Particle swarm optimization approach to portfolio construction

Particle swarm optimization (PSO) is an artificial intelligence technique that can be used to find approximate solutions to extremely difficult or impossible numeric optimization problems. Recently, PSO algorithms have been widely used in solving complex financial optimization problems. This paper presents a PSO approach to solve a portfolio construction problem, since this methodology is a population-based heuristic algorithm that is suitable for solving high-dimensional constrained optimization problems. The computational results show that PSO algorithms have advantages in optimizing the Sortino ratio, especially in speed, when the size of the portfolio is large.     

A Markov-switching COGARCH approach to cryptocurrency portfolio selection and optimization

Financial Markets and Portfolio Management - Blockchain is a new technology slowly integrating our economy with cryptocurrencies such as Bitcoin and many more applications. Bitcoin and other...     

Dynamic portfolio optimization with liquidity cost and market impact: a simulation-and-regression approach

We present a simulation-and-regression method for solving dynamic portfolio optimization problems in the presence of general transaction costs, liquidity costs and market impact. This method extends the classical least squares Monte Carlo algorithm to incorporate switching costs, corresponding to transaction costs and transient liquidity costs, as well as multiple endogenous state variables, namely the portfolio value and the asset prices subject to permanent market impact. To handle endogenous state variables, we adapt a control randomization approach to portfolio optimization problems and further improve the numerical accuracy of this technique for the case of discrete controls. We validate our modified numerical method by solving a realistic cash-and-stock portfolio with a power-law liquidity model. We identify the certainty equivalent losses associated with ignoring liquidity effects, and illustrate how our dynamic optimization method protects the investor's capital under illiquid market conditions. Lastly, we analyze, under different liquidity conditions, the sensitivities of certainty equivalent returns and optimal allocations with respect to trading volume, stock price volatility, initial investment amount, risk aversion level and investment horizon.     

On portfolio optimization: Imposing the right constraints

We reassess the recent finding that no established portfolio strategy outperforms the naively diversified portfolio, 1/N, by developing a constrained minimum-variance portfolio strategy on a shrinkage theory based framework. Our results show that our constrained minimum-variance portfolio yields significantly lower out-of-sample variances than many established minimum-variance portfolio strategies. Further, we observe that our portfolio strategy achieves higher Sharpe ratios than 1/N, amounting to an average Sharpe ratio increase of 32.5% across our six empirical datasets. We find that our constrained minimum-variance strategy is the only strategy that achieves the goal of improving the Sharpe ratio of 1/N consistently and significantly. At the same time, our developed portfolio strategy achieves a comparatively low turnover and exhibits no excessive short interest.     

A geometric approach to portfolio optimization in models with transaction costs

We consider a continuous-time stochastic optimization problem with infinite horizon, linear dynamics, and cone constraints which includes as a particular case portfolio selection problems under transaction costs for models of stock and currency markets. Using an appropriate geometric formalism we show that the Bellman function is the unique viscosity solution of a HJB equation.Mathematics Subject Classification (1991): 60G44JEL Classification: G13, G11This research was done at Munich University of Technology supported by a Mercator Guest Professorship of the German Science Foundation (Deutsche Forschungsgemeinschaft). The authors also express their thanks to Mark Davis, Steve Shreve, and Michael Taksar for useful discussions concerning the principle of dynamic programming.     

A differential evolution copula-based approach for a multi-period cryptocurrency portfolio optimization

Recent years have seen a growing interest among investors in the new technology of blockchain and cryptocurrencies and some early investors in this new type of digital assets have made significant gains. The heuristic algorithm, differential evolution, has been advocated as a powerful tool in portfolio optimization. We propose in this study two new approaches derived from the traditional differential evolution (DE) method: the GARCH-differential evolution (GARCH-DE) and the GARCH-differential evolution t-copula (GARCH-DE-t-copula). We then contrast these two models with DE (benchmark) in single and multi-period optimizations on a portfolio consisting of five cryptoassets under the coherent risk measure CVaR constraint. Our analysis shows that the GARCH-DE-t-copula outperforms the DE and GARCH-DE approaches in both single- and multi-period frameworks. For these notoriously volatile assets, the GARCH-DE-t-copula has shown risk-control ability, hereby confirming the ability of t-copula to capture the dependence structure in the fat tail.     

Risk discriminating portfolio optimization

Risk discriminating portfolio optimization provides a risk-related path to performance optimization     

On portfolio optimization: forecasting covariances and choosing the risk model

We evaluate the performance of models for the covariance structureof stock returns, focusing on their use for optimal portfolioselection. We compare the models' forecasts of future covariancesand the optimized portfolios' out-of-sample performance. A fewfactors capture the general covariance structure. Portfoliooptimization helps for risk control, and a three-factor modelis adequate for selecting the minimum-variance portfolio. Undera tracking error volatility criterion, which is widely usedin practice, larger differences emerge across the models. Ingeneral more factors are necessary when the objective is tominimize tracking error volatility.     

Systemic risk contributions: A credit portfolio approach

We put forward a framework for measuring systemic risk and attributing it to individual banks. Systemic risk is coherently measured as the expected loss to depositors and investors when a systemic event occurs. The risk contributions are calculated so as to ensure a full risk allocation among institutions. Applying our methodology to a panel of 54–86 of the world’s major commercial banks for a 13-year time span with monthly frequency not only allows us to closely match the list of G-SIBs; we can also use individual risk contributions to compute bank-specific surcharges: systemic capital charges as well as countercyclical buffers. We therefore address both dimensions of systemic risk – cross-sectional and time-series – in a single integrated approach. As the analysis of risk drivers confirms, the main focus of macroprudential supervision should be on a solid capital base throughout the financial cycle and de-correlation of banks’ asset values.     

Private equity benchmarks and portfolio optimization

Portfolio optimization using private equity is typically based on one of three indices: listed private equity, transaction-based private equity, or appraisal value-based private equity indices. However, we show that none of these indices is fully suitable for portfolio optimization. We introduce here a new benchmark index for venture capital and buyouts, which is updated monthly, adjusted for autocorrelation (de-smoothing), and available contemporaneously. We illustrate how our benchmark enables superior quantitative portfolio optimization.     

Dynamic portfolio optimization with ambiguity aversion

This paper investigates portfolio selection in the presence of transaction costs and ambiguity about return predictability. By distinguishing between ambiguity aversion to returns and to return predictors, we derive the optimal dynamic trading rule in closed form within the framework of Gârleanu and Pedersen (2013), using the robust optimization method. We characterize its properties and the unique mechanism through which ambiguity aversion impacts the optimal robust strategy. In addition to the two trading principles documented in Gârleanu and Pedersen (2013), our model further implies that the robust strategy aims to reduce the expected loss arising from estimation errors. Ambiguity-averse investors trade toward an aim portfolio that gives less weight to highly volatile return-predicting factors, and loads less on the securities that have large and costly positions in the existing portfolio. Using data on various commodity futures, we show that the robust strategy outperforms the corresponding non-robust strategy in out-of-sample tests.     

Mathematical foundation of the replicating portfolio approach

In the last few years, the first theoretical foundations for replicating portfolios – probably the most prevailing technique for risk capital calculation in life insurance – have been given in a series of papers by Beutner, Pelsser and Schweizer. In these papers, the asymptotic behaviour of replicating portfolios concerning the approximation of the terminal value (TVL) and the fair value distribution of the liabilities (FVL) has been investigated in detail. We complement this line of research by providing results on approximations based on a finite number of replicating instruments. We do so by providing the link between the approximation error of the TVL distribution, the FVL distribution and the error in the resulting risk capital figure, either value at risk or some coherent risk measure. We further allow for a variety of practically relevant formulations of the replication problem, including cash flow matching approaches. In contrast to the existing literature, all our results apply to approaches both under the risk-neutral and the real-world measure. Our strongest bounds are due to the observation that in discrete time, the measure change from the real-world to the risk-neutral measure can be both bounded below and above by a suitable constant in the first period.     

Dynamic hedge fund portfolio construction: A semi-parametric approach

In this article, we evaluate alternative optimization frameworks for constructing portfolios of hedge funds. We compare the standard mean–variance optimization model with models based on CVaR, CDaR and Omega, for both conservative and aggressive hedge fund investment strategies. In order to implement the CVaR, CDaR and Omega optimization models, we propose a semi-parametric methodology, which is based on extreme value theory, copula and Monte Carlo simulation. We compare the semi-parametric approach with the standard, non-parametric approach, used to compute CVaR, CDaR and Omega, and the benchmark parametric approach, based on both static and dynamic mean–variance optimization. We report two main findings. The first is that the CVaR, CDaR and Omega models offer a significant improvement in terms of risk-adjusted portfolio performance over the parametric mean–variance model. The second is that semi-parametric estimation of the CVaR, CDaR and Omega models offers a very substantial improvement over non-parametric estimation. Our results are robust to the choice of target return, risk limit and estimation sample size.     

Marriage and other risky assets: A portfolio approach

We study the joint impact of gender and marital status on financial investments by testing the hypothesis that marriage represents – in a portfolio framework – a sort of safe asset and that this attribute may change over time. We show that married individuals have a higher propensity to invest in risky assets than single ones, that this marital status gap is stronger for women and that, for women only, it evolves and declines at the end of the sample period. Next we explore a number of possible explanations of the observed gender differences by controlling for background factors that capture the evolution of family and society. We find that both the higher female marital status gap and its time variability vanish for those women who are employed. Our empirical investigation is based on a dataset drawn from the 1993–2006 Bank of Italy Survey of Household Income and Wealth.     

Dynamic portfolio optimization across hidden market regimes

Regime-based asset allocation has been shown to add value over rebalancing to static weights and, in particular, reduce potential drawdowns by reacting to changes in market conditions. The predominant approach in previous studies has been to specify in advance a static decision rule for changing the allocation based on the state of financial markets or the economy. In this article, model predictive control (MPC) is used to dynamically optimize a portfolio based on forecasts of the mean and variance of financial returns from a hidden Markov model with time-varying parameters. There are computational advantages to using MPC when estimates of future returns are updated every time a new observation becomes available, since the optimal control actions are reconsidered anyway. MPC outperforms a static decision rule for changing the allocation and realizes both a higher return and a significantly lower risk than a buy-and-hold investment in various major stock market indices. This is after accounting for transaction costs, with a one-day delay in the implementation of allocation changes, and with zero-interest cash as the only alternative to the stock indices. Imposing a trading penalty that reduces the number of trades is found to increase the robustness of the approach.     

Transaction cost optimization for online portfolio selection

To improve existing online portfolio selection strategies in the case of non-zero transaction costs, we propose a novel framework named Transaction Cost Optimization (TCO). The TCO framework incorporates the L1 norm of the difference between two consecutive allocations together with the principles of maximizing expected log return. We further solve the formulation via convex optimization, and obtain two closed-form portfolio update formulas, which follow the same principle as Proportional Portfolio Rebalancing (PPR) in industry. We empirically evaluate the proposed framework using four commonly used data-sets. Although these data-sets do not consider delisted firms and are thus subject to survival bias, empirical evaluations show that the proposed TCO framework may effectively handle reasonable transaction costs and improve existing strategies in the case of non-zero transaction costs.     

Bond portfolio optimization using dynamic factor models

A general class of dynamic factor models is used to obtain optimal bond portfolios, and to develop a duration-constrained mean-variance optimization, which can be used to improve bond indexing. An empirical application involving two large data sets of U.S. Treasuries shows that the proposed portfolio policy outperforms a set of yield curve strategies used in bond desks. Additionally, we propose a dynamic rule to switch among alternative bond investment strategies, and find that the benefits of such dynamic rule are even more pronounced when the set of available policies is augmented with the proposed mean-variance portfolios.     

Replicating portfolio approach to capital calculation

The replicating portfolio (RP) approach to the calculation of capital for life insurance portfolios is an industry standard. The RP is obtained from projecting the terminal loss of discounted asset–liability cash flows on a set of factors generated by a family of financial instruments that can be efficiently simulated. We provide the mathematical foundations and a novel dynamic and path-dependent RP approach for real-world and risk-neutral sampling. We show that our RP approach yields asymptotically consistent capital estimators if the chaotic representation property holds. We illustrate the tractability of the RP approach by three numerical examples.     

Multiobjective portfolio optimization with non-convex policy constraints: Evidence from the Eurostoxx 50

Our purpose in this paper is to depart from the intrinsic pathology of the typical mean–variance formalism, due to both the restriction of its assumptions and difficulty of implementation. We manage to co-assess a set of sophisticated real-world non-convex investment policy limitations, such as cardinality constraints, buy-in thresholds, transaction costs, particular normative rules, etc., within the frame of complex scenarios, which demand for simultaneous optimization of multiple investment objectives. In such a case, the portfolio selection process reflects a mixed-integer multiobjective portfolio optimization problem. On this basis, we meticulously develop all the corresponding modeling procedures and then solve the underlying problem by use of a new, fast and very effective algorithm. The value of the suggested framework is integrated with the introduction of two novel concepts in the field of multiobjective portfolio optimization, i.e. the security impact plane and the barycentric portfolio. The first represents a measure of each security's impact in the efficient surface of Pareto optimal portfolios. The second serves as the vehicle for implementing a balanced strategy of iterative portfolio tuning. Moreover, a couple of some very informative graphs provide thorough visualization of all empirical testing results. The validity of the attempt is verified through an illustrative application on the Eurostoxx 50. The results obtained are characterized as very encouraging, since a sufficient number of efficient or Pareto optimal portfolios produced by the model, appear to possess superior out-of-sample returns with respect to the underlying benchmark.