The paper compares three portfolio optimization models. Modern portfolio theory (MPT) is a short-horizon volatility model. The relevant time horizon is the sampling interval. MPT is myopic and implies that investors are not concerned with long-term variance or mean-reversion. Intertemporal portfolio choice is a multiple period model that revises portfolios continuously in response to relevant signals to reduce variance of terminal wealth over the holding period. Digital portfolio theory (DPT) is a non-myopic, discrete time, long-horizon variance model that does not include volatility. DPT controls mean-reversion variances in single period solutions based on holding period and hedging and speculative demand.
Merton, R.C. (1969) Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case. Review of Economics and Statistics, 51, 247-257. https://doi.org/10.2307/1926560
Samuelson, P.A. (1969) Lifetime Portfolio Selection by Dynamic Stochastic Programming. Review of Economics and Statistics, 51, 239-246. https://doi.org/10.2307/1926559
Merton, R.C. (1971) Optimum Consumption and Portfolio Rules in a Continuous-Time Model. Journal of Economic Theory, 3, 373-413.
Merton, R.C. (1973) An Intertemporal Capital Asset Pricing Model. Econometrica, 41, 867-887.
Jones, C.K. (2008) Calendar Based Mean Reversion Risk and Digital Signal Processing. SSRN Working Paper. http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1361886
Campbell, J.Y. and Viceira, L.M. (1999) Consumption and Portfolio Decisions When Expected Returns Are Time Varying. Quarterly Journal of Economics, 114, 433-495. https://doi.org/10.1162/003355399556043
Brandt, M.W. (1999) Estimating Portfolio and Consumption Choice: A Conditional Euler Equation Approach. Journal of Finance, 54, 1609-1645. https://doi.org/10.1111/0022-1082.00162
Ait-Sahalia, Y. and Brandt, M.W. (2001) Variable Selection for Portfolio Choice. Journal of Finance, 56, 1297-1351. https://doi.org/10.3386/w8127
Barberis, N. (2000) Investing for the Long Run When Returns Are Predicable. Journal of Finance, 55, 225-264. https://doi.org/10.1111/0022-1082.00205
Brennan, M.J., Schwartz, E.S. and Lagnado, R. (1997) Strategic Asset Allocation. Journal of Economics Dynamics and Control, 21, 1377-1403.
Kim, T.S. and Omberg, E. (1996) Dynamic Nonmyopic Portfolio Behavior. Review of Financial Studies, 9, 141-161. https://doi.org/10.1093/rfs/9.1.141
Liu, J. (2007) Portfolio Selection in Stochastic Environments. Review of Financial Studies, 20, 1-39. https://doi.org/10.1093/rfs/hhl001
Campbell, J.Y. and Viceira, L.M. (2002) Strategic Asset Allocation: Portfolio Choice for Long-Term Investors. Oxford University Press, Oxford. https://doi.org/10.1093/0198296940.001.0001
Balduzzi, P. and Lynch, A.W. (1999) Transaction Costs and Predictability: Some Utility Cost Calculations. Journal of Financial Economics, 52, 47-78.
Chacko, G. and Viceira, L.M. (1999) Dynamic Consumption and Portfolio Choice with Stochastic Volatility in Incomplete Markets. NBER Working Paper No. 7377. https://doi.org/10.3386/w7377
Lynch, A.W. (2001) Portfolio Choice and Equity Characteristics: Characterizing the Hedging Demands Induced by Return Predictability. Journal of Financial Economics, 62, 67-130.
Brandt, M.W. and Santa-Clara, P. (2006) Dynamic Portfolio Selection by Augmenting the Asset Space. Journal of Finance, 61, 2187-2217. https://doi.org/10.1111/j.1540-6261.2006.01055.x
Merton, R.C. and Samuelson, P.A. (1974) Fallacy of the Log-Normal Approximation to Optimal Portfolio Decision-making over Many Periods. Journal of Financial Economics, 1, 67-95.
Michaud, R.O. (1989) The Markowitz Optimization Enigma: Is “Optimized” Optimal? Financial Analysts Journal, 45, 31-42. https://doi.org/10.2469/faj.v45.n1.31
Green, R.C. and Hollifield, B. (1992) When Will Mean-Variance Efficient Portfolios Be Well Diversified? Journal of Finance, 47, 1785-1809. https://doi.org/10.1111/j.1540-6261.1992.tb04683.x
Frost, P.A. and Savarino, J.E. (1988) For Better Performance: Constrain Portfolio Weights. Journal of Portfolio Management, 15, 29-34. https://doi.org/10.3905/jpm.1988.409181
Jagannathan, R. and Ma, T. (2003) Risk Reduction in Large Portfolios: Why Imposing the Wrong Constraints Helps. Journal of Finance, 58, 1651-1684. https://doi.org/10.1111/1540-6261.00580
Jobson, J.D. and Korkie, B. (1980) Estimation of Markowitz Efficient Portfolios. Journal of the American Statistical Association, 75, 544-554. https://doi.org/10.1080/01621459.1980.10477507
Black, F. and Litterman, R. (1992) Global Portfolio Optimization. Financial Analysis Journal, 48, 28-43. https://doi.org/10.2469/faj.v48.n5.28
Jobson, J.D. and Korkie, B. (1981) Putting Markowitz Theory to Work. Journal of Portfolio Management, 7, 70-74. https://doi.org/10.3905/jpm.1981.408816
Ledoit, O. and Wolf, M. (2004) Honey, I Shrunk the Sample Covariance Matrix. Journal of Portfolio Management, 30, 110-119. https://doi.org/10.3905/jpm.2004.110
Treynor, J.L. and Black, F. (1973) How to Use Security Analysis to Improve Portfolio Selection. Journal of Business, 46, 66-86. https://doi.org/10.1086/295508
Pastor, L. and Stambaugh, R.F. (2000) Comparing Asset Pricing Models: An Investment Perspective. Journal of Financial Economics, 56, 335-381.
Lynch A.W. and Balduzzi, P. (2000) Predictability and Transaction Costs: The Impact on Rebalancing Rules and Behavior. Journal of Finance, 55, 2285-2310. https://doi.org/10.1111/0022-1082.00287
Wachter, J.A. (2002) Portfolio and Consumption Decisions under Mean-Reverting Returns: An Explicit Solution for Complete Market. Journal of Financial and Quantitative Analysis, 37, 63-91. https://doi.org/10.2307/3594995
Jones, C.K. (1992) Portfolio Management: New Model for Successful Investment. McGraw-Hill, London.
Jones, C.K. (1983) Portfolio Selection in the Frequency Domain. American Institute of Decision Sciences Proceedings November, 67-70.
Jones, C.K. (2004) Calendar Based Risk, Firm Size, and the Random Walk Hypothesis. SSRN Working Paper. http://ssrn.com/abstract=639683
Markowitz, H. M. (1959) Portfolio Selection: Efficient Diversification of Investments. John Wiley & Sons, New York.
Jones, C.K. (2007) Fixed Trading Costs, Signal Processing and Stochastic Portfolio Networks. European Journal of Industrial Engineering, 1, 5-21. https://doi.org/10.1504/EJIE.2007.012651
Jones, C.K. (2013) Portfolio Size in Stochastic Portfolio Networks Using Digital Portfolio Theory. Journal of Mathematical Finance, 3, 280-290. https://doi.org/10.4236/jmf.2013.32028
Broadie, M. (1994) Portfolio Management: New Models for Successful Investment Decisions. Journal of Finance, 49, 361-364. https://doi.org/10.2307/2329151
Glover, F. and Jones, C.K. (1988) A Stochastic Generalized Network Model and Large-Scale Mean-Variance Algorithm for Portfolio Selection. Journal of Information and Optimization Sciences, 9, 299-316. https://doi.org/10.1080/02522667.1988.10698932