Multiperiod portfolio optimization with multiple risky assets and general transaction costs

We analyze the optimal portfolio policy for a multiperiod mean-variance investor facing multiple risky assets in the presence of general transaction costs. For proportional transaction costs, we give a closed-form expression for a no-trade region, shaped as a multi-dimensional parallelogram, and show how the optimal portfolio policy can be efficiently computed for many risky assets by solving a single quadratic program. For market impact costs, we show that at each period it is optimal to trade to the boundary of a state-dependent rebalancing region. Finally, we show empirically that the losses associated with ignoring transaction costs and behaving myopically may be large

Cover-up of vehicle defects: the role of regulator investigation announcements

Automakers such as Toyota and GM were recently caught by the U.S. regulator for deliberately hiding product defects in an attempt to avoid massive recalls. Interestingly, regulators in the U.S. and U.K. employ different policies in informing consumers about potential defects: The U.S. regulator publicly announces all on-going investigations of potential defects to provide consumers with early information, whereas the U.K. regulator does not. To understand how these different announcement policies may affect cover-up decisions of automakers, we model the strategic interaction between a manufacturer and a regulator. We find that, under both countries' policies, the manufacturer has an incentive to cover up a potential defect when there is a high chance that the defect indeed exists and it may in inflict only moderate harm. However, if there is only a moderate chance that the defect exists, only under the U.S. policy does the manufacturer have an incentive to cover up a potential defect with significant harm. We show that the U.S policy generates higher social welfare only for very serious issues for which both the expected harm and recall cost are very high and the defect is likely to exist. We make four policy recommendations that could help mitigate manufacturers' cover-ups, including a hybrid policy in which the regulator conducts a confidential investigation of a potential defect only when it may inflict significant harm

Technical note: a robust perspective on transaction costs in portfolio optimization

We prove that the portfolio problem with transaction costs is equivalent to three different problems designed to alleviate the impact of estimation error: a robust portfolio optimization problem, a regularized regression problem, and a Bayesian portfolio problem. Motivated by these results, we propose a data-driven approach to portfolio optimization that tackles transaction costs and estimation error simultaneously by treating the transaction costs as a regularization term to be calibrated. Our empirical results demonstrate that the data-driven portfolios perform favorably because they strike an optimal trade-off between rebalancing the portfolio to capture the information in recent historical return data, and avoiding the large transaction costs and impact of estimation error associated with excessive trading

A simple scheme for allocating capital in a foreign exchange proprietary trading firm

We present a model of capital allocation in a foreign exchange proprietary trading firm. The owner allocates capital to individual traders, who operate within strict risk limits. Traders specialize in individual currencies, but are given discretion over their choice of trading rule. The owner provides the simple formula that determines position sizes – a formula that does not require estimation of the firm-level covariance matrix. We provide supporting empirical evidence of excess risk-adjusted returns to the firm-level portfolio, and we discuss a modification of the model in which the owner dictates the choice of trading rule

Machine Learning and Fund Characteristics Help to Select Mutual Funds with Positive Alpha

Machine-learning methods exploit fund characteristics to select tradable long-only portfolios of mutual funds that earn significant out-of-sample annual alphas of 2.4% net of all costs. The methods unveil interactions in the relation between fund characteristics and future performance. For instance, past performance is a particularly strong predictor of future performance for more active funds. Machine learning identifies managers whose skill is not sufficiently offset by diseconomies of scale, consistent with informational frictions preventing investors from identifying the outperforming funds. Our findings demonstrate that investors can benefit from active management, but only if they have access to sophisticated prediction methods

Regularizing Portfolio Optimization

The optimization of large portfolios displays an inherent instability to estimation error. This poses a fundamental problem, because solutions that are not stable under sample fluctuations may look optimal for a given sample, but are, in effect, very far from optimal with respect to the average risk. In this paper, we approach the problem from the point of view of statistical learning theory. The occurrence of the instability is intimately related to over-fitting which can be avoided using known regularization methods. We show how regularized portfolio optimization with the expected shortfall as a risk measure is related to support vector regression. The budget constraint dictates a modification. We present the resulting optimization problem and discuss the solution. The L2 norm of the weight vector is used as a regularizer, which corresponds to a diversification "pressure". This means that diversification, besides counteracting downward fluctuations in some assets by upward fluctuations in others, is also crucial because it improves the stability of the solution. The approach we provide here allows for the simultaneous treatment of optimization and diversification in one framework that enables the investor to trade-off between the two, depending on the size of the available data set

An Evolutionary Optimization Approach to Risk Parity Portfolio Selection

In this paper we present an evolutionary optimization approach to solve the risk parity portfolio selection problem. While there exist convex optimization approaches to solve this problem when long-only portfolios are considered, the optimization problem becomes non-trivial in the long-short case. To solve this problem, we propose a genetic algorithm as well as a local search heuristic. This algorithmic framework is able to compute solutions successfully. Numerical results using real-world data substantiate the practicability of the approach presented in this paper

Strategies used as spectroscopy of financial markets reveal new stylized facts

We propose a new set of stylized facts quantifying the structure of financial markets. The key idea is to study the combined structure of both investment strategies and prices in order to open a qualitatively new level of understanding of financial and economic markets. We study the detailed order flow on the Shenzhen Stock Exchange of China for the whole year of 2003. This enormous dataset allows us to compare (i) a closed national market (A-shares) with an international market (B-shares), (ii) individuals and institutions and (iii) real investors to random strategies with respect to timing that share otherwise all other characteristics. We find that more trading results in smaller net return due to trading frictions. We unveiled quantitative power laws with non-trivial exponents, that quantify the deterioration of performance with frequency and with holding period of the strategies used by investors. Random strategies are found to perform much better than real ones, both for winners and losers. Surprising large arbitrage opportunities exist, especially when using zero-intelligence strategies. This is a diagnostic of possible inefficiencies of these financial markets.Comment: 13 pages including 5 figures and 1 tabl