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Register a new userOutperformance and Tracking: Dynamic Asset Allocation for Active and Passive Portfolio Management
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Portfolio management problems are often divided into two types: active and passive, where the objective is to outperform and track a preselected benchmark, respectively. Here, we formulate and solve a dynamic asset allocation problem that combines these two objectives in a unified framework. We look to maximize the expected growth rate differential between the wealth of the investors portfolio and that of a performance benchmark while penalizing risk-weighted deviations from a given tracking portfolio. Using stochastic control techniques, we provide explicit closed-form expressions for the optimal allocation and we show how the optimal strategy can be related to the growth optimal portfolio. The admissible benchmarks encompass the class of functionally generated portfolios (FGPs), which include the market portfolio, as the only requirement is that they depend only on the prevailing asset values. Finally, some numerical experiments are presented to illustrate the risk-reward profile of the optimal allocation.
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We address a portfolio selection problem that combines active (outperformance) and passive (tracking) objectives using techniques from convex analysis. We assume a general semimartingale market model where the assets growth rate processes are driven by a latent factor. Using techniques from convex analysis we obtain a closed-form solution for the optimal portfolio and provide a theorem establishing its uniqueness. The motivation for incorporating latent factors is to achieve improved growth rate estimation, an otherwise notoriously difficult task. To this end, we focus on a model where growth rates are driven by an unobservable Markov chain. The solution in this case requires a filtering step to obtain posterior probabilities for the state of the Markov chain from asset price information, which are subsequently used to find the optimal allocation. We show the optimal strategy is the posterior average of the optimal strategies the investor would have held in each state assuming the Markov chain remains in that state. Finally, we implement a number of historical backtests to demonstrate the performance of the optimal portfolio.
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We employ perturbation analysis technique to study multi-asset portfolio optimisation with transaction cost. We allow for correlations in risky assets and obtain optimal trading methods for general utility functions. Our analytical results are supported by numerical simulations in the context of the Long Term Growth Model.
Markowitz (1952, 1959) laid down the ground-breaking work on the mean-variance analysis. Under his framework, the theoretical optimal allocation vector can be very different from the estimated one for large portfolios due to the intrinsic difficulty of estimating a vast covariance matrix and return vector. This can result in adverse performance in portfolio selected based on empirical data due to the accumulation of estimation errors. We address this problem by introducing the gross-exposure constrained mean-variance portfolio selection. We show that with gross-exposure constraint the theoretical optimal portfolios have similar performance to the empirically selected ones based on estimated covariance matrices and there is no error accumulation effect from estimation of vast covariance matrices. This gives theoretical justification to the empirical results in Jagannathan and Ma (2003). We also show that the no-short-sale portfolio is not diversified enough and can be improved by allowing some short positions. As the constraint on short sales relaxes, the number of selected assets varies from a small number to the total number of stocks, when tracking portfolios or selecting assets. This achieves the optimal sparse portfolio selection, which has close performance to the theoretical optimal one. Among 1000 stocks, for example, we are able to identify all optimal subsets of portfolios of different sizes, their associated allocation vectors, and their estimated risks. The utility of our new approach is illustrated by simulation and empirical studies on the 100 Fama-French industrial portfolios and the 400 stocks randomly selected from Russell 3000.
The problem of portfolio management represents an important and challenging class of dynamic decision making problems, where rebalancing decisions need to be made over time with the consideration of many factors such as investors preferences, trading environments, and market conditions. In this paper, we present a new portfolio policy network architecture for deep reinforcement learning (DRL)that can exploit more effectively cross-asset dependency information and achieve better performance than state-of-the-art architectures. In particular, we introduce a new property, referred to as textit{asset permutation invariance}, for portfolio policy networks that exploit multi-asset time series data, and design the first portfolio policy network, named WaveCorr, that preserves this invariance property when treating asset correlation information. At the core of our design is an innovative permutation invariant correlation processing layer. An extensive set of experiments are conducted using data from both Canadian (TSX) and American stock markets (S&P 500), and WaveCorr consistently outperforms other architectures with an impressive 3%-25% absolute improvement in terms of average annual return, and up to more than 200% relative improvement in average Sharpe ratio. We also measured an improvement of a factor of up to 5 in the stability of performance under random choices of initial asset ordering and weights. The stability of the network has been found as particularly valuable by our industrial partner.
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