Optimal omega-ratio portfolio performance constrained by tracking error
-
DOIhttp://dx.doi.org/10.21511/imfi.17(3).2020.20
-
Article InfoVolume 17 2020, Issue #3, pp. 263-280
- 611 Views
-
483 Downloads
This work is licensed under a
Creative Commons Attribution 4.0 International License
The mean-variance framework coupled with the Sharpe ratio identifies optimal portfolios under the passive investment style. Optimal portfolio identification under active investment approaches, where performance is measured relative to a benchmark, is less well-known. Active portfolios subject to tracking error (TE) constraints lie on distorted elliptical frontiers in return/risk space. Identifying optimal active portfolios, however defined, have only recently begun to be explored. The Ω – ratio considers both down and upside portfolio potential. Recent work has established a technique to determine optimal Ω – ratio portfolios under the passive investment approach. The authors apply the identification of optimal Ω – ratio portfolios to the active arena (i.e., to portfolios constrained by a TE) and find that while passive managers should always invest in maximum Ω – ratio portfolios, active managers should first establish market conditions (which determine the sign of the main axis slope of the constant TE frontier). Maximum Sharpe ratio portfolios should be engaged when this slope is > 0 and maximum Ω – ratios when < 0.
- Keywords
-
JEL Classification (Paper profile tab)C51, D81, G11
-
References44
-
Tables0
-
Figures11
-
- Figure 1. Ω frontier, analogous capital market line, and location of the optimal Ω portfolio
- Figure 2. Orientation of relevant components in Oct-05. TE = 6% and rf = 7.0%. The Ω – ratio as a function of risk is shown as a solid black line, tied to the right-hand axis (the maximum Ω – ratio on this curve is indicated). All other elements are linke
- Figure 3. Orientation of relevant components in Oct-14. TE = 6% and rf = 5.8%
- Figure 4(a)-(b). Ω frontiers and (b) maximum Ω(τ) for Oct-00 – Oct-05 and Oct-09 – Oct-14
- Figure 5. Weights in optimal, unconstrained Ω portfolios for Oct-00 – Oct-05 and Oct-09 – Oct-14
- Figure 6(a). Return/risk profiles for relevant portfolios as a function of TE (percentages indicate TE values)
- Figure 6(b). Sharpe ratios versus TE for Oct-00 – Oct-05
- Figure 7(a). Return/risk profiles for relevant portfolios as a function of TE
- Figure 7(b). Sharpe ratios versus TE for Oct-14
- Figure 8. Benchmark weight deviations for relevant portfolios in (a) Oct-00 – Oct-05 and (b) Oct-09 – Oct-14
- Figure 9. Asset K’s deviation in weight from the benchmark for the relevant portfolios in (a) Oct-00 – Oct-05 and (b) Oct-09 – Oct-14
-
- Anadu, K., Kruttli, M., McCabe, P., Osambela, E., & Shin, C. H. (2018). The shift from active to passive investing: potential risks to financial stability? (Finance and Economics Discussion Series 2018-060). Washington: Board of Governors of the Federal Reserve System.
- Beasley, J. E., Meade, N., & Chang, T. J. (2003). An evolutionary heuristic for the index tracking problem. European Journal of Operational Research, 148(3), 621-643.
- Berk, J., & van Binsbergen, J. (2015). Measuring skill in the mutual fund industry. Journal of Financial Economics, 118(1), 1-20.
- Bertrand, P., Prigent, J. L., & Sobotka, R. (2001). Optimisation de portefeuille sous contrainte de variance de la tracking-error. Banque & Marchés, 54(1), 19-28.
- Calvo, C., Ivorra, C., & Liern, V. (2012). On the computation of the efficient frontier of the portfolio selection problem. Journal of Applied Mathematics, 2012(1), 1-25.
- Canakgoz, N. A., & Beasley, J. E. (2008). Mixed-integer programming approaches for index tracking and enhanced indexation. European Journal of Operational Research, 196(1), 384-399.
- Courtney Capital. (2020). JSE top 40 shares.
- Cremers, K. J. M., Fulkerson, A., & Riley, T. B. (2019). Challenging the conventional wisdom on active management: a review of the past 20 years of academic literature on actively managed mutual funds. Financial Analysts Journal, 75(4), 8-35.
- Daly, M., Maxwell, M., & van Vuuren, G. (2018). Feasible portfolios under tracking error, β, α and utility constraints. Investment Management and Financial Innovations, 15(1), 141-153.
- Dolvin, S., Fulkerson, J., & Krukover, A. (2018). Do “good guys” finish last? The relationship between Morningstar sustainability ratings and mutual fund performance. Journal of Investing, 28(2), 77-91.
- Evans, C., & van Vuuren, G. (2019). Investment strategy performance under tracking error constraints. Investment Management and Financial Innovations, 16(1), 239-257.
- Filippi, C., Guastaroba, G., & Speranza, M. (2016). A heuristic framework for the bi-objective enhanced index tracking problem. Omega, 65(C), 122-137.
- Gilli, M., Schumann, E., Di Tollo, G., & Cabej, G. (2008). Constructing long/short portfolios with Ω -ratio(Swiss Finance Institute Research Paper No. 08-34). Swiss Finance Institute.
- Gnagi, M., & Strub, O. (2020). Tracking and outperforming large stock market indices. Omega, 90(C), 119-129.
- Guastaroba, G., & Speranza, M. G. (2012). Kernel Search: An application to the index tracking problem. European Journal of Operational Research, 217(1), 54-68.
- Guastaroba, G., Mansini, R., Ogryczak, W., & Speranza, M. G. (2016). Linear programming models based on Omega ratio for the enhanced index tracking problem. European Journal of Operational Research, 251(3), 938-956.
- Gunning, W., & van Vuuren, G. (2019). Exploring the drivers of tracking error constrained portfolio performance. Cogent Economics, 7(1), 1-15.
- Janabi, M. (2009). Commodity price risk management: Valuation of large trading portfolios under adverse and illiquid market settings. Journal of Derivatives and Hedge Funds, 15(2), 15-50.
- Jorion, P. (2003). Portfolio optimization with tracking-error constraints. Financial Analysts Journal, 59(5), 70-82.
- Kane, S. J., Bartholomew-Biggs, M. C., Cross, M., & Dewar, M. (2005). Optimizing Omega. Journal of Global Optimization, 45(1), 153-167.
- Kapsos, M., Zymler, S., Christofides, N., & Rustem, B. (2011). Optimizing the Omega ratio using linear programming. Journal of Computational Finance, 17(4), 49-57.
- Keating, C., & Shadwick, W. F. (2002). A universal performance measure. Journal of Performance Measurement, 6(3), 59-84.
- Kwan, C. C. (2003). Improving the efficient frontier. The Journal of Portfolio Management, 29(2), 69-79.
- Larsen, G. A., & Resnick, B. G. (2001). Parameter estimation techniques, optimization frequency, and portfolio return enhancement. Journal of Portfolio Management, 27(4), 27-34.
- Lo, A. (2012). The statistics of Sharpe ratios. Financial Analysts Journal, 58(4), 36-52.
- Marhfor, A. (2016). Portfolio performance measurement: review of literature and avenues of future research. American Journal of Industrial and Business Management, 6(4), 432-438.
- Markowitz, H. (1952). Portfolio selection. The Journal of Finance, 7(1), 77-91.
- Markowitz, H., Schirripa, F., & Tecotzky, N. (1999). A more efficient frontier. The Journal of Portfolio Management, 25(5), 99-108.
- Mausser, H., Saunders, D., & Seco, L. (2006). Optimising Omega. Risk, 88-92.
- Maxwell, M., & van Vuuren, G. (2019). Active investment strategies under tracking error constraints. International Advances in Economic Research, 25(3), 309-322.
- Maxwell, M., Daly, M., Thomson, D., & van Vuuren, G. (2018). Optimizing tracking error-constrained portfolios. Applied Economics, 50(54), 5846-5858.
- Merton, R. (1972). An analytic derivation of the efficient portfolio frontier. The Journal of Financial and Quantitative Analysis, 7(4), 1851-1872.
- Muralidhar, A. (2015). The Sharpe ratio revisited: what it really tells us. Journal of Performance Measurement, 19(3), 6-12.
- Mutunge, P., & Haugland, D. (2018). Minimizing the tracking error of cardinality constrained portfolios. Computers and Operations Research, 90, 33-41.
- Passow, A. (2004). Omega portfolio construction with Johnson distributions (FAME Research Paper Series RP120). International Center for Financial Asset Management and Engineering.
- Pedersen, L. (2018). Sharpening the arithmetic of active management. Financial Analysts Journal, 74(1), 21-36.
- Qi, J., Rekkas, M., & Wong, A. (2018). Highly accurate inference on the Sharpe ratio for autocorrelated return data. Journal of Statistical and Econometric Methods, 7(1), 21-50.
- Roll, R. (1992). A mean/variance analysis of tracking error. The Journal of Portfolio Management, 18(4), 13-22.
- Rudd, A. (1980). Optimal selection of passive portfolios. Financial Management, 9(1), 57-66.
- Sharpe, W. F. (1966). Mutual fund performance. Journal of Business, 39(1), 119-138.
- Sharpe, W. F. (1994). The Sharpe ratio. The Journal of Portfolio Management, 21(1), 49-58.
- Stowe, D. L. (2014). Tracking error volatility optimization and utility improvements (Working paper).
- Strub, O., & Baumann, P. (2018). Optimal construction and rebalancing of index-tracking portfolios. European Journal of Operational Research, 264(1), 370-387.
- Thomson, D., & van Vuuren, G. (2016). Forecasting the South African business cycle using Fourier Analysis. International Business and Economics Research Journal, 15(4), 175-192.