Portfolio Selection Algorithm Research Articles

On‐Line Portfolio Selection Using Multiplicative Updates

We present an on‐line investment algorithm that achieves almost the same wealth as the best constant‐rebalanced portfolio determined in hindsight from the actual market outcomes. The algorithm employs a multiplicative update rule derived using a framework introduced by Kivinen and Warmuth. Our algorithm is very simple to implement and requires only constant storage and computing time per stock in each trading period. We tested the performance of our algorithm on real stock data from the New York Stock Exchange accumulated during a 22‐year period. On these data, our algorithm clearly outperforms the best single stock as well as Cover's universal portfolio selection algorithm. We also present results for the situation in which the investor has access to additional “side information.”

Earnings announcements and portfolio selection. Do they add value?

One of the thorniest problems in investment research is to integrate academic research into a viable investment product. Research techniques that have shown promise in academic studies do not translate well into financial products. The concern of this paper is the academic research that indicates that there is usable information in earnings announcements. A number of articles have explored analysts' earnings estimates, analysts' forecasting ability and the reaction of stock prices to earnings announcements. One research areas is the group of stocks whose earnings announcements constitute positive “earnings surprise” given a consensus of analysts' expected earnings. The consensus derives from a twenty quarter, seasonally adjusted earnings trend and the median analysts' forecasts from I/B/E/S, Inc. The quantitative research department of a major securities firm has identified and published a list of “earnings surprise” stocks for the past 9 years. The major issue addressed in this paper is whether the information contained in earnings announcements is useful as a security screening technique for a portfolio selection process, i.e., Do earnings announcements add value to the performance of a portfolio? Previous studies focused on individual securities. There have been no attempts at integrating earnings surprise into a systematic portfolio approach. The study conducts a comprehensive backtest of whether there is new investment information in earnings surprise data when used with a portfolio selection algorithm. Since the focus is on a usable financial product, this study uses economic return performance to evaluate its results rather than the more commonly used statistical methodology. The results indicate that using earnings surprise information in a periodic revision of a portfolio does not add value. Any value added derives from the portfolio selection algorithm not from the fact that the stocks in the analysis are “earnings surprise” stocks. In addition, the earnings surprise stocks are a source of increased volatility when used in 15–30 asset portfolios.

Switching portfolios.

A constant rebalanced portfolio is an asset allocation algorithm which keeps the same distribution of wealth among a set of assets along a period of time. Recently, there has been work on on-line portfolio selection algorithms which are competitive with the best constant rebalanced portfolio determined in hindsight (Cover, 1991; Helmbold et al., 1996; Cover and Ordentlich, 1996). By their nature, these algorithms employ the assumption that high returns can be achieved using a fixed asset allocation strategy. However, stock markets are far from being stationary and in many cases the wealth achieved by a constant rebalanced portfolio is much smaller than the wealth achieved by an ad hoc investment strategy that adapts to changes in the market. In this paper we present an efficient portfolio selection algorithm that is able to track a changing market. We also describe a simple extension of the algorithm for the case of a general transaction cost, including the transactions cost models recently investigated in (Blum and Kalai, 1997). We provide a simple analysis of the competitiveness of the algorithm and check its performance on real stock data from the New York Stock Exchange accumulated during a 22-year period. On this data, our algorithm outperforms all the algorithms referenced above, with and without transaction costs.

Forecasting the return and risk on a portfolio of assets

Portfolio selection algorithms use estimates of expected return and risk as their primary input. It is axiomatic that the accuracy of this input has a major impact on the quality of the final selection decision. This paper examines the forecasting performance of the models used to provide these estimates of return and risk. The approach used looks at both pricing models and time series models. Pricing models describe the inter-relationships between returns on different assets and the associated risk. Time series models describe the evolution of returns and risk over time. A random portfolio approach is used to test the forecasting performance of the combinations of each type of model, in terms of expected return and risk. The choice of models is shown to be critical and the relative performance of the models is described.

An Algorithm for Portfolio Selection in a Lognormal Market

Ohlson and Ziemba developed an approximation for the solution of the portfolio problem with lognormally distributed assets when the investor has a power utility function. The approximating problem has been analyzed by Schaible and Ziemba and it may fail to be quasiconcave. In this paper a convergent finite algorithm that finds a global optimum is presented for this problem. The algorithm is an adaption of Markowitz's critical line algorithm for parametric convex quadratic programming.

A Stochastic Generalized Network Model and Large-Scale Mean-Variance Algorithm for Portfolio Selection

Abstract This paper describes a generalized network framework and an efficient, practical algorithm for large scale mean-variance portfolio selection, based on the nonparametric description of stochastic processes in the frequency domain. A constraint on the variance of uncertain incoming flows to a node in a network model results in a quadratic expression, involving the variance aαd covariance of the distributions of these flows. We show that, when the portfolio variance is decomposed into its frequency components using the Fourier transform, this kind of nonlinear side constraint can be relaxed to produce a set of linear side constraints. Our approach based on this relationship is particularly convenient for large scale problems since no covariance matrix input is required.

OPTIMAL PORTFOLIO SELECTION WITH UPPER BOUNDS FOR INDIVIDUAL SECURITIES*

ABSTRACTIn this paper, we consider optimal portfolio selection with no short sales and with upper bounds for individual securities. The solution is reached by directy revising the optimal portfolio without upper bounds. Specifically, our analysis is based on the single‐index model, as well as the general multi‐index model that provides the return generating process for securities in the arbitrage pricing theory. As demonstrated in a simulation study, the proposed algorithm for optimal portfolio selection usually requires very few iterations. Also, since our approach is developed using intuitive reasoning and simple linear algebra, we are able to provide direct and intuitive justifications for the resulting portfolio choice. Therefore this paper should be of interest to both finance academics and practitioners in portfolio management.

Empirical Bayes stock market portfolios

We exhibit a compound sequential Bayes portfolio selection algorithm based solely on the past which not only lives off market fluctuations but follows the drift as well. In fact, this sequential portfolio performs as well (up to first order terms in the exponent) as the optimal portfolio based on advance knowledge of the n-period empirical distribution of the market. Moreover, to first order in the exponent, the capital resulting from this portfolio will be no less than the best of the available stocks. This is a result that holds for every sample sequence. Thus bull markets and bear markets can not fool the investor into over-committing or under-committing his capital to the risky alternatives available to him. The goal is accomplished by a choice of portfolio which is robust with respect to futures that may differ drastically from the past.

Unit trusts and portfolio selection on the Johannesburg Stock Exchange

The application of the standard techniques of portfolio selection on the 34 sectors comprising the JSE All Share index is undertaken for the three equal non-overlapping five-year periods between February 1965 and January 1980. Efficient portfolios in each period which carry the same risk as the market index are seen to outperform the market substantially. Portfolios chosen at random to span the efficient frontier in each period reveal the consistent inefficiency of 10 sectors over the 15-year period. Three of these sectors, namely Mining Holding, Mining Houses and Industrial Holding are shown to be favoured in the Association of Unit Trusts portfolio relative to these sectors' proportion of the market. On the presumption that unit trust managers attempt to act efficiently, holding these sectors is only justified if the measure of risk used in the portfolio selection algorithm, namely standard deviation of expected return, is less appropriate than other measures of risk such as earnings volatility. If standard deviation of expected return is a more appropriate measure of risk in the selection of efficient portfolios, it must be concluded that the large sophisticated investors managing the unit trusts act inefficiently.

A Simple Algorithm for Optimal Portfolio Selection with Fixed Transaction Costs

The general optimal portfolio selection problem with fixed transaction costs is a complex mathematical programming problem. However, by placing reasonable restrictions on the variance-covariance matrix of returns, it is possible to simplify the solution of the problem. Specifically if the structure of returns between securities is such that the pairwise correlation coefficients are approximately the same, a fairly simple algorithm which requires little computational effort can be employed. This method can also be extended to the case where changes in the information set necessitate a revision of an existing portfolio.

An integer programming algorithm for portfolio selection with fixed charges

AbstractA mean‐variance portfolio selection model with limited diversification is formulated in which transaction and management costs are incorporated as the sum of a linear cost and a fixed cost. The problem is a fixed charge integer programming problem solved by hypersurface search using dynamic programming. Fathoming is performed in the forward pass of dynamic programming so that values of the state variable which correspond to infeasible solutions are eliminated from the tables. This logic permits the solution of problems with 20–30 possible investments.

An Algorithm for Counting the Number of Possible Portfolios Given Linear Restrictions on the Weights

In application of portfolio selection algorithms [3,4] and in tests of the effectiveness of these approaches [1,2], it is sometimes useful to know, a priori, the size of the set of possible portfolios that may be encountered. Given a set of linear restrictions such as that worked by Frankfurter, Phillips, and Seagle [1,2], the set of possible portfolios is finite. This note presents a simple algorithm for determining the size of this set. Only two inputs are required: 1. The size of the universe of securities under study, and 2. A functional relationship which acts as a constraint on the weights. The following is a heuristic algorithm without a rigorous, generalized proof. Assuming that the portfolio weights are stepped from 0 to 1 in steps of 0.10, then Matrix I displays the generation of the Total (T.) of possible port?

A Linear Programming Algorithm for Mutual Fund Portfolio Selection

The portfolio selection problem faced by a mutual fund manager can be formulated following the Markowitz approach: find those portfolios that are efficient in terms of predicted expected return and standard deviation of return, subject to legal constraints in the form of upper bounds on the proportion of the fund invested in any single security. This paper suggests that such problems be re-formulated as parametric linear-programming problems, utilizing a linear approximation to the true (quadratic) formula for a portfolio's risk. Limited empirical evidence suggests that the approximation is acceptable. Moreover, it allows the use of an extremely simple and efficient special-purpose solution algorithm. With appropriate modifications, this algorithm may prove useful to the managers of mutual funds with a wide variety of objectives.