A Semiparametric Two-Factor Term Structure Model

This article proposes a semiparametric two-factor term structuremodel based on a consol rate and the spread between a shortrate and the consol rate. The diffusion functions in both theconsol rate and spread processes are nonparametrically specifiedso that the model allows for maximal flexibility of diffusionfunctions in fitting into data. The drift function of the spreadprocess is specified as a mean-reverting function, while thedrift function of the consol rate process is left unrestricted.A nonparametric procedure is developed for estimating the diffusionfunctions. The asymptotic biases of the nonparametric estimatorsare quantified when the step of discretization is fixed, whilethe asymptotic distributions of the nonparametric estimatorsare derived when the step of discretization tends to zero. Thepricing and hedging performances of the model are evaluatedin a simulated economic environment. Results show that the modelperforms quite well in the simulated economy.     

Hedge fund allocation: Evaluating parametric and nonparametric forecasts using alternative portfolio construction techniques

We propose a model for constructing Asian funds of hedge funds. We compare the accuracy of forecasts of hedge fund returns using an ordinary least squares (OLS) regression model, a nonparametric regression model, and a nonlinear nonparametric model. We backtest to assess these forecasts using three different portfolio construction processes: an “optimized” portfolio, an equally-weighted portfolio, and the Kelly criterion-based portfolio. We find that the Kelly criterion is a reasonable method for constructing a fund of hedge funds, producing better results than a basic optimization or an equally-weighted portfolio construction method. Our backtests also indicate that the nonparametric forecasts and the OLS forecasts produce similar performance at the hedge fund index level. At the individual fund level, our analysis indicates that the OLS forecasts produce higher directional accuracy than the nonparametric methods but the nonparametric methods produce more accurate forecasts than OLS. In backtests, the highest information ratio to predict hedge fund returns is obtained from a combination of the OLS regression with the Fung–Hsieh eight-factor variables as predictors using the Kelly criterion portfolio construction method. Similarly, the highest information ratio using forecasts generated from a combination of the nonparametric regression using the Fung–Hsieh eight-factor model variables is achieved using the Kelly criterion portfolio construction method. Simulations using risk-adjusted total returns indicate that the nonparametric regression model generates superior information ratios than the analogous backtest results using the OLS. However, the benefits of diversification plateau with portfolios of more than 20 hedge funds. These results generally hold with portfolio implementation lags up to 12 months.     

Nonlinear portfolio selection using approximate parametric Value-at-Risk

As the skewed return distribution is a prominent feature in nonlinear portfolio selection problems which involve derivative assets with nonlinear payoff structures, Value-at-Risk (VaR) is particularly suitable to serve as a risk measure in nonlinear portfolio selection. Unfortunately, the nonlinear portfolio selection formulation using VaR risk measure is in general a computationally intractable optimization problem. We investigate in this paper nonlinear portfolio selection models using approximate parametric Value-at-Risk. More specifically, we use first-order and second-order approximations of VaR for constructing portfolio selection models, and show that the portfolio selection models based on Delta-only, Delta–Gamma-normal and worst-case Delta–Gamma VaR approximations can be reformulated as second-order cone programs, which are polynomially solvable using interior-point methods. Our simulation and empirical results suggest that the model using Delta–Gamma-normal VaR approximation performs the best in terms of a balance between approximation accuracy and computational efficiency.     

Auctions with ex post uncertainty

Uncertainty about ex post realized values is an inherent component in many auction environments. In this article, we develop a structural framework to analyze auction data subject to ex post uncertainty as a pure risk. We consider a low‐price sealed‐bid auction model with heterogeneous bidders' preferences and ex post uncertainty. The uncertainty can be common to all bidders or idiosyncratic. We derive the model restrictions and study nonparametric and semiparametric identification of the model primitives under exogenous and endogenous participation. We then develop multistep nonparametric and semiparametric estimation procedures in both cases.     

Semiparametric estimation of multi-asset portfolio tail risk

When correlations between assets turn positive, multi-asset portfolios can become riskier than single assets. This article presents the estimation of tail risk at very high quantiles using a semiparametric estimator which is particularly suitable for portfolios with a large number of assets. The estimator captures simultaneously the information contained in each individual asset return that composes the portfolio, and the interrelation between assets. Noticeably, the accuracy of the estimates does not deteriorate when the number of assets in the portfolio increases. The implementation is as easy for a large number of assets as it is for a small number. We estimate the probability distribution of large losses for the American stock market considering portfolios with ten, fifty and one hundred assets of stocks with different market capitalization. In either case, the approximation for the portfolio tail risk is very accurate. We compare our results with well known benchmark models.     

Effectiveness of copula-extreme value theory in estimating value-at-risk: empirical evidence from Asian emerging markets

A traditional Monte Carlo simulation using linear correlations induces estimation bias in measuring portfolio value-at-risk (VaR), due to the well-documented existence of fat-tail, skewness, truncations, and non-linear relations in return distributions. In this paper, we consider the above issues in modeling VaR and evaluate the effectiveness of using copula-extreme-value-based semiparametric approaches. To assess portfolio risk in six Asian markets, we incorporate a combination of extreme value theory (EVT) and various copulas to build joint distributions of returns. A backtesting analysis using a Monte Carlo VaR simulation suggests that the Clayton copula-EVT evinces the best performance regardless of the shapes of the return distributions, and that in general the copulas with the EVT provide better estimations of VaRs than the copulas with conventionally employed empirical distributions. These findings still hold in conditional-coverage-based backtesting. These findings indicate the economic significance of incorporating the down-side shock in risk management.     

Data-driven robust mean-CVaR portfolio selection under distribution ambiguity

In this paper, we present a computationally tractable optimization method for a robust mean-CVaR portfolio selection model under the condition of distribution ambiguity. We develop an extension that allows the model to capture a zero net adjustment via a linear constraint in the mean return, which can be cast as a tractable conic programme. Also, we adopt a nonparametric bootstrap approach to calibrate the levels of ambiguity and show that the portfolio strategies are relatively immune to variations in input values. Finally, we show that the resulting robust portfolio is very well diversified and superior to its non-robust counterpart in terms of portfolio stability, expected returns and turnover. The results of numerical experiments with simulated and real market data shed light on the established behaviour of our distributionally robust optimization model.     

Portfolio allocation using multivariate variance gamma models

In this paper, we investigate empirically the effect of using higher moments in portfolio allocation when parametric and nonparametric models are used. The nonparametric model considered in this paper is the sample approach; the parametric model is constructed assuming multivariate variance gamma (MVG) joint distribution for asset returns.We consider the MVG models proposed by Madan and Seneta (1990), Semeraro (2008) and Wang (2009). We perform an out-of-sample analysis comparing the optimal portfolios obtained using the MVG models and the sample approach. Our portfolio is composed of 18 assets selected from the S&P500 Index and the dataset consists of daily returns observed from 01/04/2000 to 01/09/2011.     

Diversification in financial and crypto markets

This article investigates the conditional value at risk (CVaR) of two portfolio optimiza- tion approaches containing assets from the financial and crypto markets. We first catch the conditional interdependence structure among each variable through the vine-copula-GARCH model before merging it with the Mean-CVaR model. We then optimize each portfolio and find out the optimal allocation while evaluating the precise risk. The results indicate that the D-Vine copula is more suitable for both portfolios and that, when different conditional stock indices information are being taken into consideration, the crypto-market components can act as a weak hedge/safe haven against financial market indices. Furthermore, as CVaR is found to outperform the mean-variance of Markowitz in both portfolios, both risk measures similarly show that when including cryptocurrencies in a portfolio, the S&P 500 shall not be included. Additionally, the inclusion of Ethereum in a portfolio already containing Bitcoin does not boost the return.     

Benefits of diversifying investments into emerging markets with time-varying correlations: An Australian perspective

Australian investors can reduce their overall portfolio risk by diversifying into equities from other markets. Emerging markets have attracted significant interest because of their low correlations with Australian equity market returns; however, a number of studies have indicated that correlations between equity returns are increasing over time, so using unconditional estimates of correlations in a portfolio optimization model can result in the selection of a portfolio that may not be optimal.We use an Asymmetric Dynamic Conditional Correlation GARCH model to estimate time-varying correlations and include these correlation estimates in the portfolio optimization model. The assets used for portfolio construction comprise seven emerging market indices that are available to foreign investors. This study finds that, despite increasing correlations, there are still potential benefits for Australian investors who diversify into international emerging markets.     

Yield curve modeling and forecasting using semiparametric factor dynamics

Using a dynamic semiparametric factor model (DSFM) we investigate the term structure of interest rates. The proposed methodology is applied to monthly interest rates for four southern European countries: Greece, Italy, Portugal and Spain from the introduction of the Euro to the recent European sovereign-debt crisis. Analyzing this extraordinary period, we compare our approach with the standard market method – dynamic Nelson–Siegel model. Our findings show that two nonparametric factors capture the spatial structure of the yield curve for each of the bond markets separately. We attributed both factors to the slope of the yield curve. For panel term structure data, three nonparametric factors are necessary to explain 95% variation. The estimated factor loadings are unit root processes and reveal high persistency. In comparison with the benchmark model, the DSFM technique shows superior short-term forecasting in times of financial distress.     

Land Value and Parcel Size: A Semiparametric Analysis

We use a semiparametric estimator to analyze the relationship between land values and parcel size in a sample of 158 undeveloped parcels in the Portland, Oregon, metropolitan area. The semiparametric estimator combines the benefits of parametric and nonparametric estimation. The value-size relationship is estimated nonparametrically, which permits the function to be linear, convex, and concave in different regions. A simple log-linear parametric relationship is assumed for the rest of the model, which conserves degrees of freedom and simplifies hypothesis testing. Our semiparametric estimates do not reject log-linearity for the value-size relationship.     

Dynamic correlations and volatility linkages between stocks and sukuk: Evidence from international markets

An understanding of volatility and co-movements in financial markets is important for portfolio allocation and risk management practices. The current financial crisis caused a shrinkage in values of most assets, an increased volatility and a threat to the survival of several institutional investors. Managing risks and returns within the classic portfolio theory, when correlations across securities soar, is increasingly challenging. In this paper, we investigate the volatility behavior and the co-movements between sukuk and international stock indexes. Symmetric multivariate GARCH models with dynamic conditional correlations (DCC) were estimated under Student-t distribution. We provide evidence of high correlations between sukuk and US and EU stock markets, without finding the well-known flight to quality behavior affecting Islamic bonds. We also show that volatility linkages between sukuk and regional market indexes are higher during financial crisis. We argue that investors could obtain diversification benefits including sukuk in a well-diversified equity portfolio, given their lower volatility compared to equity. But higher volatility linkages and dynamic correlations during financial crises show that they are hybrid instruments between bonds and equity. Our findings are relevant for institutional investors and asset managers that include Islamic bonds in a diversified portfolio.     

Characteristic-based mean-variance portfolio choice

We study empirical mean-variance optimization when the portfolio weights are restricted to be direct functions of underlying stock characteristics such as value and momentum. The closed-form solution to the portfolio weights estimator shows that the portfolio problem in this case reduces to a mean-variance analysis of assets with returns given by single-characteristic strategies (e.g., momentum or value). In an empirical application to international stock return indexes, we show that the direct approach to estimating portfolio weights clearly beats a naive regression-based approach that models the conditional mean. However, a portfolio based on equal weights of the single-characteristic strategies performs about as well, and sometimes better, than the direct estimation approach, highlighting again the difficulties in beating the equal-weighted case in mean-variance analysis. The empirical results also highlight the potential for ‘stock-picking’ in international indexes using characteristics such as value and momentum with the characteristic-based portfolios obtaining Sharpe ratios approximately three times larger than the world market.     

A dynamic model of active portfolio management with benchmark orientation

This paper studies optimal dynamic portfolios for investors concerned with the performance of their portfolios relative to a benchmark. Assuming that asset returns follow a multi-linear factor model similar to the structure of Ross (1976) [Ross, S., 1976. The arbitrage theory of the capital asset pricing model. Journal of Economic Theory, 13, 342–360] and that portfolio managers adopt a mean tracking error analysis similar to that of Roll (1992) [Roll, R., 1992. A mean/variance analysis of tracking error. Journal of Portfolio Management, 18, 13–22], we develop a dynamic model of active portfolio management maximizing risk adjusted excess return over a selected benchmark. Unlike the case of constant proportional portfolios for standard utility maximization, our optimal portfolio policy is state dependent, being a function of time to investment horizon, the return on the benchmark portfolio, and the return on the investment portfolio. We define a dynamic performance measure which relates portfolio’s return to its risk sensitivity. Abnormal returns at each point in time are quantified as the difference between the realized and the model-fitted returns. Risk sensitivity is estimated through a dynamic matching that minimizes the total fitted error of portfolio returns. For illustration, we analyze eight representative mutual funds in the U.S. market and show how this model can be used in practice.     

Portfolio credit-risk optimization

This paper evaluates several alternative formulations for minimizing the credit risk of a portfolio of financial contracts with different counterparties. Credit risk optimization is challenging because the portfolio loss distribution is typically unavailable in closed form. This makes it difficult to accurately compute Value-at-Risk (VaR) and expected shortfall (ES) at the extreme quantiles that are of practical interest to financial institutions. Our formulations all exploit the conditional independence of counterparties under a structural credit risk model. We consider various approximations to the conditional portfolio loss distribution and formulate VaR and ES minimization problems for each case. We use two realistic credit portfolios to assess the in- and out-of-sample performance for the resulting VaR- and ES-optimized portfolios, as well as for those which we obtain by minimizing the variance or the second moment of the portfolio losses. We find that a Normal approximation to the conditional loss distribution performs best from a practical standpoint.     

SYMMETRIC VERSUS ASYMMETRIC CONDITIONAL COVARIANCE FORECASTS: DOES IT PAY TO SWITCH?

Volatilities and correlations for equity markets rise more after negative returns shocks than after positive shocks. Allowing for these asymmetries in covariance forecasts decreases mean‐variance portfolio risk and improves investor welfare. We compute optimal weights for international equity portfolios using predictions from asymmetric covariance forecasting models and a spectrum of expected returns. Investors who are moderately risk averse, have longer rebalancing horizons, and hold U.S. equities benefit most and may be willing to pay around 100 basis points annually to switch from symmetric to asymmetric forecasts. Accounting for asymmetry in both variances and correlations significantly lowers realized portfolio risk.     

Mean–variance and mean–semivariance portfolio selection: a multivariate nonparametric approach

While univariate nonparametric estimation methods have been developed for estimating returns in mean-downside risk portfolio optimization, the problem of handling possible cross-correlations in a vector of asset returns has not been addressed in portfolio selection. We present a novel multivariate nonparametric portfolio optimization procedure using kernel-based estimators of the conditional mean and the conditional median. The method accounts for the covariance structure information from the full set of returns. We also provide two computational algorithms to implement the estimators. Via the analysis of 24 French stock market returns, we evaluate the in-sample and out-of-sample performance of both portfolio selection algorithms against optimal portfolios selected by classical and univariate nonparametric methods for three highly different time periods and different levels of expected return. By allowing for cross-correlations among returns, our results suggest that the proposed multivariate nonparametric method is a useful extension of standard univariate nonparametric portfolio selection approaches.     

Aggregation of exponential smoothing processes with an application to portfolio risk evaluation

In this paper we propose a unified framework to analyse contemporaneous and temporal aggregation of a widely employed class of integrated moving average (IMA) models. We obtain a closed-form representation for the parameters of the contemporaneously and temporally aggregated process as a function of the parameters of the original one. These results are useful due to the close analogy between the integrated GARCH (1, 1) model for conditional volatility and the IMA (1, 1) model for squared returns, which share the same autocorrelation function. In this framework, we present an application dealing with Value-at-Risk (VaR) prediction at different sampling frequencies for an equally weighted portfolio composed of multiple indices. We apply the aggregation results by inferring the aggregate parameter in the portfolio volatility equation from the estimated vector IMA (1, 1) model of squared returns. Empirical results show that VaR predictions delivered using this suggested approach are at least as accurate as those obtained by applying standard univariate methodologies, such as RiskMetrics.     

INVESTOR TAX-TRADING OPPORTUNITIES AND DISCOUNTS ON CLOSED-END MUTUAL FUNDS

Discounts on closed-end mutual funds are a puzzle to financial economists, because arbitrage activities should eliminate discounts in a perfect capital market. In this paper I develop a model that explains discounts, using Merton's option pricing theorem. By holding shares of a closed-end mutual fund, investors lose valuable tax-trading opportunities associated with the constituent securities of the closed-end mutual fund's portfolio. However, investors can take advantage of all tax-trading opportunities by directly holding the closed-end mutual fund's portfolio. I also show that both variances of individual securities and correlations among securities in the portfolio are important factors in determining the magnitude of discounts.