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Multi-asset allocation of exchange traded funds: Application of Black–Litterman model
Abstract
The Black–Litterman (BL) model allows investors to apply their subjective views to asset allocation optimisation. In this study, we construct a multi-asset allocation portfolio of iShares exchange traded funds (ETFs) using mean–variance (MV) and BL models. Two investment strategies, namely lump-sum investment and a systematic investment plan (SIP), are also investigated and applied to ETF portfolios. On the basis of a momentum strategy, three subjective views of investors are developed for the BL model. The contributions of this empirical study are threefold. First, under the SIP strategy, BL portfolios outperform the MV portfolio in terms of cumulative values, even when an investment starts with bad market timing (i.e., 2008). Second, the asset allocation weights of BL portfolios are demonstrated to be closely related to investors’ subjective views and significantly different from those of the MV portfolio. Third, the three BL portfolios constructed on the basis of the momentum strategy exhibit similar performance patterns in their cumulative returns during the period from 2008 to mid-2021, indicating that investors’ views are consistently reflected in the BL portfolios and consequently contribute to the similarity of the portfolios’ performance as they share similarities in the application of momentum strategies.
... In our paper, ETFs are thus considered as assets to build optimal portfolios, differently from other contributions that investigate the optimal composition of an ETF [50,51]. A number of studies already focused on ETFs liquidity implications, e.g., [50], and portfolio optimization models applied to ETFs (for instance [52,53]), but investigations specific to portfolio selection with liquidity constraints and ETFs on alternative investment markets have not been fully considered. This paper is organized as follows. ...
Recently, liquidity issues in financial markets and portfolio asset management have attracted much attention among investors and scholars, fuelling a stream of research devoted to exploring the role of liquidity in investment decisions. In this paper, we aim to investigate the effects of introducing liquidity in portfolio optimization problems. For this purpose, first we consider three volume-based liquidity measures proposed in the literature and we build a new one particularly suited to portfolio optimization. Secondly, we formulate an extended version of the Markowitz portfolio selection problem, named mean–variance–liquidity, wherein the goal is to minimize the portfolio variance subject to the usual constraint on the expected portfolio return and an additional constraint on the portfolio liquidity. Thirdly, we consider a sensitivity analysis, with the aim to assess the trade-offs between liquidity and return, on the one hand, and between liquidity and risk, on the other hand. In the second part of the paper, the portfolio optimization framework is applied to a dataset of US ETFs comprising both standard and alternative, often illiquid, investments. The analysis is carried out with all the liquidity measures considered, allowing us to shed light on the relationships among risk, return and liquidity. Finally, we study the effects of the introduction of a Bitcoin ETF, as an asset with an extremely high expected return and risk.
... Our analysis utilised the following company abbreviations from Portfolio formation. We created portfolios using two methods: the classical mean variance portfolio optimisation method (Markowitz, 1952(Markowitz, , 2009 and the mean variance with Black-Litterman portfolio optimisation method (Black & Litterman, 1990;Xiao & Valdez, 2015;Min et al., 2021;Tang et al., 2021). ...
The prevailing assumption holds that investors include in their portfolios securities that they know well, are located near their place of residence, or align with their fields of interest. This article analyse familiarity in investment through gender perspective and their fields of interest. Women and men field of interest is defined by enabling online magazines’ article’s themes. The aim of this paper is to investigate gender-based behavioural differences in investment decisions – i.e. to define women’s and men’s fields of interests and value investment portfolios. Portfolios differ according to whether they are formed from securities that are consistent with women’s fields of interest, men’s fields of interest or both women’s and men’s fields of interest. Textual analysis was employed to identify men’s and women’s fields of interest. Investment portfolios were built using mean variance (MV) and Black–Litterman (BL) models. The analysis revealed that portfolios built from men’s fields of interests are more diversified than are portfolios built either from women’s fields of interests or from both men’s and women’s fields of interest. Analysing 12 portfolios’ efficiency revealed that women’s portfolio returns are more stable than are men’s. Moreover, the study demonstrated that time impacts investment portfolio returns to a greater extent than do gendered fields of interest. The article complements the existing knowledge about bias in investor familiarity, which results from differences in men’s and women’s fields of interest.
The paper makes analytical overviews of the Markowitz portfolio and the Capital Asset Pricing models and motivates the advances of the Black-Litterman (BL) one. This overview implies that for a small set of assets the BL model needs the characteristics of a specific market point, which cannot be taken from a global market index. The paper derives analytic relations for the new specific market point with analytical approximation of the efficient frontier. The BL model insists also expert views, which influence the portfolio solution. The paper derives formalization of the expert views from the difference between the evaluated implied returns and historical mean assets returns. Such form of expert views makes modifications of the BL model. This allows comparisons between Markowitz (MV) and BL portfolio performance. Benefits of this research are demonstrated with market data and comparison of the MV and BL portfolio results.
Investors are not all alike, and neither are their sentiments. We show that the sentiment of Wall Street strategists is unrelated to the sentiment of individual investors or that of newsletter writers, although the sentiment of the last two groups is closely related. Sentiment can be useful for tactical asset allocation. We found a negative relationship between the sentiment of each of these three groups and future stock returns, and the relationship is statistically significant for Wall Street strategists and individual investors.
Empirical evidence from a database free of survivorship bias shows that the excess return patterns of long-only industry-level momentum strategies are highly correlated with active fund returns in the growth and the core domains, especially since publication of the momentum effect phenomenon in 1993. The best-performing managers are more strongly similar than the poorest-performing managers, who have low correlation with momentum. Investment performance of momentum strategies at the industry level is competitive, or between the top 10% and top 25% of funds in each period. The source and the persistence of these patterns compared to optimal asset allocation are cause for speculation.
Several versions of the Markowitz portfolio model are evaluated with respect to patterns in the equity markets. Much research
has shown that strategies based on momentum have generated superior risk adjusted returns. We form a long-only portfolio of
momentum strategies via industry-level assets; the strategy beats, many others over numerous markets and time periods and
provides a good benchmark for competing optimization models. Simple Markowitz models are quite effective, as long as the proper
historical period of time is chosen for the stochastic projections. Investment performance of optimal asset allocation models
can be improved by considering the momentum effects in the parameter estimation procedures.
By following the approach of [12], we combine the momentum strategy with the Black-Litterman model in the Taiwan Stock market, to compare the portfolio performance of component stocks in the Taiwan ETF Top 50 (0050) with the its index performance. To test the robustness of our empirical results, we also use different asset allocation strategies covering the same periods of sampled data. We find that by replacing investors’ views with momentum strategy, Black-Litterman model is capable of delivering better performance than traditional global minimum variance portfolio whether in returns or risks.
The Black-Litterman (BL) model aims to enhance asset allocation decisions by overcoming the weaknesses often experienced with standard mean-variance (MV) portfolio optimization. In this study we implement the BL model in a multi-asset portfolio context. Using an investment universe of global stock indices, bonds, and commodities, we empirically test the out-of-sample portfolio performance of BL optimized portfolios and compare the results to mean-variance (MV), minimum-variance, and naïve diversified portfolios (1/N-rule) for the period from January 1993 to December 2011. We find that BL optimized portfolios perform better than MV and naïve diversified portfolios in terms of out-of-sample Sharpe ratios even after controlling for different levels of risk aversion, realistic investment constraints, and transaction costs. Interestingly, the BL approach is well suited to alleviate most of the shortcomings of MV optimization. The resulting portfolios are less risky, provide a higher level of diversification across asset classes, and exhibit less extreme asset allocations. Sensitivity analyses indicate that the outperformance of the BL model is due to the consideration of additional information on the reliability of return estimates and a lower portfolio turnover.
This paper provides a clear and complete explanation of the Black-Litterman model. Drawing from the key papers in the literature it provides a complete derivation of the Black-Litterman model from Theil's Mixed Estimation Model as described in Black and Litterman's original paper. We then show the derivation from Bayesian Theory for comparison. We discuss several of the key papers from the literature. For each paper we provide a complete derivation and explanation of the results, along with a worked example where possible. Where relevant we compare the results from the various papers. The parameters of the model are considered along with information on their computation or calibration. Several methods of measuring or calibrating the results of the model are also presented.
This paper proposes to estimate the covariance matrix of stock returns by an optimally weighted average of two existing estimators: the sample covariance matrix and single-index covariance matrix. This method is generally known as shrinkage, and it is standard in decision theory and in empirical Bayesian statistics. Our shrinkage estimator can be seen as a way to account for extra-market covariance without having to specify an arbitrary multifactor structure. For NYSE and AMEX stock returns from 1972 to 1995, it can be used to select portfolios with significantly lower out-of-sample variance than a set of existing estimators, including multifactor models.
Using a sample free of survivor bias, the author demonstrates that common factors in stock returns and investment expenses almost completely explain persistence in equity mutual funds' mean and risk-adjusted returns. Darryll Hendricks, Jayendu Patel, and Richard Zeckhauser's (1993) 'hot hands' result is mostly driven by the one-year momentum effect of Narasimham Jegadeesh and Sheridan Titman (1993), but individual funds do not earn higher returns from following the momentum strategy in stocks. The only significant persistence not explained is concentrated in strong underperformance by the worst-return mutual funds. The results do not support the existence of skilled or informed mutual fund portfolio managers. Copyright 1997 by American Finance Association.
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