Foreign reserves’ strategic asset allocation

Despite foreign reserves’ strategic asset allocation relies mainly on Modern Portfolio Theory (MPT), the unique characteristics of central banks obliges them to articulate and reconcile typical optimization procedures with reserves’ management objectives such as providing confidence regarding the ability to meet the country’s external commitments. Moreover, further involvedness come from broad economic factors as diverse as the openness of capital and current accounts, external debt’s maturity and currency composition, and exchange rate regime. Therefore, in order to alleviate the divergence from theory and practice regarding foreign reserves’ strategic asset allocation, this paper describes the methodologies and procedures developed and employed by the Foreign Reserves Department of Banco de la República. The mainstay of the paper is a long-term-dependence-adjusted and non-loss-constrained version of the Black-Litterman model for obtaining the efficient frontier from a set of investments complying with safety, liquidity and return criteria, where the choice of the portfolio which maximizes utility makes use of an estimation of the Board of Directors’ risk aversion. Results exhibit the effects of the unique nature of foreign reserves management for emerging markets. Typical features of foreign reserves management by central banks, such as non-loss restrictions due to capital preservation objectives, result in increased complexity in the optimization process and in asset allocations significantly distant from standard MPT’s optimality.Foreign reserves, Black-Litterman, strategic asset allocation. Classification JEL: G11, E58, C11, C61.

Employing behavioural portfolio theory for sustainable investment: Examining drawdown risks and ESG factors

This study uses behavioural portfolio theory (BPT) within the Markowitz Portfolio Theory framework to enhance portfolio management by focusing on sustainability and risk mitigation during market downturns. It selects portfolios to hedge against market lows using Conditional Drawdown at Risk (CDaR) and Expected Regret of Drawdown (ERoD). These measures help choose securities that perform well during a market decline. This study applies drawdown-based risk metrics to assist institutional investors and fiduciaries in making informed investment and fund management decisions. By merging BPT with Markowitz’s mean–variance framework, selected investments are maintained above a safety threshold, contributing to the portfolio’s overall quality and sustainability. Additionally, by incorporating an Environmental, Social, and Governance (ESG) preference function, the findings suggest that BPT built portfolios meet traditional performance standards and align with socially responsible investment principles, thereby offering higher utility and alignment with investor values focused on sustainable investing

Approximating the Growth Optimal Portfolio and its applications in quantitative finance

The Benchmark Approach (BA) represents an alternative framework to quantitative finance that relies on the existence of a Growth Optimal Portfolio (GOP) to be used as Numeraire for financial modeling. When employed as a benchmark, the GOP makes any other non-negative portfolio either trendless or mean-decreasing. This property is known as supermartingale property, and it allows to exclude ex-ante some basic forms of arbitrage in the financial markets. Moreover, the GOP is constructed to maximize the long-term growth rate of the investment, and it delivers the best long-term performance when compared to any other strictly positive portfolio. These results are particularly interesting to apply the BA framework in the context of portfolio optimization and valuation of contingent claims. By introducing the Diversification Theorem, Platen and Heath (2006) show that Diversified Portfolios (DPs) converge to the Numeraire when composed by a sufficiently large number of constituents. In the present research, we build on this result and exploit naive-diversification as a tool to construct valid proxies of the GOP. More specifically, we follow the methodology proposed by Platen and Rendek (2020) to construct a Hierarchically Weighted Index (HWI), a particular class of equally-weighted strategies that proved to be very robust to approximate the GOP. We evaluate the performance of different specifications of the HWI against the traditional Equally Weighted Index (EWI) and the MSCI-World Index. As a final result, we prove that the HWI approximates well the GOP, by showing robust statistical evidence that the supermartingale property of benchmarked returns cannot be easily rejected when our preferred HWI specification is used as a benchmark.The Benchmark Approach (BA) represents an alternative framework to quantitative finance that relies on the existence of a Growth Optimal Portfolio (GOP) to be used as Numeraire for financial modeling. When employed as a benchmark, the GOP makes any other non-negative portfolio either trendless or mean-decreasing. This property is known as supermartingale property, and it allows to exclude ex-ante some basic forms of arbitrage in the financial markets. Moreover, the GOP is constructed to maximize the long-term growth rate of the investment, and it delivers the best long-term performance when compared to any other strictly positive portfolio. These results are particularly interesting to apply the BA framework in the context of portfolio optimization and valuation of contingent claims. By introducing the Diversification Theorem, Platen and Heath (2006) show that Diversified Portfolios (DPs) converge to the Numeraire when composed by a sufficiently large number of constituents. In the present research, we build on this result and exploit naive-diversification as a tool to construct valid proxies of the GOP. More specifically, we follow the methodology proposed by Platen and Rendek (2020) to construct a Hierarchically Weighted Index (HWI), a particular class of equally-weighted strategies that proved to be very robust to approximate the GOP. We evaluate the performance of different specifications of the HWI against the traditional Equally Weighted Index (EWI) and the MSCI-World Index. As a final result, we prove that the HWI approximates well the GOP, by showing robust statistical evidence that the supermartingale property of benchmarked returns cannot be easily rejected when our preferred HWI specification is used as a benchmark

Tail risk constraints and maximal entropy

Portfolio selection in the financial literature has essentially been analyzed under two central assumptions: full knowledge of the joint probability distribution of the returns of the securities that will comprise the target portfolio; and investors’ preferences are expressed through a utility function. In the real world, operators build portfolios under risk constraints which are expressed both by their clients and regulators and which bear on the maximal loss that may be generated over a given time period at a given confidence level (the so-called Value at Risk of the position). Interestingly, in the finance literature, a serious discussion of how much or little is known from a probabilistic standpoint about the multi-dimensional density of the assets’ returns seems to be of limited relevance. Our approach in contrast is to highlight these issues and then adopt throughout a framework of entropy maximization to represent the real world ignorance of the “true” probability distributions, both univariate and multivariate, of traded securities’ returns. In this setting, we identify the optimal portfolio under a number of downside risk constraints. Two interesting results are exhibited: (i) the left- tail constraints are sufficiently powerful to override all other considerations in the conventional theory; (ii) the “barbell portfolio” (maximal certainty/ low risk in one set of holdings, maximal uncertainty in another), which is quite familiar to traders, naturally emerges in our construction

A constrained swarm optimization algorithm for large-scale long-run investments using Sharpe ratio-based performance measures

We study large-scale portfolio optimization problems in which the aim is to maximize a multi-moment performance measure extending the Sharpe ratio. More specifically, we consider the adjusted for skewness Sharpe ratio, which incorporates the third moment of the returns distribution, and the adjusted for skewness and kurtosis Sharpe ratio, which exploits in addition the fourth moment. Further, we account for two types of real-world trading constraints. On the one hand, we impose stock market restrictions through cardinality, buy-in thresholds, and budget constraints. On the other hand, a turnover threshold restricts the total allowed amount of trades in the rebalancing phases. To deal with these asset allocation models, we embed a novel hybrid constraint-handling procedure into an improved dynamic level-based learning swarm optimizer. A repair operator maps candidate solutions onto the set characterized by the first type of constraints. Then, an adaptive l1-exact penalty function manages turnover violations. The focus of the paper is to highlight the importance of including higher-order moments in the performance measures for long-run investments, in particular when the market is turbulent. We carry out empirical tests on two worldwide sets of assets to illustrate the scalability and effectiveness of the proposed strategies, and to evaluate the performance of our investments compared to the strategy maximizing the Sharpe ratio

Risk Parity Portfolio Optimization under Heavy-Tailed Returns and Time-Varying Volatility

Risk parity portfolio optimization, using expected shortfall as the risk measure, is investigated when asset returns are fat-tailed and heteroscedastic. The conditional return distribution is modeled by an elliptical multivariate generalized hyperbolic distribution, allowing for fast parameter estimation, via an expectation-maximization algorithm and a semi-closed form of the risk contributions. The efficient computation of non-Gaussian risk parity weights sidesteps the need for numerical simulations or Cornish-Fisher-type approximations. Accounting for fat-tailed returns, the risk parity allocation is less sensitive to volatility shocks, thereby generating lower portfolio turnover, in particular during market turmoils such as the global financial crisis. Although risk parity portfolios are surprisingly robust to the misuse of the Gaussian distribution, a more realistic model for conditional returns and time-varying volatilies can improve risk-adjusted returns, reduces turnover during periods of market stress and enables the use of a holistic risk model for portfolio and risk management

Eficiencia y persistencia de los fondos de retorno absolutos españoles

URL del artículo en la web de la Revista: https://www.upo.es/revistas/index.php/RevMetCuant/article/view/2703Performance measurement is an area of crucial interest in asset valuation and investment management. High volatility as well as time aggregation of returns, amongst other characteristics, may distort the results of conventional measures of performance. In this work, we study the performance of 115 Spanish Absolute Return Funds in the period 2010-2015, using the Sharpe, Treynor, Jensen and Modified Sharpe ratios. We then apply Data Envelopment Analysis to classify the funds in order to avoid the problems arising from the non-normality of their returns, since non-gaussian returns do not pose a problem in Data Envelopment Analysis implementation. In addition, we apply the Malkiel, Brown and Goetzman test and the Rude and Khan test in annual periods to determine the existence of persistence. Finally, we study the relationship between efficiency and persistence in order to determine the relationship between both measures and to support decision-making processes. The results show a significant relationship between cross efficiency and Modified Sharpe ratios as well as the existence of persistence for annual periods. Nevertheless, the results do not allow concluding any relationship amongst efficiency and persistence.La medida de la performance es un área de crucial interés en la valoración de activos y selección de inversiones. Elevadas volatilidades, así como la agregación temporal de rendimientos, entre otras características, pueden distorsionar los resultados de las medidas convencionales de performance. En este trabajo, estudiamos la performance de 115 fondos de retorno absoluto españoles en el periodo 2010¿2015 usando los ratios de Sharpe, Treynor y Jensen y el ratio de Sharpe modificado. Posteriormente, para clasificar los fondos se aplica el Análisis Envolvente de Datos (Data Envelopment Analysis, DEA) en aras de evitar los problemas derivados de la no normalidad de los rendimientos, dado que rendimientos no gaussianos no suponen un problema a la hora de implementar el Análisis Envolvente de Datos. Adicionalmente, se aplica el test de Malkiel, Brown y Goetzman y el test de Rude y Khan en periodos anuales para determinar la existencia de persistencia. Finalmente. se estudia la relación entre eficiencia y persistencia con objeto de determinar la relación entre ambas medidas y apoyar el proceso de toma de decisiones. Los resultados muestran una significativa relación entre eficiencia cruzada y el ratio de Sharpe modificado así como la existencia de persistencia en periodos anuales. No obstante, los resultados no permiten concluir en ninguna relación directa entre eficiencia y persistencia.Universidad Pablo de Olavid

Optimalizace portfolia na burze cenných papírů v Hongkongu

Portfolio optimization is the process of selecting the best portfolio from all the portfolios to be considered. The purpose of this thesis is to compare the out-of-sample performance of the selected portfolio optimisation strategies in terms of return and risk, and thus to select the investment strategy or model that finds the best portfolio for a given situation. The thesis is structured into five chapters. In Chapter 1, we briefly describe the overall framework. In Chapter 2, we focus on describing the history, characteristics and performance of stock exchanges. In Chapter 3, we describe the strategy theory that we apply in the practical part. Portfolio backtesting and portfolio performance measures are also described. In Chapter 4, we divide the analysis into in-sample and out-of-sample periods. We apply the strategies in each of these two periods and backtest the strategies in the out-of-sample period. Finally, we compare the strategies in the out-of-sample period by means of performance indicators and select the best portfolio strategy. Chapter 5 provides a concluding description of the full thesis.Optimalizace portfolia je proces výběru nejlepšího portfolia ze všech uvažovaných portfolií. Cílem této práce je porovnat výkonnost vybraných strategií optimalizace portfolia v out-of-sample období z hlediska výnosu a rizika, a vybrat tak investiční strategii nebo model, který najde nejlepší portfolio pro danou situaci. Diplomová práce je strukturována do pěti kapitol. V první kapitole stručně popisujeme celkový rámec. V druhé kapitole se zaměřujeme na popis historie, charakteristik a výkonnosti burz cenných papírů. V třetí kapitole popisujeme teorii strategií, kterou aplikujeme v praktické části práce. Dále je popsáno zpětné testování portfolia a měření výkonnosti portfolia. Ve čtvrté kapitole rozdělujeme analýzu na období in-sample a out-of-sample. V každém z těchto dvou období aplikujeme strategie a v out-of-sample období strategie zpětně testujeme. Nakonec porovnáváme strategie v out-of-sample období pomocí ukazatelů výkonnosti a vybereme nejlepší strategii. Pátá kapitola obsahuje závěrečný popis celé práce.154 - Katedra financívýborn