Tracking Portfolio Research Articles

Mutual Funds: Portfolio Structures, Analysis, Management, and Stewardship

Mutual Funds: Portfolio Structures, Analysis, Management, and Stewardship

A two-stage stochastic mixed-integer programming approach to the index tracking problem

We consider the problem of tracking a target portfolio or index under uncertainty. Due to an embedded NP-hard subproblem, many of the current index tracking models only consider a small number of important portfolio elements such as transaction costs, number of securities to hold, rebalancing, etc. We formulate a tracking portfolio model that includes a comprehensive set of real-world portfolio elements, one of which involves uncertainty. An index tracking model is defined in a Stochastic Mixed-Integer Programming (SMIP) framework. Due to the size and complexity of the stochastic problem, the SMIP model is decomposed into subproblems and an iterative algorithm is developed that exploits the decomposition. A two-stage SMIP is solved and the results are compared with actual index values. We also provide single-scenario dynamic comparisons to illustrate the performance and strengths of the method.

Tracking Down Distress Risk

This paper shows that exposure to aggregate distress risk is the underlying source of the premiums for the Fama-French size (SMB) and value (HML) factors. Using a unique dataset of aggregate business failures of both private and public firms from 1926 to 1997, I build portfolios that track news about future firm failures. These tracking portfolios optimally hedge aggregate distress risk and earn a CAPM alpha of approximately -4% a year. Both HML and SMB predict changes in future failure rates. Small stocks have lower returns than large stocks and value stocks have lower returns than growth stocks when the market expects an increase in future failure rates. Finally, a two-factor model with the market and the tracking portfolio for aggregate distress as factors does as well as the Fama-French three-factor model in pricing the 25 size and book-to-market sorted portfolios and 30 industry sorted portfolios.

Production-Based Asset Pricing and Economic Tracking Portfolios: Establishing a Dynamic Partial Equilibrium Link between Economic State and Investment Levels

This paper investigates the link between economic state and investment levels in an economy within the premise of a partial equilibrium econometric setup based on the central philosophies of production-based asset pricing model and economic tracking portfolio models. By employing a simple linear combination of a functional transformation of an exhaustive set of economic variables, constituting both broad based macro-variables and variables associated with explicitly identified sectors of the economy, as a model to define an economic state reflecting the available information at any point in time, the paper employs a series of cointegration regression models to establish a dynamic partial equilibrium link between stock market index levels and a dynamically changing/evolving economic state with a one-period lag. A similar dynamic partial equilibrium link, in the spirit of economic tracking portfolio models, is established between sector based indices, constituting the broad market index, and the corresponding economic state model for each of these sectors that take into account explicit economic variables representing these sectors, also with a one-period lag. Finally, the paper extends this framework to establish a similar relationship between economic state and aggregate and sector-based venture capital investment levels, linking the central ideas behind production based asset pricing models and economic tracking portfolio models. The stability of each of these models is investigated by making out-of-sample forecasts and calculating the average time needed for re-evaluation of the models and the recalculation of the associated parameters, before the quality of such forecasts suffer, because of a change in the evolving economic state and effects of such a change on the investment levels in an economy.

A hybrid optimization approach to index tracking

Index tracking consists in reproducing the performance of a stock-market index by investing in a subset of the stocks included in the index. A hybrid strategy that combines an evolutionary algorithm with quadratic programming is designed to solve this NP-hard problem: Given a subset of assets, quadratic programming yields the optimal tracking portfolio that invests only in the selected assets. The combinatorial problem of identifying the appropriate assets is solved by a genetic algorithm that uses the output of the quadratic optimization as fitness function. This hybrid approach allows the identification of quasi-optimal tracking portfolios at a reduced computational cost.

Tracking error: a multistage portfolio model

We study multistage tracking error problems. Different tracking error measures, commonly used in static models, are discussed as well as some problems which arise when we move from static to dynamic models. We are interested in dynamically replicating a benchmark using only a small subset of assets, considering transaction costs due to rebalancing and introducing a liquidity component in the portfolio. We formulate and solve a multistage tracking error model in a stochastic programming framework. We numerically test our model by dynamically replicating the MSCI Euro index. We consider an increasing number of scenarios and assets and show the superior performance of the dynamically optimized tracking portfolio over static strategies.

Volatility Risk Premium, Risk Aversion and the Cross-Section of Stock Returns

We test if innovations in investor risk aversion are a priced factor in the stock market as is predicted by models incorporating habit formation in preferences. Our proxy for time-varying risk aversion is based on the volatility risk premium series constructed by Bollerslev et al. (2007). Time-series tests show that a mimicking portfolio tracking innovations in risk aversion partly captures the strong momentum effect in stock returns and produces only two significant alphas for 25 momentum portfolios. Furthermore, using 25 portfolios sorted on book-to-market and size as test assets in Fama-MacBeth regressions, our new factor together with the market factor explains 64% of the variation in average returns compared to 60% for the Fama-French three factor model. The new factor is generally significant with an estimated risk premium close to its time series mean also when industry portfolios and portfolios sorted on previous returns are included among the test assets.

Are economic tracking portfolios useful for forecasting output and inflation in Austria?*

We construct economic tracking portfolios from Austrian stock market returns, euro/dollar exchange rate changes and changes in the oil price to extract revisions of market expectations about future industrial production growth and inflation in Austria. The forecasting ability of the portfolios is evaluated in-sample and in a pseudo out-of-sample forecasting experiment. It turns out that the tracking portfolios track both target variables in-sample. The portfolios also help to forecast annual industrial production growth out-of-sample. The predictive ability of the tracking portfolios for inflation is rather low. *The opinions expressed do not necessarily reflect those of the Oesterreichische Nationalbank.

Volatility filter for index tracking and long–short market-neutral strategies

Trading strategies utilising price co-movements between financial assets often require that underlying portfolios have high correlations with certain benchmarks and low tracking errors. Since correlations among financial assets are known to be time varying, these portfolios need to be rebalanced dynamically to maintain high ‘tracking efficiency’. The presence of transaction costs, however, prohibits investors from switching market positions too often. It is well known that correlations between equities tend to increase when market volatility is high. The primary objective of this paper is to apply volatility confirmation filters to dynamic index tracking, and long–short market-neutral trading, to enhance the performance of such strategies after transaction costs. In particular, I propose a dynamic rebalancing scheme where the underlying market volatility functions as a timing device and tracking portfolios are only rebalanced when the underlying volatility regime changes. Tracking portfolios studied are optimised by minimising three widely used tracking error measurements: tracking error variance (TEV), mean absolute deviation (MAD) and mean error (ME). Empirical results show that the addition of the volatility filter improves on the excess returns generated from the index tracking strategy. The trading performance of the long–short market-neutral strategy is also significantly enhanced with such a filter in terms of annualised return, annualised volatility and the risk-adjusted Sharpe ratio.

Index tracking with constrained portfolios

AbstractPassive portfolio management strategies, such as index tracking, are popular in the industry, but so far little research has been done on the cardinality of such a portfolio, i.e. on how many different assets ought to be included in it. One reason for this is the computational complexity of the associated optimization problems. Traditional optimization techniques cannot deal appropriately with the discontinuities and the many local optima emerging from the introduction of explicit cardinality constraints. More recent approaches, such as heuristic methods, on the other hand, can overcome these hurdles. This paper demonstrates how one of these methods, differential evolution, can be used to solve the constrained index‐tracking problem. We analyse the financial implication of cardinality constraints for a tracking portfolio using an empirical study of the Down Jones Industrial Average. We find that the index can be tracked satisfactorily with a subset of its components and, more important, that the deviation between computed actual tracking error and the theoretically achievable tracking error out of sample is negligibly affected by the portfolio's cardinality. Copyright © 2007 John Wiley & Sons, Ltd.

Minimizing tracking error while restricting the number of assets

Tracking error minimization is commonly used by the traditional passive fund managers as well as alternative portfolio (for example, hedge fund) managers. We propose a graduated non-convexity method to minimize portfolio tracking error with the total number of assets no greater than a specified integer K. The solution of this tracking error minimization problem is a global minimizer of a minimization problem with a discontinuous counting function in a constraint. We attempt to track the globally minimal tracking error portfolio by approximating the discontinuous counting function with a sequence of continuously differentiable non-convex functions, a graduated non-convexity process. We discuss the advantages of this approach, present numerical results, and compare it with two methods from recent literature.

Forecasting the macroeconomy with contemporaneous financial market information: Europe and the United States

Using Economic Tracking Portfolios (ETP), I find that it is possible to forecast future values of inflation and changes in industrial production in the United States and three core euro countries – Italy, France and Germany – utilizing only current and past financial market information. The longer the forecasting horizon, the better the forecasts based solely on financial market information compared to results from other methods. Of the countries I analyze, the overall forecasting performance of the tracking portfolios is the best for the U.S., and my method outperforms the forecasting performance of a VAR approach.

Integrating market and credit risk: A simulation and optimisation perspective

We introduce a modelling paradigm which integrates credit risk and market risk in describing the random dynamical behaviour of the underlying fixed income assets. We then consider an asset and liability management (ALM) problem and develop a multistage stochastic programming model which focuses on optimum risk decisions. These models exploit the dynamical multiperiod structure of credit risk and provide insight into the corrective recourse decisions whereby issues such as the timing risk of default is appropriately taken into consideration. We also present an index tracking model in which risk is measured (and optimised) by the CVaR of the tracking portfolio in relation to the index. In-sample as well as out-of-sample (backtesting) experiments are undertaken to validate our approach. The main benefits of backtesting, that is, ex-post analysis are that (a) we gain insight into asset allocation decisions, and (b) we are able to demonstrate the feasibility and flexibility of the chosen framework.

Clustering of financial time series with application to index and enhanced index tracking portfolio

A stochastic-optimization technique based on time series cluster analysis is described for index tracking and enhanced index tracking problems. Our methodology solves the problem in two steps, i.e., by first selecting a subset of stocks and then setting the weight of each stock as a result of an optimization process (asset allocation). Present formulation takes into account constraints on the number of stocks and on the fraction of capital invested in each of them, whilst not including transaction costs. Computational results based on clustering selection are compared to those of random techniques and show the importance of clustering in noise reduction and robust forecasting applications, in particular for enhanced index tracking.

Index-plus-alpha tracking under concave transaction cost

We will propose a new scheme to construct an index-plus-alpha portfolio which outperforms a given index by a small positive amount alpha. Among such methods is index tilting where the weight of an index tracking portfolio is slightly modified by taking into account the various information about individual assets. However, portfolios generated by these methods need not outperform the index, particularly when we compare the performance on the net basis, i.e., return after subtracting the transaction cost. &nbsp The method to be proposed in this paper is to calculate a portfolio which keeps track of an index-plus-alpha portfolio with minimal transaction cost. The problem is formulated as a concave minimization under linear constraints, which can be solved in an efficient manner by a branch and bound algorithm. We will demonstrate that this method can usually outperform the given index when alpha is chosen in an appropriate manner.

A methodology for index tracking based on time-series clustering

With the increased acceptance of capital market efficiency, there has been a significant increase in the money managed on an indexed basis. Several methodologies are available to replicate the target index. In this paper, we discuss the problems of (1) defining suitable performance objectives and tracking error that scale properly over the entire management period and (2) implementing an optimal investment strategy when full replication of an index is not deemed suitable. We then argue that clustering might be a viable methodology for building parsimonious tracking portfolios. With suitably defined distances between the time series of asset prices, clustering ‘discovers’ the correlation and cointegration structure of an index. Sampling the clusters with appropriate heuristics and optimization techniques, an optimal tracking portfolio can be constructed. One advantage of this approach is that it eschews the difficulties and computational burden of density forecasts and full optimization.

Honey, I Shrunk the Sample Covariance Matrix

The central message of this article is that no one should use the sample covariance matrix for portfolio optimization. It is subject to estimation error of the kind most likely to perturb a mean-variance optimizer. Instead, a matrix can be obtained from the sample covariance matrix through a transformation called shrinkage. This tends to pull the most extreme coefficients toward more central values, systematically reducing estimation error when it matters most. Statistically, the challenge is to know the optimal shrinkage intensity. Shrinkage reduces portfolio tracking error relative to a benchmark index, and substantially raises the manager9s realized information ratio.

The performance of economic tracking portfolios in an IT-intensive stock market

In this paper we use an economic tracking portfolio (ETP) approach for forecasting future values of macroeconomic variables in the IT-intensive Finnish stock market. The results confirm recently obtained conclusions in Lamont [J. Econ. 105 (2001) 161] and Hayes [Bank of England Working Paper 137/2001] that ETPs contain relevant information about macroeconomic variables. When compared to the market portfolio, some industry portfolios seem to forecast the future macroeconomy better than others. In addition, our results give support for the use of industry portfolios in out-of-sample forecasting in the ETP framework. Especially the ‘new economy’ stock returns have clear forecasting power for future inflation and changes in industrial production in the Finnish economy at short horizons.

Forecasting the Economic State with Financial Market Information and Term Structure of Interest Rates

This study examines whether financial markets, especially excess stock returns, contain information about changes in future values of certain macroeconomic variables. Earlier literature documents that term spreads of interest rates can predict both nominal activity, i.e. inflation, and real activity, i.e. output, consumption and industrial production, in economy. We combine stock returns and term spreads in an economic tracking portfolio framework and show that economic tracking portfolios can forecast changes in future macroeconomic variables, most accurately with 12 month forecasting horizon. The information content of industry stock portfolios depends on the target macroeconomic variable. The importance of term spreads is supported in two ways: first, they improve the performance of the ETP model even though the omission of them from the analysis seems to have only marginal effect; second, the only benchmark model that outperforms the ETP model in some cases uses solely term spreads as explanatory variables.

The Performance of Economic Tracking Portfolios in an IT-sensitive Stock Market

In this paper we use an economic tracking portfolio (ETP) approach for forecasting future values of macroeconomic variables in the IT-sensitive Finnish stock market. The results confirm recently obtained conclusions in Lamont (2001), Hayes (2001) and Junttila (2002) that ETPs contain relevant information about macroeconomic variables. According to our results, when compared to the market portfolio, different industry portfolios might forecast the future macroeconomic variables better. The analysis also shows that the control variables may not play such an important role in a closed-economy context when compared to earlier studies using an international asset return data set in the ETP framework. It seems to be more important to consider carefully the choice of base assets and their account. The results also give clear support for the use of industry portfolios in out-of-sample forecasting in the ETP framework. Especially the 'new economy' stock returns (like the IT-return) have clear forecasting power for future inflation and changes in industrial production in the Finnish economy at short horizons.