Modern portfolio management with conditioning information

This paper studies models in which active portfolio managers utilize conditioning information unavailable to their clients to optimize performance relative to a benchmark. We derive explicit solutions for the optimal strategies with multiple risky assets, with or without a risk-free asset, and consider various constraints on portfolio risks or weights. The optimal strategies feature a mean–variance efficient component (to minimize portfolio variance), and a hedging demand for the benchmark portfolio (to maximize correlation with the benchmark). A currency portfolio example shows that the optimal strategies improve the measured performance by 53% out of sample, compared with portfolios ignoring conditioning information.     

Downside risk and asset pricing

We analyze if the value-weighted stock market portfolio is stochastic dominance (SD) efficient relative to benchmark portfolios formed on size, value, and momentum. In the process, we also develop several methodological improvements to the existing tests for SD efficiency. Interestingly, the market portfolio seems third-order SD (TSD) efficient relative to all benchmark sets. By contrast, the market portfolio is inefficient if we replace the TSD criterion with the traditional mean–variance criterion. Combined these results suggest that the mean–variance inefficiency of the market portfolio is caused by the omission of return moments other than variance. Especially downside risk seems to be important for explaining the high average returns of small/value/winner stocks.     

A Bayesian non-parametric model for small population mortality

This paper proposes a Bayesian non-parametric mortality model for a small population, when a benchmark mortality table is also available and serves as part of the prior information. In particular, we extend the Poisson-gamma model of Hardy and Panjer to incorporate correlated and age-specific mortality coefficients. These coefficients, which measure the difference in mortality levels between the small and the benchmark population, follow an age-indexed autoregressive gamma process, and can be stochastically extrapolated to ages where the small population has no historical exposure. Our model substantially improves the computation efficiency of existing two-population Bayesian mortality models by allowing for closed form posterior mean and variance of the future number of deaths, and an efficient sampling algorithm for the entire posterior distribution. We illustrate the proposed model with a life insurance portfolio from a French insurance company.     

Linear beta pricing with efficient/inefficient benchmarks and short-selling restrictions

We provide two security pricing models that can be used when short sales of risky securities are not permitted. The first model uses a benchmark located on the expected return-standard deviation efficient frontier without short sales and presents security expected returns as a weighted linear function of two betas, one induced by the benchmark and the other adjusting for the short-sale constraints. The second model uses a benchmark that is inefficient relative to the efficient frontier, does not allow short sales, and expresses security returns as a weighted linear function of three betas:one induced by the inefficient benchmark, and the other two adjusting simultaneously for the short-sales restrictions and the benchmark's inefficiency.These results complement the linear pricing models that link expected returns and betas by allowing, for efficient or inefficient expected return-standard deviation, benchmarks with restricted short sales.     

Granularity adjustment for mark-to-market credit risk models

The impact of undiversified idiosyncratic risk on value-at-risk and expected shortfall can be approximated analytically via a methodology known as granularity adjustment (GA). In principle, the GA methodology can be applied to any risk-factor model of portfolio risk. Thus far, however, analytical results have been derived only for simple models of actuarial loss, i.e., credit loss due to default. We demonstrate that the GA is entirely tractable for single-factor versions of a large class of models that includes all the commonly used mark-to-market approaches. Our approach covers both finite ratings-based models and models with a continuum of obligor states. We apply our methodology to CreditMetrics and KMV Portfolio Manager, as these are benchmark models for the finite and continuous classes, respectively. Comparative statics of the GA reveal striking and counterintuitive patterns. We explain these relationships with a stylized model of portfolio risk.     

Measuring fund style,performance and activity: a new style‐profiling approach

We construct new measures of fund style, performance and activity from linear combinations of off‐the‐shelf stock‐market indices. A fund's benchmark portfolio is a linear combination of two or more reference portfolios that in a least‐squares sense most closely approximates the fund's portfolio. The resulting linear combination scalar is itself a measure of fund style and the distance between a fund and its benchmark is a measure of fund activity. Our approach has a number of advantages over existing characteristic‐matching methods. We illustrate our approach using a data set of US institutional funds.     

Robust and adaptive algorithms for online portfolio selection

We present an online approach to portfolio selection. The motivation is within the context of algorithmic trading, which demands fast and recursive updates of portfolio allocations as new data arrives. In particular, we look at two online algorithms: Robust-Exponentially Weighted Least Squares (R-EWRLS) and a regularized Online minimum Variance algorithm (O-VAR). Our methods use simple ideas from signal processing and statistics, which are sometimes overlooked in the empirical financial literature. The two approaches are evaluated against benchmark allocation techniques using four real data sets. Our methods outperform the benchmark allocation techniques in these data sets in terms of both computational demand and financial performance.     

The performance of international asset allocation strategies using conditioning information

The existence of predictable components in conditional expected returns has been widely reported. We propose a test of the economic significance of this phenomenon by designing dynamic international allocation strategies based on a conditioning information set. We compare the performance of these dynamic strategies with some market portfolio benchmark and with unconditionally efficient portfolios (among the set of primitive assets). We find the performance of the dynamic strategies to be superior. The difference is not only statistically significant, it is economically large.     

Benchmarking the performance of recommended allocations to equities,bonds, and cash by international investment houses

We conduct performance tests of the recommended asset allocations made by a panel of international investment houses (the “Houses”) from 1982 through 2005. We compare the returns and Sharpe Ratios from the recommended-weight portfolio against those of several benchmark portfolios and to a set of 10,000 returns and Sharpe Ratios from randomly shuffled-weight and shuffled-weight change portfolios. We find that the Houses generally fail to outperform the benchmarks. The shuffled-weight change benchmark exhibits a robust “style-preserving” property in that the average portfolio standard deviation is nearly equal to the portfolio standard deviation from the actual recommended weights.     

Comparative issues between linear and non-linear risk measures for non-convex portfolio optimization: evidence from the S&P 500

Abstract

This article focuses on inferring critical comparative conclusions as far as the application of both linear and non-linear risk measures in non-convex portfolio optimization problems. We seek to co-assess a set of sophisticated real-world non-convex investment policy limitations, such as cardinality constraints, buy-in thresholds, transaction costs, particular normative rules, etc. within the frame of four popular portfolio selection cases: (a) the mean-variance model, (b) the mean-semi variance model, (c) the mean-MAD (mean-absolute deviation) model and (d) the mean-semi MAD model. In such circumstances, the portfolio selection process reflects to a mixed-integer bi-objective (or in general multiobjective) mathematical programme. We precisely develop all corresponding modelling procedures and then solve the underlying problem by use of a novel generalized algorithm, which was exclusively introduced to cope with the above-mentioned singularities. The validity of the attempt is verified through empirical testing on the S&P 500 universe of securities. The technical conclusions obtained not only confirm certain findings of the particular limited existing theory but also shed light on computational issues and running times. Moreover, the results derived are characterized as encouraging enough, since a sufficient number of efficient or Pareto optimal portfolios produced by the models appear to possess superior out-of-sample returns with respect to the benchmark.     

Semiparametric estimation of multi-asset portfolio tail risk

When correlations between assets turn positive, multi-asset portfolios can become riskier than single assets. This article presents the estimation of tail risk at very high quantiles using a semiparametric estimator which is particularly suitable for portfolios with a large number of assets. The estimator captures simultaneously the information contained in each individual asset return that composes the portfolio, and the interrelation between assets. Noticeably, the accuracy of the estimates does not deteriorate when the number of assets in the portfolio increases. The implementation is as easy for a large number of assets as it is for a small number. We estimate the probability distribution of large losses for the American stock market considering portfolios with ten, fifty and one hundred assets of stocks with different market capitalization. In either case, the approximation for the portfolio tail risk is very accurate. We compare our results with well known benchmark models.     

Private equity benchmarks and portfolio optimization

Portfolio optimization using private equity is typically based on one of three indices: listed private equity, transaction-based private equity, or appraisal value-based private equity indices. However, we show that none of these indices is fully suitable for portfolio optimization. We introduce here a new benchmark index for venture capital and buyouts, which is updated monthly, adjusted for autocorrelation (de-smoothing), and available contemporaneously. We illustrate how our benchmark enables superior quantitative portfolio optimization.     

Correlation structure forecasting & ex ante portfolio selection strategies in the Japan market

Using monthly data for 160 stocks covering January 1977 to December 1991, we find that both the Historical Mean and the Industry Mean Models dominate the Global Mean and the Single Index Models. In theex-ante portfolio selection, the Historical Model dominates all other models when evaluated against the benchmark of the Global Minimum Variance Portfolio but a combination of historical correlation structure and Bayes-Stein Shrinkage expected returns dominates other models when the Optimal Tangency Portfolio is used as a benchmark for evaluation.     

Multiobjective portfolio optimization with non-convex policy constraints: Evidence from the Eurostoxx 50

Our purpose in this paper is to depart from the intrinsic pathology of the typical mean–variance formalism, due to both the restriction of its assumptions and difficulty of implementation. We manage to co-assess a set of sophisticated real-world non-convex investment policy limitations, such as cardinality constraints, buy-in thresholds, transaction costs, particular normative rules, etc., within the frame of complex scenarios, which demand for simultaneous optimization of multiple investment objectives. In such a case, the portfolio selection process reflects a mixed-integer multiobjective portfolio optimization problem. On this basis, we meticulously develop all the corresponding modeling procedures and then solve the underlying problem by use of a new, fast and very effective algorithm. The value of the suggested framework is integrated with the introduction of two novel concepts in the field of multiobjective portfolio optimization, i.e. the security impact plane and the barycentric portfolio. The first represents a measure of each security's impact in the efficient surface of Pareto optimal portfolios. The second serves as the vehicle for implementing a balanced strategy of iterative portfolio tuning. Moreover, a couple of some very informative graphs provide thorough visualization of all empirical testing results. The validity of the attempt is verified through an illustrative application on the Eurostoxx 50. The results obtained are characterized as very encouraging, since a sufficient number of efficient or Pareto optimal portfolios produced by the model, appear to possess superior out-of-sample returns with respect to the underlying benchmark.     

Efficient fund of hedge funds construction under downside risk measures

We consider portfolio allocation in which the underlying investment instruments are hedge funds. We consider a family of utility functions involving the probability of outperforming a benchmark and expected regret relative to another benchmark. Non-normal return vectors with prescribed marginal distributions and correlation structure are modeled and simulated using the normal-to-anything method. A Monte Carlo procedure is used to obtain, and establish the quality of, a solution to the associated portfolio optimization model. Computational results are presented on a problem in which we construct a fund of 13 CSFB/Tremont hedge-fund indices.     

Long-Term Synthetic Puts

We present the possibility of replicating the performance of a long-term put, which is not available in the financial markets, by a set of other traded financial assets. First, a benchmark portfolio is formed out of one share of stock and one put on the stock with a certain exercise price and a long time until maturity. The general form of a portfolio, consisting of shares of stock, bonds, and options on the stock, is discussed, which is expected to perform like the benchmark portfolio. Then a class of these synthetic puts is examined to determine which type of synthetic put may dominate the others.     

INTERNATIONAL DIVERSIFICATION OF EQUITIES AND FIXED-INCOME SECURITIES

Portfolio selection models have been applied principally to common stocks traded in the United States and in foreign stock markets. This study examines the efficient set of portfolios selected from a choice set that includes returns derived from domestic and international corporate bond and government bond indices as well as domestic and international stock indices. To assess the benefits of international multi-asset diversification, the authors examine the following issues: (1) the extent to which international and domestic fixed-income securities are included in efficient portfolios; (2) the effect on efficient set composition of using the Sharpe portfolio selection model as compared to the Markowitz portfolio selection model; (3) the sensitivity of efficient set characteristics produced from a single-index based portfolio selection model to alternative world market indices; and (4) the correspondence between expected and realized portfolio risk and return for the different portfolio selection models.     

Collective mental accounting: an integrated behavioural portfolio selection model for multiple mental accounts

We propose a behavioural portfolio selection model called collective mental accounting (CMA), which integrates all mental sub-portfolios (mental accounts) in one mathematical model. Moreover, this study contributes to the literature of behavioural portfolio selection in three further ways: first, the CMA model can determine the proportions of wealth allocated to each mental sub-portfolio with and without input from the investor. Second, unlike other mental accounting models (MA), in CMA it is possible to define constraints on total asset holdings such as short-selling, and cardinality constraints. Third, in order to make CMA more tractable and mathematically elegant, we obtain a semi-definite programming representation of the model. We also present a numerical example to investigate the effects of short-selling constraints as well as to compare the portfolio recommendations, utility functions, feasibility, and optimality of the CMA and MA models. The results reveal that although both models’ solutions are mean-variance efficient, CMA outperforms MA in terms of behavioural efficient frontier and utility functions.     

Alternative to beta coefficients in the context of diffusions

We develop an alternative to the beta coefficient of the CAPM theory. We show the link between this notion and the Wiener chaos expansion of the underlying processes. In the setting of Markov diffusions, we define the drift-neutral beta, which is the quantity of benchmark such that the resulting portfolio is immune to an infinitesimal change of drift on the Brownian motion driving the benchmark. Our approach yields a coefficient which in many practical cases depends on the initial values of both the portfolio and its benchmark. It can also be used to take into account extreme risks and not only the variance. We study several classical diffusion processes and give a full analysis in the case of Jacobi processes. Examples with credit indices show the efficiency of the method in hedging a portfolio.