Portfolio optimization for student t and skewed t returns

We consider the problem of valuing a European option written on an asset whose dynamics are described by an exponential Lévy-type model. In our framework, both the volatility and jump-intensity are allowed to vary stochastically in time through common driving factors—one fast-varying and one slow-varying. Using Fourier analysis we derive an explicit formula for the approximate price of any European-style derivative whose payoff has a generalized Fourier transform; in particular, this includes European calls and puts. From a theoretical perspective, our results extend the class of multiscale stochastic volatility models of Fouque et al. [Multiscale Stochastic Volatility for Equity, Interest Rate, and Credit Derivatives, 2011] to models of the exponential Lévy type. From a financial perspective, the inclusion of jumps and stochastic volatility allow us to capture the term-structure of implied volatility, as demonstrated in a calibration to S&;P500 options data.     

Haar wavelets-based approach for quantifying credit portfolio losses

This paper proposes a new methodology to compute Value at Risk (VaR) for quantifying losses in credit portfolios. We approximate the cumulative distribution of the loss function by a finite combination of Haar wavelet basis functions and calculate the coefficients of the approximation by inverting its Laplace transform. The Wavelet Approximation (WA) method is particularly suitable for non-smooth distributions, often arising in small or concentrated portfolios, when the hypothesis of the Basel II formulas are violated. To test the methodology we consider the Vasicek one-factor portfolio credit loss model as our model framework. WA is an accurate, robust and fast method, allowing the estimation of the VaR much more quickly than with a Monte Carlo (MC) method at the same level of accuracy and reliability.     

Neural network copula portfolio optimization for exchange traded funds

This paper attempts to investigate if adopting accurate forecasts from Neural Network (NN) models can lead to statistical and economically significant benefits in portfolio management decisions. In order to achieve that, three NNs, namely the Multi-Layer Perceptron, Recurrent Neural Network and the Psi Sigma Network (PSN), are applied to the task of forecasting the daily returns of three Exchange Traded Funds (ETFs). The statistical and trading performance of the NNs is benchmarked with the traditional Autoregressive Moving Average models. Next, a novel dynamic asymmetric copula model (NNC) is introduced in order to capture the dependence structure across ETF returns. Based on the above, weekly re-balanced portfolios are obtained and compared using the traditional mean–variance and the mean–CVaR portfolio optimization approach. In terms of the results, PSN outperforms all models in statistical and trading terms. Additionally, the asymmetric skewed t copula statistically outperforms symmetric copulas when it comes to modelling ETF returns dependence. The proposed NNC model leads to significant improvements in the portfolio optimization process, while forecasting covariance accounting for asymmetric dependence between the ETFs also improves the performance of obtained portfolios.     

A comparison of non-Gaussian VaR estimation and portfolio construction techniques

We propose a multivariate model of returns that accounts for four of the stylised facts of financial data: heavy tails, skew, volatility clustering, and asymmetric dependence with the aim of improving the accuracy of risk estimates and increasing out-of-sample utility of investors’ portfolios. We accommodate volatility clustering, the generalised Pareto distribution to capture heavy tails and skew, and the skewed-t copula to provide for asymmetric dependence. The proposed approach produces more accurate VaR estimates than seven competing approaches across eight data sets encompassing five asset classes. We show that this produces portfolios with higher utility, and lower downside risk than alternative approaches including mean–variance. We confirm that investors can substantially increase utility by accounting for departures from normality.     

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.     

Risk parity portfolio optimization under a Markov regime-switching framework

We formulate and solve a risk parity optimization problem under a Markov regime-switching framework to improve parameter estimation and to systematically mitigate the sensitivity of optimal portfolios to estimation error. A regime-switching factor model of returns is introduced to account for the abrupt changes in the behaviour of economic time series associated with financial cycles. This model incorporates market dynamics in an effort to improve parameter estimation. We proceed to use this model for risk parity optimization and also consider the construction of a robust version of the risk parity optimization by introducing uncertainty structures to the estimated market parameters. We test our model by constructing a regime-switching risk parity portfolio based on the Fama–French three-factor model. The out-of-sample computational results show that a regime-switching risk parity portfolio can consistently outperform its nominal counterpart, maintaining a similar ex post level of risk while delivering higher-than-nominal returns over a long-term investment horizon. Moreover, we present a dynamic portfolio rebalancing policy that further magnifies the benefits of a regime-switching portfolio.     

Two-sided coherent risk measures and their application in realistic portfolio optimization

By using a different derivation scheme, a new class of two-sided coherent risk measures is constructed in this paper. Different from existing coherent risk measures, both positive and negative deviations from the expected return are considered in the new measure simultaneously but differently. This innovation makes it easy to reasonably describe and control the asymmetry and fat-tail characteristics of the loss distribution and to properly reflect the investor’s risk attitude. With its easy computation of the new risk measure, a realistic portfolio selection model is established by taking into account typical market frictions such as taxes, transaction costs, and value constraints. Empirical results demonstrate that our new portfolio selection model can not only suitably reflect the impact of different trading constraints, but find more robust optimal portfolios, which are better than the optimal portfolio obtained under the conditional value-at-risk measure in terms of diversification and typical performance ratios.     

Dynamic mean–VaR portfolio selection in continuous time

The value-at-risk (VaR) is one of the most well-known downside risk measures due to its intuitive meaning and wide spectra of applications in practice. In this paper, we investigate the dynamic mean–VaR portfolio selection formulation in continuous time, while the majority of the current literature on mean–VaR portfolio selection mainly focuses on its static versions. Our contributions are twofold, in both building up a tractable formulation and deriving the corresponding optimal portfolio policy. By imposing a limit funding level on the terminal wealth, we conquer the ill-posedness exhibited in the original dynamic mean–VaR portfolio formulation. To overcome the difficulties arising from the VaR constraint and no bankruptcy constraint, we have combined the martingale approach with the quantile optimization technique in our solution framework to derive the optimal portfolio policy. In particular, we have characterized the condition for the existence of the Lagrange multiplier. When the opportunity set of the market setting is deterministic, the portfolio policy becomes analytical. Furthermore, the limit funding level not only enables us to solve the dynamic mean–VaR portfolio selection problem, but also offers a flexibility to tame the aggressiveness of the portfolio policy.     

A note on portfolio choice for sovereign wealth funds

The current vast account surpluses of commodity-rich nations, combined with record account deficits in developed markets (the United States, Britain) have created a new type of investor. Sovereign wealth funds (SWF) are instrumental in deciding how these surpluses will be invested. We need to better understand the investment problem for an SWF in order to project future investment flows. Extending Gintschel and Scherer (J. Asset Manag. 9(3):215–238, 2008), we apply the portfolio choice problem for a sovereign wealth fund in a Campbell and Viceira (Strategic Asset Allocation, 2002) strategic asset allocation framework. Changing the analysis from a one to a multi-period framework allows us to establish a three-fund separation. We split the optimal portfolio for an SWF into speculative demand as well as hedge demand against oil price shocks and shocks to the short-term risk-free rate. In addition, all terms now depend on the investor’s time horizon. We show that oil-rich countries should hold bonds and that the optimal investment policy for an SWF as a long-term investor is determined by long-run covariance matrices that differ from the correlation inputs that one-period (myopic) investors use.

Power mapping with dynamical adjustment for improved portfolio optimization

For financial risk management it is of vital interest to have good estimates for the correlations between the stocks. It has been found that the correlations obtained from historical data are covered by a considerable amount of noise, which leads to a substantial error in the estimation of the portfolio risk. A method to suppress this noise is power mapping. It raises the absolute value of each matrix element to a power q while preserving the sign. In this paper we use the Markowitz portfolio optimization as a criterion for the optimal value of q and find a K/T dependence, where K is the portfolio size and T the length of the time series. Both in numerical simulations and for real market data we find that power mapping leads to portfolios with considerably reduced risk. It compares well with another noise reduction method based on spectral filtering. A combination of both methods yields the best results.     

A jackknife-type estimator for portfolio revision

This article proposes a novel approach to portfolio revision. The current literature on portfolio optimization uses a somewhat naïve approach, where portfolio weights are always completely revised after a predefined fixed period. However, one shortcoming of this procedure is that it ignores parameter uncertainty in the estimated portfolio weights, as well as the biasedness of the in-sample portfolio mean and variance as estimates of the expected portfolio return and out-of-sample variance. To rectify this problem, we propose a jackknife procedure to determine the optimal revision intensity, i.e. the percent of wealth that should be shifted to the new, in-sample optimal portfolio. We find that our approach leads to highly stable portfolio allocations over time, and can significantly reduce the turnover of several well established portfolio strategies. Moreover, the observed turnover reductions lead to statistically and economically significant performance gains in the presence of transaction costs.     

The impact of global economic policy uncertainty on portfolio optimization: A Black–Litterman approach

This paper investigates the asymmetric impact of global economic policy uncertainty (GEPU) on global asset allocation. We employ the Double Asymmetric GARCH-MIDAS (DAGM) model to examine the asymmetric effect of GEPU shocks on long-term volatilities of global equities, bonds, commodities, clean energy and Bitcoin. The GEPU-based volatility is used as a proxy for the uncertainty of the investor’s views in the Black-Litterman (BL) framework. Empirical results show that the BL model with GEPU-based views yields higher out-of-sample risk-adjusted returns than other traditional benchmarks in most cases. The findings suggest that investors should consider the influence of GEPU when making portfolio decisions.     

Non-parametric estimation of operational risk losses adjusted for under-reporting

Not all claims are reported when a database for financial operational risk is created. The probability of reporting increases with the size of the operational risk loss, and converges towards one for big losses. Losses in operational risk have different causes, and usually follow a wide variety of distributional shapes. Therefore, a method for modelling operational risk based on one or two parametric models is deemed to fail. In this paper, we introduce a semi-parametric method for modelling operational risk that is capable of taking under-reporting into account and being guided by prior knowledge of the distributional shape.     

Comparative issues between linear and non-linear risk measures for non-convex portfolio optimization: evidence from the S&P 500

Abstract

This article focuses on inferring critical comparative conclusions as far as the application of both linear and non-linear risk measures in non-convex portfolio optimization problems. We seek 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 four popular portfolio selection cases: (a) the mean-variance model, (b) the mean-semi variance model, (c) the mean-MAD (mean-absolute deviation) model and (d) the mean-semi MAD model. In such circumstances, the portfolio selection process reflects to a mixed-integer bi-objective (or in general multiobjective) mathematical programme. We precisely develop all corresponding modelling procedures and then solve the underlying problem by use of a novel generalized algorithm, which was exclusively introduced to cope with the above-mentioned singularities. The validity of the attempt is verified through empirical testing on the S&P 500 universe of securities. The technical conclusions obtained not only confirm certain findings of the particular limited existing theory but also shed light on computational issues and running times. Moreover, the results derived are characterized as encouraging enough, since a sufficient number of efficient or Pareto optimal portfolios produced by the models appear to possess superior out-of-sample returns with respect to the benchmark.     

A model of returns for the post-credit-crunch reality: hybrid Brownian motion with price feedback

Recent market events have reinvigorated the search for realistic return models that capture greater likelihoods of extreme movements. In this paper we model the medium-term log-return dynamics in a market with both fundamental and technical traders. This is based on a trade arrival model with variable size orders and a general arrival-time distribution. With simplifications we are led in the jump-free case to a local volatility model defined by a hybrid SDE mixing both arithmetic and geometric or CIR Brownian motions, whose solution in the geometric case is given by a class of integrals of exponentials of one Brownian motion against another, in forms considered by Yor and collaborators. The reduction of the hybrid SDE to a single Brownian motion leads to an SDE of the form considered by Nagahara, which is a type of ‘Pearson diffusion’, or, equivalently, a hyperbolic OU SDE. Various dynamics and equilibria are possible depending on the balance of trades. Under mean-reverting circumstances we arrive naturally at an equilibrium fat-tailed return distribution with a Student or Pearson Type~IV form. Under less-restrictive assumptions, richer dynamics are possible, including time-dependent Johnson-SU distributions and bimodal structures. The phenomenon of variance explosion is identified that gives rise to much larger price movements that might have a priori been expected, so that ‘25σ’ events are significantly more probable. We exhibit simple example solutions of the Fokker–Planck equation that shows how such variance explosion can hide beneath a standard Gaussian facade. These are elementary members of an extended class of distributions with a rich and varied structure, capable of describing a wide range of market behaviors. Several approaches to the density function are possible, and an example of the computation of a hyperbolic VaR is given. The model also suggests generalizations of the Bougerol identity. We touch briefly on the extent to which such a model is consistent with the dynamics of a ‘flash-crash’ event, and briefly explore the statistical evidence for our model.