New York · Zbl 0892.90142
[2] Black, F.; Scholes, M., The pricing of options and corporate liabilities, Journal of political economy, 81, 637-654, (1973) · Zbl 1092.91524
[3] Blomvall, J., Lindberg, P.O., 2000a. A Riccati-based primal interior point solver for multistage stochastic programming. Technical Report LiTH-MAT-R-2000-28, Department of Mathematics, Linköping University, Sweden, to appear in European Journal of Operational Research. · Zbl 1058.90074
[4] Blomvall, J., Lindberg, P.O., 2000b. Validation of a Riccati-based primal interior point solver for multistage stochastic programming. Technical Report LiTH-MAT-R-2000-29, Department of Mathematics, Linköping University, Sweden. · Zbl 1058.90074
[5] Cagan, L.; Carriero, N.; Zenios, S., A computer network approach to pricing mortgage-backed securities, Financial analysts journal, 49, 55-62, (1993)
[6] Cariño, D.; Myers, D.; Ziemba, W., Concepts, technical issues, and uses of the russell – yasuda kasai financial planning model, Operations research, 46, 450-462, (1998) · Zbl 0993.91502
[7] Cariño, D.; Turner, A., Multiperiod asset allocation with derivative assets, (), 182-204 · Zbl 0942.91043
[8] Cariño, D.; Ziemba, W., Formulation of the russell – yasuda kasai financial planning model, Operations research, 46, 433-449, (1998) · Zbl 0993.91503
[9] Chopra, V.; Ziemba, W., The effects of errors in means, variances, and covariances on optimal portfolio choice, Journal of portfolio management, 19, 6-11, (1993)
[10] Fama, E., The behavior of stock-market prices, Journal of business, 38, 34-105, (1965)
[11] Golub, B.; Holmer, M.; McKendall, R.; Pohlman, L.; Zenios, S., A stochastic programming model for money management, European journal of operations research, 85, 282-296, (1995) · Zbl 0912.90020
[12] Gondzio, J., Kouwenberg, R., Vorst, T., 2002. Hedging options under transaction costs and stochastic volatility. Journal of Economic Dynamics & Control, this issue. · Zbl 1178.91196
[13] Grauer, R.; Hakansson, N., Returns on levered, actively managed long-run portfolios of stocks, bonds and bills, 1934-1983, Financial analysts journal, 41, 24-43, (1985)
[14] Grauer, R.; Hakansson, N., A half century of returns on levered and unlevered portfolios of stocks, bonds and bills, with and without small stocks, Journal of business, 59, 287-318, (1986)
[15] Grauer, R.; Hakansson, N., Gains from international diversification: 1968-85 returns on portfolios of stocks and bonds, Journal of finance, 42, 721-739, (1987)
[16] Grauer, R.; Hakansson, N., On the use of mean – variance and quadratic approximations in implementing dynamic investment strategies: a comparison of returns and investment policies, Management science, 39, 856-871, (1993)
[17] Hodges, S., 1998. A generalization of the sharpe ratio and its applications to valuation bounds and risk measures. Technical Paper 88, University of Warwick.
[18] Holmer, M., The asset – liability management strategy system at fannie mae, Interfaces, 24, 3-21, (1994)
[19] Kelly, J.L., A new interpretation of information rate, Bell system technical journal, 35, 917-926, (1956)
[20] Li, Y., Growth – security investment strategy for long and short runs, Management science, 39, 915-924, (1993) · Zbl 0785.90016
[21] Long, J., The numeraire portfolio, Journal of financial economics, 26, 29-69, (1990)
[22] MacLean, L.; Ziemba, W., Growth versus security in a risky investment model, (), 78-87 · Zbl 0581.90005
[23] MacLean, L.; Ziemba, W., Growth – security profiles in capital accumulation under risk, Annals of operations research, 31, 501-509, (1991) · Zbl 0741.90008
[24] MacLean, L.; Ziemba, W.; Blazenko, G., Growth versus security in dynamic investment analysis, Management science, 38, 1562-1585, (1992) · Zbl 0765.90014
[25] Markowitz, H., Portfolio selection: efficient diversification of investments, (1972), Wiley New York
[26] Markowitz, H., Investment for the long run: new evidence for an old rule, Journal of finance, 31, 1273-1286, (1976)
[27] Mulvey, J., An asset – liability investment system, Interfaces, 24, 22-33, (1994)
[28] Mulvey, J., 1994b. Financial planning via multi-stage stochastic programs. In: Birge, J., Murty, K. (Eds.), Mathematical Programming: State of the Art. University of Michigan, Ann Arbor, pp. 151-171.
[29] Mulvey, J., Generating scenarios for the towers Perrin investment system, Interfaces, 26, 1-15, (1996)
[30] Mulvey, J.; Ziemba, W., Asset and liability management systems for long-term investors: discussion of the issues, (), 1-35
[31] Mulvey, J.; Rosenbaum, D.; Shetty, B., Strategic financial risk management and operations research, European journal of operations research, 97, 1-16, (1997) · Zbl 0920.90008
[32] RiskMetrics, 1996. Technical Document, 4th Edition. J.P. Morgan.
[33] Salinger, D.H., Rockafellar, R.T., 1999. Dynamic splitting: an algorithm for deterministic and stochastic multiperiod optimization. Working Paper, Department of Mathematics, University of Washington, Seattle.
[34] Vassiadou-Zeniou, C.; Zenios, S., Robust optimization models for managing callable bond portfolios, European journal of operations research, 91, 264-273, (1996) · Zbl 0924.90027
[35] von Neumann, J.; Morgenstern, O., Theory of games and economic behavior, (1953), Princeton University Press Princeton · Zbl 0053.09303
[36] Worzel, K.; Vassiadou-Zeniou, C.; Zenios, S., Integrated simulation and optimization models for tracking indices of fixed-income securities, Operations research, 42, 223-233, (1994) · Zbl 0925.90026
[37] Zenios, S.; Kang, P., Mean – absolute deviation portfolio optimization for mortgage-backed securities, Annals of operations research, 45, 433-450, (1993) · Zbl 0800.90049
[38] Zenios, S.; Holmer, M.; McKendall, R.; Vassiadou-Zeniou, C., Dynamic models for fixed-income portfolio management under uncertainty, Journal of economic dynamics and control, 22, 1517-1541, (1998) · Zbl 0914.90028
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