The Optimal Log-Utility Asset Management under Incomplete Information

In this paper, we propose a theory for deriving the optimal portfolio that assures the log-utility investors of maximizing their expected utility. Restricting investors' information at defined levels, we propose the sample path-wise optimal portfolio (SPOP), which is consistent with the back-test framework used in actualinvestment. It is proven that, at any finite terminal time, this SPOP is asymptotically optimal among all the portfolios which are predictable under investors' incompleteinformation. The optimality is guaranteed by the continuous Bayesian updating formula. Finally, we discuss an algorithm for searching the SPOP, based on asset prices at discrete time intervals.     

Investment decisions when utility depends on wealth and other attributes

The problem of optimal investment under a multivariate utility function allows for an investor to obtain utility not only from wealth, but other (possibly correlated) attributes. In this paper we implement multivariate mixtures of exponential (mixex) utility to address this problem. These utility functions allow for stochastic risk aversions to differing states of the world. We derive some new results for certainty equivalence in this context. By specifying different distributions for stochastic risk aversions, we are able to derive many known, plus several new utility functions, including models of conditional certainty equivalence and multivariate generalisations of HARA utility, which we call dependent HARA utility. Focusing on the case of asset returns and attributes being multivariate normal, we optimise the asset portfolio, and find that the optimal portfolio consists of the Markowitz portfolio and hedging portfolios. We provide an empirical illustration for an investor with a mixex utility function of wealth and sentiment.     

Conditional Value-at-Risk,spectral risk measures and (non-)diversification in portfolio selection problems – A comparison with mean–variance analysis

We study portfolio selection under Conditional Value-at-Risk and, as its natural extension, spectral risk measures, and compare it with traditional mean–variance analysis. Unlike the previous literature that considers an investor’s mean-spectral risk preferences for the choice of optimal portfolios only implicitly, we explicitly model these preferences in the form of a so-called spectral utility function. Within this more general framework, spectral risk measures tend towards corner solutions. If a risk free asset exists, diversification is never optimal. Similarly, without a risk free asset, only limited diversification is obtained. The reason is that spectral risk measures are based on a regulatory concept of diversification that differs fundamentally from the reward-risk tradeoff underlying the mean–variance framework.     

A dynamic model of active portfolio management with benchmark orientation

This paper studies optimal dynamic portfolios for investors concerned with the performance of their portfolios relative to a benchmark. Assuming that asset returns follow a multi-linear factor model similar to the structure of Ross (1976) [Ross, S., 1976. The arbitrage theory of the capital asset pricing model. Journal of Economic Theory, 13, 342–360] and that portfolio managers adopt a mean tracking error analysis similar to that of Roll (1992) [Roll, R., 1992. A mean/variance analysis of tracking error. Journal of Portfolio Management, 18, 13–22], we develop a dynamic model of active portfolio management maximizing risk adjusted excess return over a selected benchmark. Unlike the case of constant proportional portfolios for standard utility maximization, our optimal portfolio policy is state dependent, being a function of time to investment horizon, the return on the benchmark portfolio, and the return on the investment portfolio. We define a dynamic performance measure which relates portfolio’s return to its risk sensitivity. Abnormal returns at each point in time are quantified as the difference between the realized and the model-fitted returns. Risk sensitivity is estimated through a dynamic matching that minimizes the total fitted error of portfolio returns. For illustration, we analyze eight representative mutual funds in the U.S. market and show how this model can be used in practice.     

Size matters: Optimal calibration of shrinkage estimators for portfolio selection

We carry out a comprehensive investigation of shrinkage estimators for asset allocation, and we find that size matters—the shrinkage intensity plays a significant role in the performance of the resulting estimated optimal portfolios. We study both portfolios computed from shrinkage estimators of the moments of asset returns (shrinkage moments), as well as shrinkage portfolios obtained by shrinking the portfolio weights directly. We make several contributions in this field. First, we propose two novel calibration criteria for the vector of means and the inverse covariance matrix. Second, for the covariance matrix we propose a novel calibration criterion that takes the condition number optimally into account. Third, for shrinkage portfolios we study two novel calibration criteria. Fourth, we propose a simple multivariate smoothed bootstrap approach to construct the optimal shrinkage intensity. Finally, we carry out an extensive out-of-sample analysis with simulated and empirical datasets, and we characterize the performance of the different shrinkage estimators for portfolio selection.     

Portfolio selection with commodities under conditional copulas and skew preferences

This article investigates the portfolio selection problem of an investor with three-moment preferences taking positions in commodity futures. To model the asset returns, we propose a conditional asymmetric t copula with skewed and fat-tailed marginal distributions, such that we can capture the impact on optimal portfolios of time-varying moments, state-dependent correlations, and tail and asymmetric dependence. In the empirical application with oil, gold and equity data from 1990 to 2010, the conditional t copulas portfolios achieve better performance than those based on more conventional strategies. The specification of higher moments in the marginal distributions and the type of tail dependence in the copula has significant implications for the out-of-sample portfolio performance.     

The Role of the Investment Horizon in Optimal Portfolio Sequencing (An Intuitive Demonstration in Discrete Time)

This paper examines the role played by the investor's investment horizon in the choice of optimal portfolios. A complete discrete-time, multiperiod, portfolio model is presented with a choice criterion that is consistent with the traditional utility approach but which is more amenable to a multiperiod environment. It is shown that investors should choose progressively less risky single-period portfolios as their investment horizons grow shorter, even if they do not become more risk averse. This result holds both in the presence and in the absence of a riskless asset. The results are consistent with empirical evidence and the financial planning practice of moving investors into progressively less risky portfolios as they grow older.     

Agency and Institutional Investment

In this paper we summarise and extend the agency‐based model of asset pricing of Brennan (1993) to show that the implied agency effects on asset pricing are too small to be empirically detectable: empirical tests confirm this and we show that the positive findings of Gomez and Zapatero (2003) are due to their choice of sample. We also derive new empirical implications for the composition of institutional investment portfolios and empirically confirm the major result, that institutional portfolios will be short the minimum variance portfolio.     

Cardinality versus q-norm constraints for index tracking

Index tracking aims at replicating a given benchmark with a smaller number of its constituents. Different quantitative models can be set up to determine the optimal index replicating portfolio. In this paper, we propose an alternative based on imposing a constraint on the q-norm (0?<?q?<?1) of the replicating portfolios’ asset weights: the q-norm constraint regularises the problem and identifies a sparse model. Both approaches are challenging from an optimization viewpoint due to either the presence of the cardinality constraint or a non-convex constraint on the q-norm. The problem can become even more complex when non-convex distance measures or other real-world constraints are considered. We employ a hybrid heuristic as a flexible tool to tackle both optimization problems. The empirical analysis of real-world financial data allows us to compare the two index tracking approaches. Moreover, we propose a strategy to determine the optimal number of constituents and the corresponding optimal portfolio asset weights.     

Mean-variance versus utility maximization revisited: The case of constant relative risk aversion

We examine if mean-variance (M-V) is a good proxy for portfolios based on the Constant Relative Risk Aversion (CRRA) utility function. M-V portfolios are considered good proxies for portfolios from several utility functions which is why they are routinely used in the portfolio theory literature as the benchmark. Our results clearly show this is not the case. Low risk CRRA portfolios are in many cases very different to M-V portfolios, especially with respect to downside risk. If a risk-free asset is available, in many cases, no M-V portfolio is an adequate proxy for CRRA portfolios. The implications of our findings are that: i) M-V portfolios are a poor proxy for investors with CRRA preferences, ii) CRRA portfolios are more suited to investors who care about downside risk than M-V portfolios, and iii) the efficacy of M-V to proxy for utility maximization should be examined more thoroughly.     

Mitigating Estimation Risk in Asset Allocation: Diagonal Models Versus 1/N Diversification

Recent literature suggests that optimal asset‐allocation models struggle to consistently outperform the 1/N naïve diversification strategy, which highlights estimation‐risk concerns. We propose a dichotomous classification of asset‐allocation models based on which elements of the inverse covariance matrix that a model uses: diagonal only versus full matrix. We argue that parsimonious diagonal‐only strategies, which use limited information such as volatility or idiosyncratic volatility, are likely to offer a good tradeoff between incorporating limited information while mitigating estimation risk. Evaluating five sets of portfolios over 1926–2012, we find that 1/N is generally not optimal when compared with these diagonal strategies.     

Index tracking with utility enhanced weighting

Passive index investing involves investing in a fund that replicates a market index. Enhanced indexation uses the returns of an index as a reference point and aims at outperforming this index. The motivation behind enhanced indexing is that the indices and portfolios available to academics and practitioners for asset pricing and benchmarking are generally inefficient and, thus, susceptible to enhancement. In this paper we propose a novel technique based on the concept of cumulative utility area ratios and the Analytic Hierarchy Process (AHP) to construct enhanced indices from the DJIA and S&P500. Four main conclusions are forthcoming. First, the technique, called the utility enhanced tracking technique (UETT), is computationally parsimonious and applicable for all return distributions. Second, if desired, cardinality constraints are simple and computationally parsimonious. Third, the technique requires only infrequent rebalancing, monthly at the most. Finally, the UETT portfolios generate consistently higher out-of-sample utility profiles and after-cost returns for the fully enhanced portfolios as well as for the enhanced portfolios adjusted for cardinality constraints. These results are robust to varying market conditions and a range of utility functions.     

Dynamic Portfolio Selection by Augmenting the Asset Space

We present a novel approach to dynamic portfolio selection that is as easy to implement as the static Markowitz paradigm. We expand the set of assets to include mechanically managed portfolios and optimize statically in this extended asset space. We consider “conditional” portfolios, which invest in each asset an amount proportional to conditioning variables, and “timing” portfolios, which invest in each asset for a single period and in the risk‐free asset for all other periods. The static choice of these managed portfolios represents a dynamic strategy that closely approximates the optimal dynamic strategy for horizons up to 5 years.     

MDP algorithms for portfolio optimization problems in pure jump markets

We consider the problem of maximizing the expected utility of the terminal wealth of a portfolio in a continuous-time pure jump market with general utility function. This leads to an optimal control problem for piecewise deterministic Markov processes. Using an embedding procedure we solve the problem by looking at a discrete-time contracting Markov decision process. Our aim is to show that this point of view has a number of advantages, in particular as far as computational aspects are concerned. We characterize the value function as the unique fixed point of the dynamic programming operator and prove the existence of optimal portfolios. Moreover, we show that value iteration as well as Howard’s policy improvement algorithm works. Finally, we give error bounds when the utility function is approximated and when we discretize the state space. A numerical example is presented and our approach is compared to the approximating Markov chain method.      

Optimal multi-period consumption and investment with short-sale constraints

This article examines agents’ consumption-investment problem in a multi-period pure exchange economy where agents are constrained with the short-sale of state-dependent risky contingent claims. In equilibrum, agents hold options written on aggregate consumption in their optimal portfolios. Furthermore, under the specific case of quadratic utility, the optimal risk-sharing rule derived for the pricing agent leads to a multifactor conditional consumption-based capital asset pricing model (CCAPM), where excess option returns appear as factors.     

A multivariate model of strategic asset allocation

We develop an approximate solution method for the optimal consumption and portfolio choice problem of an infinitely long-lived investor with Epstein–Zin utility who faces a set of asset returns described by a vector autoregression in returns and state variables. Empirical estimates in long-run annual and post-war quarterly U.S. data suggest that the predictability of stock returns greatly increases the optimal demand for stocks. The role of nominal bonds in long-term portfolios depends on the importance of real interest rate risk relative to other sources of risk. Long-term inflation-indexed bonds greatly increase the utility of conservative investors.     

Size and Value Anomalies under Regime Shifts

This paper finds strong evidence of time-variations in the jointdistribution of returns on a stock market portfolio and portfoliostracking size- and value effects. Mean returns, volatilitiesand correlations between these equity portfolios are found tobe driven by underlying regimes that introduce short-run markettiming opportunities for investors. The magnitude of the premiaon the size and value portfolios and their hedging propertiesare found to vary across regimes. Regimes are shown to havea large impact both on the optimal asset allocation—especiallyunder rebalancing—and on investors' utility. Regimes alsohave a considerable impact on hedging demands, which are positivewhen the investor starts from more favorable regimes and negativewhen starting from bad states. Recursive out-of-sample forecastingexperiments show that portfolio strategies based on models thataccount for regimes dominate single-state benchmarks.     

The efficiency of Greek public pension fund portfolios

Greek public pension funds can invest up to 23% into risky assets and are not allowed to invest outside Greece. This paper seeks to investigate the costs of investment constraints on pension fund portfolios. In particular we try to quantify the losses that portfolios suffer due to under-diversification and sub-optimal asset allocation. We find that the high concentration of Greek equity portfolios imposes a substantial return and utility loss which is further increased when the lack of international diversification is taken into account. Restricting the weight of equities to 23% of the total portfolio, leads to sub-optimal asset allocation that costs as much as 2% (3%) per annum compared to a balanced domestic (global) benchmark.     

Optimal asset allocation under linear loss aversion

We study the asset allocation of a linear loss-averse (LA) investor and compare it to the more traditional mean-variance (MV) and conditional value-at-risk (CVaR) investors. First we derive conditions under which the LA problem is equivalent to the MV and CVaR problems and solve analytically the two-asset problem of the LA investor for a risk-free and a risky asset. Then we run simulation experiments to study properties of the optimal LA and MV portfolios under more realistic assumptions. We find that under asymmetric dependence LA portfolios outperform MV portfolios, provided investors are sufficiently loss-averse and dependence is large. Finally, using 13 EU and US assets, we implement the trading strategy of a linear LA investor who reallocates his/her portfolio on a monthly basis. We find that LA portfolios clearly outperform MV and CVaR portfolios and that incorporating a dynamic update of the LA parameters significantly improves the performance of LA portfolios.