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Rebalancing Strategies for Multi-Period Asset Allocation



Alternative investments, such as hedge funds, venture capital, and private equity, can improve portfolio performance, especially for long-term institutional and high net worth individual investors. Difficulties arise when rebalancing a portfolio that includes alternative investments due to the nature of the commitments. Transaction costs can be sizable and money flows are restricted by illiquid markets, covenants, and related restrictions. Following a review of the pros and cons of including alternative investments in a traditional portfolio, the authors show the intrinsic advantages of a multi-period asset allocation strategy and present an optimizing approach for addressing transaction costs.
... This concept has been well documented in both theory and practice. There has been a large literature (Mulvey et al. 2001, Mulvey et al. 2004, Mulvey et al. 2007, Mulvey and Kim 2009, Dempster et al. 2008, Dempster et al. 2010, Luenberger 2013) that shows the benefits of rebalancing a portfolio as compared with the traditional buy-and-hold rule embedded in the classical Markowitz portfolio model. In particular, we can evaluate the level of rebalancing gains when stocks are approximated as correlated geometric Brownian motions. ...
... This shows that our approach of applying graphical model combined with rebalancing strategy is able to reap rebalancing gains compared with the traditional 'buy-andhold' strategy. This empirically conforms with the theories of rebalancing gains discussed in Luenberger (2013) and Mulvey et al. 2001, etc. ...
We propose a new stock selection strategy that exploits rebalancing returns and improves portfolio performance. To effectively harvest rebalancing gains, we apply ideas from elliptical-copula graphical modelling and stability inference to select stocks that are as independent as possible. The proposed elliptical-copula graphical model has a latent Gaussian representation; its structure can be effectively inferred using the regularized rank-based estimators. The resulting algorithm is computationally efficient and scales to large data-sets. To show the efficacy of the proposed method, we apply it to conduct equity selection based on a 16-year health care stock data-set and a large 34-year stock data-set. Empirical tests show that the proposed method is superior to alternative strategies including a principal component analysis-based approach and the classical Markowitz strategy based on the traditional buy-and-hold assumption.
... In addition, portfolio management is a multi-period problem (Bajeux-Besnainou, and Portait, 1998) (Mulvey et. al., 2001). Implicitly, this means that portfolio allocation and rebalancing techniques have an added dimension of assuming time persistency of asset pairwise correlation, so that portfolio assets can remain as lowly correlated as possible for as long a period as possible post portfolio allocation and rebalancing, to enjoy optimal diversification ...
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Portfolio diversification involves lowering the correlation between portfolio assets to achieve improved risk-return exposure. It is reasonable to infer from the classic Anscombe quartet, that relying on descriptive statistics, and specifically, correlation, to achieve portfolio diversification may not derive the most optimal multi-period portfolio risk-adjusted return, as stocks in a portfolio can exhibit different price trends over time, even with the same computed pair-wise correlation. This research applied shape-based time-series clustering technique of agglomerative hierarchical clustering using dynamic time series warping as a distance measure to aggregate stocks into like-trending clusters across time, as a portfolio diversification tool. Results support the use of shape-based clustering technique for (i) portfolio allocation and re-balancing, (ii) dynamic predictive portfolio construction, and (iii) individual stock selection through outlier identification. The findings will be a useful addition to existing literature in portfolio management, by providing shape-based clustering as an alternative tool for portfolio construction and security selection. KEY FINDINGS: 1. Performance results indicates a clear and significant improvement in portfolio return and Sharpe performance through shaped-based cluster diversification. Even with a 50% hair-cut in terms of mean return performance, outperformance of shape-based cluster diversification was a compelling 730bps, 816bps, and 888bps, against minimum variance portfolios, industry-diversified portfolios and a control group of randomized portfolios, respectively. Intuitively, this is a rationale result as investing in highly dissimilar trending securities across time should likely bring about diversification benefits in portfolio management. 2. Research shows time persistence of shape-based clustered assets. Rather than observing significant decline in trend similarities over time, in approximation, 8 of 10, 8 of 10, and 7 of 10 stocks displayed similar clustering trends across the one, two and three-year sub-periods under investigation respectively. Observed persistence will imply usefulness for asset allocation and rebalancing in portfolio management, and predictive analysis per-formed on such portfolio construction. 3. Research finds benefits of shape-based clustering with regards to pattern recognition – the identification of outliers, or exceptional star performers and fallen angels within an industry. Another interesting find is the usefulness of identifying non-industry-related stocks within the same shape-based cluster. This allows the identification of assets that appear unrelated, but have idiosyncratic risks and performance profiles that coincided during time periods under observation.
... One needs to be careful in choosing a risk/reward performance criterion for multi-period models. For example, volatility in asset returns can be harnessed over time to boost portfolio performance, a feature studied by Mulvey et al. [2001]. By regularly rebalancing allocations between volatile assets, one can obtain additional return over a naïve buy-and-hold strategy. ...
The Mt. Lucas index provides a systematic approach for capturing a portion of the return of trend-following commodity traders. In this article the authors analyze the Mt. Lucas Index across different historical periods, evaluating its performance within a multi-period asset allocation framework. Their results indicate that the index improves the overall return/risk characteristics of the multi-period asset allocation model. They show that the total return consists of: 1) T-bill returns on marginable assets, 2) static returns from trend-following futures markets, and 3) rebalancing gains. The importance of the third element is emphasized.
The contributions of this paper are threefold. First, by combining dynamic programs and neural networks, we provide an efficient numerical method to solve a large multiperiod portfolio allocation problem under regime-switching market and transaction costs. Second, the performance of our combined method is shown to be close to optimal in a stylized case. To our knowledge, this is the first paper to carry out such a comparison. Last, the superiority of the combined method opens up the possibility for more research on financial applications of generic methods, such as neural networks, provided that solutions to simplified subproblems are available via traditional methods. The research on combining fast starts with neural networks began about four years ago. We observed that Professor Weinan E’s approach for solving systems of differential equations by neural networks had much improved performance when starting close to an optimal solution and could stall if the current iterate was far from an optimal solution. As we all know, this behavior is common with Newton- based algorithms. As a consequence, we discovered that combining a system of differential equations with a feedforward neural network could much improve overall computational performance. In this paper, we follow a similar direction for dynamic portfolio optimization within a regime-switching market with transaction costs. It investigates how to improve efficiency by combining dynamic programming with a recurrent neural network. Traditional methods face the curse of dimensionality. In contrast, the running time of our combined approach grows approximately linearly with the number of risky assets. It is inspiring to explore the possibilities of combined methods in financial management, believing a careful linkage of existing dynamic optimization algorithms and machine learning will be an active domain going forward. Relationship of the authors: Professor John M. Mulvey is Xiaoyue Li’s doctoral advisor.
Leading pension plans employ asset and liability management systems for optimizing their strate- gic decisions. The multi-stage models link asset allocation decisions with payments to beneficia r- ies, changes to plan policies and related issues, in order to maximize the plan's surplus within a given risk tolerance. Temporal aspects complicate the problem but give rise to special opportuni- ties for dynamic investment strategies. Within these models, the portfolio must be re -revised in the face of transaction and market impact costs. The re-balancing problem is posed as a general- ized network with side conditions. We develop a specialize d algorithm for solving the resulting problem. A real-world pension example illustrates the concepts.
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Hedge funds have gained popularity for increasing investment returns. We focus on the role of this asset category for long-term investors, with attention to rebalancing a portfolio of diversified assets. An investor must seek out securities with low correlations to traditional assets to maximize asset growth. Current hedge fund returns, as measured by average performance, show dependencies with equity returns. Other limitations and opportunities for hedge funds are discussed.
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