We consider a problem where an investment manager must allocate an available budget among a set of fund managers, whose asset class allocations are not precisely known to the investment manager. In this paper, we propose a robust framework that takes into account the uncertainty stemming from the fund managers’ allocation, as well as the more traditional uncertainty due to uncertain asset class returns, in the context of manager selection and portfolio management when short sales are not allowed. A key application area is university endowments funds. We assume that only bounds on the fund managers’ holdings (expressed as fractions of the portfolio) are available, and fractions must sum to 1 for each fund manager. We define worst-case risk as the largest variance attainable by the investment manager’s portfolio over that uncertainty set. We propose two exact approaches (of different complexity) and a heuristic one to solve the problem efficiently. Numerical experiments suggest that our robust model provides better protection against risk than the nominal model when the fund managers’ allocations are not known precisely.
Accepté le :
DOI : 10.1051/ro/2015007
Mots-clés : Portfolio optimization, robust optimization, investment management
@article{RO_2015__49_4_821_0,
author = {Dong, Yang and Thiele, Aur\'elie},
title = {Robust {Investment} {Management} with {Uncertainty} in {Fund} {Managers{\textquoteright}} {Asset} {Allocation}},
journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
pages = {821--844},
publisher = {EDP-Sciences},
volume = {49},
number = {4},
year = {2015},
doi = {10.1051/ro/2015007},
zbl = {1327.90084},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/ro/2015007/}
}
TY - JOUR AU - Dong, Yang AU - Thiele, Aurélie TI - Robust Investment Management with Uncertainty in Fund Managers’ Asset Allocation JO - RAIRO - Operations Research - Recherche Opérationnelle PY - 2015 SP - 821 EP - 844 VL - 49 IS - 4 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/ro/2015007/ DO - 10.1051/ro/2015007 LA - en ID - RO_2015__49_4_821_0 ER -
%0 Journal Article %A Dong, Yang %A Thiele, Aurélie %T Robust Investment Management with Uncertainty in Fund Managers’ Asset Allocation %J RAIRO - Operations Research - Recherche Opérationnelle %D 2015 %P 821-844 %V 49 %N 4 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/ro/2015007/ %R 10.1051/ro/2015007 %G en %F RO_2015__49_4_821_0
Dong, Yang; Thiele, Aurélie. Robust Investment Management with Uncertainty in Fund Managers’ Asset Allocation. RAIRO - Operations Research - Recherche Opérationnelle, Tome 49 (2015) no. 4, pp. 821-844. doi : 10.1051/ro/2015007. http://archive.numdam.org/articles/10.1051/ro/2015007/
, and , Fundamental indexation. Financ. Anal. J. 61 (2005) 83–99. | DOI
and , Investment management and risk-sharing with multiple managers. J. Finance 39 (1984) 477–491. | DOI
A. Ben-Tal, T. Margalit and A. Nemirovski, Robust modeling of multi-stage portfolio problems, in High Performance Optimization. Kluwer Academic Publishers (2000) 125–158. | Zbl
A. Ben-Tal, L. El-Ghaoui and A. Nemirovski, Robust optimization. Princeton University Press. Princeton, NJ (2009). | Zbl
J. Benders, Partitioning procedures for solving mixed-variables programming problems. Numer. Math. (1962) 238–252. | Zbl
, and , Theory and applications of robust optimization. SIAM Rev. 53 (2011) 464–501. | DOI | Zbl
D. Bienstock and N. Ozbay, Computing robust basestock levels. Discrete Optim.5 (2008). | Zbl
, , , and , Decentralized investment management: Evidence from the pension fund industry. J. Finance 68 (2013) 1133–1178. | DOI
G. Brinson, R. Hood and G. Beebower, Determinants of portfolio performance. Financ. Anal. J. (1986) 39–44.
and , Globally solving nonconvex quadratic programming problems via completely positive programming. Math. Program. Comput. 4 (2012) 33–52. | DOI | Zbl
V. Chopra and W. Ziemba, The effect of errors in means, variances and covariances on optimal portfolio choice, in Worldwide asset and liability modeling. edited by W. Ziemba and J. Mulvey. Cambridge University Press (1998). | Zbl
and , Distributionally robust optimization under moment uncertainty with application to data-driven problems. Oper. Res. 58 (2010) 595–612. | DOI | Zbl
, and , Size matters: Optimal calibration of shrinkage estimators for portfolio selection. Journal of Banking and Finance 37 (2013) 3018–3034. | DOI
and , Portfolio selection with robust estimation. Oper. Res. 57 (2009) 560–577. | DOI | Zbl
, and , Worst-case value-at-risk and robust portfolio optimization: a conic programming approach. Oper. Res. 51 (2003) 543–556,. | DOI | Zbl
and , Optimum centralized portfolio construction with decentralized portfolio management. Financ. Quant. Anal. 39 (2004) 481–494. | DOI
, and , Portfolio selection with parameter and model uncertainty: A multi-prior approach. Rev. Financ. Stud. 20 (2007) 41–81. | DOI
and , Robust portfolio selection problems. Math. Oper. Res. 28 (2003) 1–38. | DOI | Zbl
and , Performance measurement without benchmarks: An examination of mutual fund returns. J. Business 66 (1993) 47–68. | DOI
C. Hsu and W. Myers, Performance attribution: Measuring dynamic allocation skill. Financ. Anal. J. 66 (2010).
, The performance of mutual funds in the period 1945-1964. J. Finance 23 (1968) 389–416. | DOI
, Risk, the pricing of capital assets, and the evaluation of investment performance. J. Business 42 (1969) 167–247. | DOI
and . Honey, I shrunk the sample covariance matrix. J. Portfolio Manage. 30 (2004) 110–119. | DOI
, Where do alphas come from?: A measure of the value of active investment management. J. Investment Management 6 (2008).
J. Maginn, D. Tuttle, D. McLeavey and J. Pinto, eds. Managing investment portfolios: A dynamic process. Wiley (2007).
, and , The properties of equally weighted risk contribution portfolios. J.ournal of Portfolio Manage. 36 (2010) 60–70. | DOI
, Portfolio selection. J. Finance 7 (1952) 77–91.
and , Ambiguity in portfolio selection. Quantitative Finance 7 (2007) 435–442. | DOI | MR | Zbl
, and , Decentralized downside risk management. J. Invest. Manage. 9 (2011) 72–98.
T. Roncalli, Introduction to Risk Parity and Budgeting. Financial Mathematics Series, Chapman&Hall/CRC (2013). | MR | Zbl
, Mutual fund performance. J. Business 39 (1966) 119–138. | DOI
, Decentralized investment management. J. Finance, 36 (1981) 217–234. | DOI
H.D. Sherali and W.P. Adams, A reformulation-linearization technique for solving discrete and continuous nonconvex problems. Kluwer, Dordrecht (1998). | MR | Zbl
D. Swensen, Pioneering portfolio management: an unconventional approach to institutional investment, fully revised and updated. Free Press (2009).
A. Thiele, T. Terry and M. Epelman, Robust linear optimization with recourse. Technical report, Lehigh University (2010).
, How to rate management of investment funds. Harvard Business Rev. 43 (1965) 63–75.
, Why market-valuation-indifferent indexing works. Financ. Anal. J. 61 (2005) 65–69. | DOI
and , Can mutual funds outguess the market? Harvard Business Rev. 44 (1966) 131–163.
H. Tuy, Concave minimization under linear constraints with special structure. Hanoi Inst. Math. Hanoi (1983). | MR | Zbl
, and , Optimal decentralized investment management. J. Finance 63 (2008) 1849–1894. | DOI
B. Zeng, Solving two-stage robust optimization problems by a constraint-and-column generation method. Technical report, University of South Florida (2011). | Zbl
L. Zhang, Multi-period pricing for perishable products: Uncertainty and competition. Master’s thesis, M.I.T. (2006).
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