Model Of Asset Returns Research Articles

Copula based multivariate semi-Markov models with applications in high-frequency finance

We introduce a new multivariate model of multiple asset returns. Our model is based on weighted indexed semi-Markov chains to describe the single (marginals) asset returns, whereas the dependence structure among the considered assets is described by introducing copula functions. A real application of the proposed multivariate model is presented based on the evolution of 6 stocks from the Italian Stock Exchange. We provide empirical evidence that the model is able to correctly reproduce statistical regularities of multivariate real data such as the cross-correlation function, value-at-risk, marginal value-at-risk and conditional value-at-risk. The model is also used for volatility forecasting of each stock.

Valuation of variable long-term care Annuities with Guaranteed Lifetime Withdrawal Benefits: A variance reduction approach

This paper proposes a new product, the Variable Life Care Annuity with Guaranteed Lifetime Withdrawal Benefits (LCA-GLWB), and designs an efficient valuation algorithm. This innovative product provides a comprehensive retirement solution for both longevity risk and long-term care protection. It includes the benefits of guaranteed income streams with downside risk protection and long-term care expenses for retirees. However, the valuation of this type of product is both complex and time-consuming. In this paper, we propose a Monte Carlo valuation algorithm that uses the variance reduction technique. The numerical results indicate that the proposed valuation algorithm is very efficient under a broad range of asset return models. The proposed algorithm provides a general approach for the rapid valuation of similar products and can help provide life insurance companies offering innovative products with an appropriate valuation tool.

Asymptotic Inference for Performance Fees and the Predictability of Asset Returns

In this article, we provide analytical, simulation, and empirical evidence on a test of equal economic value from competing predictive models of asset returns. We define economic value using the concept of a performance fee—the amount an investor would be willing to pay to have access to an alternative predictive model used to make investment decisions. We establish that this fee can be asymptotically normal under modest assumptions. Monte Carlo evidence shows that our test can be accurately sized in reasonably large samples. We apply the proposed test to predictions of the U.S. equity premium.

Nonlinear shrinkage estimation of large integrated covariance matrices

Integrated covariance matrices arise in intraday models of asset returns, which allow volatility to change over the trading day. When the number of assets is large, the natural estimator of such a matrix suffers from bias due to extreme eigenvalues. We introduce a novel nonlinear shrinkage estimator for the integrated covariance matrix which shrinks the extreme eigenvalues of a realized covariance matrix back to an acceptable level, and enjoys a certain asymptotic efficiency when the number of assets is of the same order as the number of data points. Novel maximum exposure and actual risk bounds are derived when our estimator is used in constructing the minimum variance portfolio. In simulations and a real-data analysis, our estimator performs favourably in comparison with other methods.

Volatility Forecasting with the Multifractal Model of Asset Returns

This paper presents an empirical application of the Multifractal Model of Asset Returns (MMAR) to intraday stock prices, with a goal of generating accurate volatility forecasts. Intraday stock volatility exhibits long tails, persistence, and strong evidence of moment scaling. This allows us to apply the MMAR. A forecasting method for the MMAR is implemented through Monte Carlo simulation, and this forecasting method is compared to Generalized Autoregressive Conditional Heteroskedasticity (GARCH) alternatives over several testing samples. The MMAR significantly outperformed the GARCH models. This suggests that the framework of multifractality has a large potential for further development and application within finance.

Extreme quantile estimation based on financial time series

ABSTRACTEstimation of market risk is an important problem in finance. Two well-known risk measures, viz., value at risk and median shortfall, turn out to be extreme quantiles of the marginal distribution of asset return. Time series on asset returns are known to exhibit certain stylized facts, such as heavy tails, skewness, volatility clustering, etc. Therefore, estimation of extreme quantiles in the presence of such features in the data seems to be of natural interest. It is difficult to capture most of these stylized facts using one specific time series model. This motivates nonparametric and extreme value theory-based estimation of extreme quantiles that do not require exact specification of the asset return model. We review these quantile estimators and compare their known properties. Their finite sample performance are compared using Monte Carlo simulation. We propose a new estimator that exhibits encouraging finite sample performance while estimating extreme quantile in the right tail region.

Performance of the Multifractal Model of Asset Returns (MMAR): Evidence from Emerging Stock Markets

In this study, the performance of the Multifractal Model of Asset Returns (MMAR) was examined for stock index returns of four emerging markets. The MMAR, which takes into account stylized facts of financial time series, such as long memory, fat tails and trading time, was developed as an alternative to the ARCH family models. Empirical analysis of the study consists of two sections. In the first section, we estimated the parameters of GARCH, EGARCH, FIGARCH, MRS-GARCH and MMAR for the stock index returns of Croatia, Greece, Poland and Turkey. In the second section, 1000 paths were obtained for each model using Monte Carlo simulations. We then compared the scaling function values of simulated and original time series for different q orders (1–5). According to the obtained results, the MMAR is mostly superior to other models and presents the best replica of the original time series. Another important finding is the achievement of the MRS-GARCH. We found that for lower levels of persistency (long memory) of return series, the performance of the MRS-GARCH excels, and for H = 0.5, it narrowly outperforms the MMAR.

Bayesian Analysis of a Threshold Stochastic Volatility Model

This paper proposes a parsimonious threshold stochastic volatility (SV) model for financial asset returns. Instead of imposing a threshold value on the dynamics of the latent volatility process of the SV model, we assume that the innovation of the mean equation follows a threshold distribution in which the mean innovation switches between two regimes. In our model, the threshold is treated as an unknown parameter. We show that the proposed threshold SV model can not only capture the time‐varying volatility of returns, but can also accommodate the asymmetric shape of conditional distribution of the returns. Parameter estimation is carried out by using Markov chain Monte Carlo methods. For model selection and volatility forecast, an auxiliary particle filter technique is employed to approximate the filter and prediction distributions of the returns. Several experiments are conducted to assess the robustness of the proposed model and estimation methods. In the empirical study, we apply our threshold SV model to three return time series. The empirical analysis results show that the threshold parameter has a non‐zero value and the mean innovations belong to two separately distinct regimes. We also find that the model with an unknown threshold parameter value consistently outperforms the model with a known threshold parameter value. Copyright © 2016 John Wiley & Sons, Ltd.

Sparse Mean-Variance Portfolios: A Penalized Utility Approach

This paper considers mean-variance optimization under uncertainty, specifically when one desires a sparsified set of optimal portfolio weights. From the standpoint of a Bayesian investor, our approach produces a small portfolio from many potential assets while acknowledging uncertainty in asset returns and parameter estimates. We demonstrate the procedure using static and dynamic models for asset returns.

Long memory and multifractality: A joint test

The properties of statistical tests for hypotheses concerning the parameters of the multifractal model of asset returns (MMAR) are investigated, using Monte Carlo techniques. We show that, in the presence of multifractality, conventional tests of long memory tend to over-reject the null hypothesis of no long memory. Our test addresses this issue by jointly estimating long memory and multifractality. The estimation and test procedures are applied to exchange rate data for 12 currencies. Among the nested model specifications that are investigated, in 11 out of 12 cases, daily returns are most appropriately characterized by a variant of the MMAR that applies a multifractal time-deformation process to NIID returns. There is no evidence of long memory.

Understanding Systematic Risk: A High-Frequency Approach

Under a large dimensional approximate factor model for asset returns, I use high-frequency data for the S&P 500 firms to estimate the latent continuous and jump factors. I estimate four very persistent continuous systematic factors for 2007 to 2012 and three from 2003 to 2006. These four continuous factors can be approximated very well by a market, an oil, a finance and an electricity portfolio. The value, size and momentum factors play no significant role in explaining these factors. For the time period 2003 to 2006 the finance factor seems to disappear. There exists only one persistent jump factor, namely a market jump factor. Using implied volatilities from option price data, I analyze the systematic factor structure of the volatilities. There is only one persistent market volatility factor, while during the financial crisis an additional temporary banking volatility factor appears. Based on the estimated factors, I can decompose the leverage effect, i.e. the correlation of the asset return with its volatility, into a systematic and an idiosyncratic component. The negative leverage effect is mainly driven by the systematic component, while it can be non-existent for idiosyncratic risk.

Minimum-Variance Kernels, Economic Risk Premia, and Tests of Multi-Beta Models

This paper uses minimum-variance (MV) admissible kernels to estimate risk premia associated with economic risk variables and to test multi-beta models. Estimating risk premia using MV kernels is appealing because it avoids the need to 1) identify all relevant sources of risk and 2) assume a linear factor model for asset returns. Testing multi-beta models in terms of restricted MV kernels has the advantage that 1) the candidate kernel has the smallest volatility and 2) test statistics are easy to interpret in terms of Sharpe ratios. The authors find that several economic variables command significant risk premia and that the signs of the premia mostly correspond to the effect that these variables have on the risk-return trade-off, consistent with the implications of the intertemporal capital asset pricing model (I-CAPM). They also find that the MV kernel implied by the I-CAPM, while formally rejected by the data, consistently outperforms a pricing kernel based on the size and book-to-market factors of Fama and French (1993).

Multifractality of the Istanbul and Moscow Stock Market Returns

There is a growing awareness among financial researchers that the traditional models of asset returns cannot capture essential time series properties of the current stock return data. We examine commonly used models, such as the autoregressive integrated moving average (ARIMA) and the autoregressive conditional heteroskedasticity (ARCH) family, and show that these models cannot account for the essential characteristics of the real Istanbul Stock Exchange and Moscow Stock Exchange returns. These models often fail, and when they succeed, they do at the cost of an increasing number of parameters and structural equations. The measures of risk obtained from these models do not reflect the true risk to traders, since they cannot capture all key features of the data. In this paper, we offer an alternative framework of analysis based on multifractal models. Compared to the traditional models, the multifractal models we use are very parsimonious and replicate all key features of the data with only three universal parameters. The multifractal models have superior risk evaluation performance. They also produce better forecasts at all scales. The paper also offers a justification of the multifractal models for financial modeling.

How Good Can Heuristic-Based Forecasts Be? A Comparative Performance of Econometric and Heuristic Models for UK and US Asset Returns

This paper systematically investigates the sources of differential out-of-sample predictive accuracy of heuristic frameworks based on internet search frequencies and a large set of econometric models. The volume of internet searches helps gauge the degree of investors' time-varying interest in specific assets. We use a wide range of state-of-the-art models, both of linear and non-linear type (regime-switching predictive regressions, threshold autoregressive, smooth transition autoregressive), extended to capture conditional heteroskedasticity through GARCH models. The predictor variables investigated are those typical of the literature featuring a range of macroeconomic and market leading indicators. Our out-of-sample forecasting exercises are conducted with reference to US, UK, French and German data, both stocks and bonds, and for 1- and 12-months-ahead horizons. We employ several forecast performance metrics and predictive accuracy tests. Internet-search-based models are found to perform better than the average of all of the alternative models. For several country-asset-horizon combinations, particularly for UK bond returns, our heuristic models compare favorably with sophisticated econometric methods. The heuristic models are also shown to perform well in forecasting realized volatility. The baseline results are supported by several extensions and robustness checks, such as using alternative search keywords, controlling for Fama-French and Cochrane-Piazzesi factors, and implementing heuristic-based trading strategies.

Sequential Modeling of Dependent Jump Processes

Two multivariate models for asset returns are introduced. Both generalize popular univariate models without altering their marginal laws; a very convenient feature, e.g., for a sequential calibration of the model's parameters to market quotes. The first is a double exponential jump-diffusion model with constant volatility as presented in the univariate case by Kou (2002). The second is a generalization of the stochastic volatility model of Gamma-Ornstein-Uhlenbeck type as first presented by Barndorff-Nielsen and Shephard (2001). Univariate processes of these kinds are driven by a Brownian motion as well as a compound Poisson process. Unlike other existing multivariate extensions of these univariate models, one important advantage of the presented approach is to keep the parameters that govern the dependence structure between the assets separate from the parameters that determine the marginal distributions of the assets. This is achieved by introducing dependence to the univariate compound Poisson processes by means of a bespoke common stochastic time change.

Multifractality and value-at-risk forecasting of exchange rates

This paper addresses market risk prediction for high frequency foreign exchange rates under nonlinear risk scaling behaviour. We use a modified version of the multifractal model of asset returns (MMAR) where trading time is represented by the series of volume ticks. Our dataset consists of 138,418 5-min round-the-clock observations of EUR/USD spot quotes and trading ticks during the period January 5, 2006 to December 31, 2007. Considering fat-tails, long-range dependence as well as scale inconsistency with the MMAR, we derive out-of-sample value-at-risk (VaR) forecasts and compare our approach to historical simulation as well as a benchmark GARCH(1,1) location-scale VaR model. Our findings underline that the multifractal properties in EUR/USD returns in fact have notable risk management implications. The MMAR approach is a parsimonious model which produces admissible VaR forecasts at the 12-h forecast horizon. For the daily horizon, the MMAR outperforms both alternatives based on conditional as well as unconditional coverage statistics.

Constrained Mean-Variance Portfolio Optimization with Alternative Return Estimation

This paper studies the problem of asset allocation in a mean-variance framework. The theoretical model of portfolio optimization is specified and then applied to a long panel data set from historic to most recent times, March 1990 – March 2013. The paper contributes in three ways. First, an alternative asset return model is proposed that combines the historical returns, capital asset pricing model (CAPM) and returns estimated based on firm fundamentals. These return estimates enter the optimization problem. The second contribution is the application of an improved covariance matrix estimator that has superior properties compared to the typical sample covariance estimator. Third, the paper proposes two investments strategies. The first proposition suggests always choosing the maximized Sharpe ratio portfolio and the second one, the portfolio with the highest information ratio. The nature of both strategies is designed for investors with different appetites for risk. The performance of these choices is analyzed in light of four types of constraints: upper/lower investment limits, group constraints and transaction costs. The one-period optimal investment portfolio is rebalanced at quarterly intervals. Both strategies are benchmarked against an alternative investment choice such as holding the S&P 500 index, or investing in a risk-free asset such as a bond. Portfolio analysis and backtesting reveal that the strategies are superior to simply holding an equally weighted portfolio, a risk-free asset or the S&P 500 index.

Risk management with high-dimensional vine copulas: An analysis of the Euro Stoxx 50

Abstract The demand for an accurate financial risk management involving larger numbers of assets is strong not only in view of the financial crisis of 2007–2009. Especially dependencies among assets have not been captured adequately. While standard multivariate copulas have added some flexibility, this flexibility is insufficient in higher dimensional applications. Vine copulas can fill this gap by benefiting from the rich class of existing bivariate parametric copula families. Exploiting this in combination with GARCH models for the margins, we develop a regular vine copula based factor model for asset returns, the Regular Vine Market Sector model, which is motivated by the classical CAPM and shown to be superior to the CAVA model proposed by Heinen and Valdesogo (2009). The model can also be used to separate the systematic and idiosyncratic risk of specific stocks, and we explicitly discuss how vine copula models can be employed for active and passive portfolio management. In particular, Value-at-Risk forecasting and asset allocation are treated in detail. All developed models and methods are used to analyze the Euro Stoxx 50 index, a major market indicator for the Eurozone. Relevant benchmark models such as the popular DCC model and the common Student's t copula are taken into account.

Conditional correlation in asset return and GARCH intensity model

In an asset return series there is a conditional asymmetric dependence between current return and past volatility depending on the current return's sign. To take into account the conditional asymmetry, we introduce new models for asset return dynamics in which frequencies of the up and down movements of asset price have conditionally independent Poisson distributions with stochastic intensities. The intensities are assumed to be stochastic recurrence equations of the GARCH type in order to capture the volatility clustering and the leverage effect. We provide an important linkage between our model and existing GARCH, explain how to apply maximum likelihood estimation to determine the parameters in the intensity model and show empirical results with the S&P 500 index return series.

A Predictive Functional Regression Model for Asset Return

Since many of predictive financial variables are highly persistent and non-stationary, it is challenging econometrically to explore the predictability of asset returns. Predictability issues are generally addressed in parametric regressions [1,2] in which rates of asset returns are regressed against the lagged values of stochastic explanatory variables, but three limitations stand ahead [3-5]. This paper studies a predictive functional regression model for asset returns, which takes account of endogeneity and integrated or nearly integrated explanatory variables. The regression function is expressed in terms of distribution of the vector of the observable variables. Estimators are nonlinear functionals of a kernel estimator for the distribution of the observable variables [6]. We find that the estimators for the distribution of the unobservable random terms and the nonparametric function are consistent and asymptotically normal. This paper obtains the similar results in many literatures, for example [1-5], but in different method.