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.     

How can investors build a better portfolio in small open economies? Evidence from Asia’s Four Little Dragons

This study investigates the role of hedging and portfolio design among stocks, exchange rates, and gold in small open economies (SOEs) from 4 January 2000 to 31 March 2020. We adopt the trivariate dynamic conditional correlation-fractionally integrated asymmetric power ARCH model and unconditional quantile regression model, and our findings show that the hedging role of the U.S. dollar (USD) and gold against stocks differs under regular and extreme market conditions. The USD can act as a powerful hedge asset for stocks in regular market periods. Moreover, during the global financial crisis and COVID-19 outbreak, the safe-haven effect of gold becomes stronger for almost all stocks, whereas the USD can serve as a strong safe haven against stock markets of Korea, Taiwan, and Singapore when stock returns are extremely low. In terms of portfolio designing, we find that adding the USD and gold to portfolios improves their hedging effectiveness, and the optimally weighted stock-USD-gold portfolio is the best portfolio strategy, irrespective of referring to return or risk.     

A reduced PDE method for European option pricing under multi-scale,multi-factor stochastic volatility

The number of tailor-made hybrid structured products has risen more prominently to fit each investor’s preferences and requirements as they become more diversified. The structured products entail synthetic derivatives such as combinations of bonds and/or stocks conditional on how they are backed up by underlying securities, stochastic volatility, stochastic interest rates or exchanges rates. The complexity of these multi-asset structures yields lots of difficulties of pricing the products. Because of the complexity, Monte-Carlo simulation is a possible choice to price them but it may not produce stable Greeks leading to a trouble in hedging against risks. In this light, it is desirable to use partial differential equations with relevant analytic and numerical techniques. Even if the partial differential equation method would generate stable security prices and Greeks for single asset options, however, it may result in the curse of dimensionality when pricing multi-asset derivatives. In this study, we make the best use of multi-scale nature of stochastic volatility to lift the curse of dimensionality for up to three asset cases. Also, we present a transformation formula by which the pricing group parameters required for the multi-asset options in illiquid market can be calculated from the underlying market parameters.     

Detection of arbitrage in a market with multi-asset derivatives and known risk-neutral marginals

In this paper we study the existence of arbitrage opportunities in a multi-asset market when risk-neutral marginal distributions of asset prices are known. We first propose an intuitive characterization of the absence of arbitrage opportunities in terms of copula functions. We then address the problem of detecting the presence of arbitrage by formalizing its resolution in two distinct ways that are both suitable for the use of optimization algorithms. The first method is valid in the general multivariate case and is based on Bernstein copulas that are dense in the set of all copula functions. The second one is easier to work with but is only valid in the bivariate case. It relies on results about improved Fréchet–Hoeffding bounds in presence of additional information. For both methods, details of implementation steps and empirical applications are provided.     

The dynamics of strategic information flows in stock markets

We model a stock market with multiple stocks in a dynamic setting. Multiple informed traders receive new and heterogeneous information about the stocks in each period and use this information strategically. We characterize the decay rate of the information as it is incorporated into prices. The presence of multiple assets speeds information release by providing more channels for market makers to acquire information and incorporate that information in prices. The result is not only that profits are reduced in multi-asset settings, but that information release tilts toward new information relative to old information, reducing the profits that can be acquired by privately informed traders.

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Electronic Supplementary Material The online version of this article () contains supplementary material, which is available to authorized users.      

Multi-asset class mutual funds: Can they time the market? Evidence from the US,UK and Canada

The importance of asset allocation decisions in wealth management is well established. However, given its importance it is perhaps surprising that so little attention has been paid to the question of whether professional fund managers are skilful at timing market movement across asset classes over time. The timing literature has tended to concentrate on the timing skill of single asset class funds. Using data on US, UK and Canadian multi-asset class funds, we apply two alternative methodologies to identify the asset class timing abilities of managers. Overall, whether we apply a returns-based method or a holdings-based testing approach, we find evidence of only a tiny minority of funds with asset class timing ability.     

Covariance dependent kernels,a Q-affine GARCH for multi-asset option pricing

This paper introduces a class of multivariate GARCH models that extends the existing literature by explicitly modeling correlation dependent pricing kernels. A large subclass admits closed-form recursive solutions for the moment generating function under the risk-neutral measure, which permits efficient pricing of multi-asset options. We perform a full calibration to three bivariate series of index returns and their corresponding volatility indexes in a joint maximum likelihood estimation. The results empirically confirm the presence of correlation dependance in addition to the well known variance dependance in the pricing kernel. The model improves both the overall likelihood and the VIX-implied likelihoods, with a better fitting of marginal distributions, e.g., 15% less error on one-asset option prices. The new degree of freedom is also shown to significantly impact the shape of marginal and joint pricing kernels, and leads to up to 53% differences for out-of-the-money two-asset correlation option prices.