Is Bitcoin a better hedging and safe-haven investment than traditional assets against currencies? Evidence from the time-frequency domain approach

Many studies have discussed hedges and safe havens against stocks, but few studies focus on the hedging/safe-haven performance of assets against the currency market over different time horizons. This paper studies the connectedness, hedging and safe-haven properties of Bitcoin/gold/crude oil/commodities against six currencies across multiple investment horizons, placing a particular focus on the performance of these assets during the recent COVID-19 outbreak. Our findings suggest that the overall dependence between assets and the currency market is the strongest in the short term, and Bitcoin is the least dependent across all investment horizons. The dynamic relationships between the four assets and the currency market vary with timescales. Bitcoin offers better hedging capability in the long term and commodities emerge as the most favorable option for the optimal portfolio of currency over all time horizons. Further analysis shows that assets are better at helping investments reduce risk in the initial stages of the pandemic, and gold is an effective and robust safe haven for currencies.     

Multivariate location–scale mixtures of normals and mean–variance–skewness portfolio allocation

We show that the distribution of any portfolio whose components jointly follow a location–scale mixture of normals can be characterised solely by its mean, variance and skewness. Under this distributional assumption, we derive the mean–variance–skewness frontier in closed form, and show that it can be spanned by three funds. For practical purposes, we derive a standardised distribution, provide analytical expressions for the log-likelihood score and explain how to evaluate the information matrix. Finally, we present an empirical application in which we obtain the mean–variance–skewness frontier generated by the ten Datastream US sectoral indices, and conduct spanning tests.     

Sequential estimation of shape parameters in multivariate dynamic models

Sequential maximum likelihood and GMM estimators of distributional parameters obtained from the standardised innovations of multivariate conditionally heteroskedastic dynamic regression models evaluated at Gaussian PML estimators preserve the consistency of mean and variance parameters while allowing for realistic distributions. We assess their efficiency, and obtain moment conditions leading to sequential estimators as efficient as their joint ML counterparts. We also obtain standard errors for VaR and CoVaR, and analyse the effects on these measures of distributional misspecification. Finally, we illustrate the small sample performance of these procedures through simulations and apply them to analyse the risk of large eurozone banks.     

Testing the Markov property with high frequency data

This paper develops a framework to nonparametrically test whether discrete-valued irregularly spaced financial transactions data follow a Markov process. For that purpose, we consider a specific optional sampling in which a continuous-time Markov process is observed only when it crosses some discrete level. This framework is convenient for it accommodates the irregular spacing that characterizes transactions data. Under such an observation rule, the current price duration is independent of a previous price duration given the previous price realization. A simple nonparametric test then follows by examining whether this conditional independence property holds. Monte Carlo simulations suggest that the asymptotic test has huge size distortions, though a bootstrap-based variant entails reasonable size and power properties in finite samples. As for an empirical illustration, we investigate whether bid–ask spreads follow Markov processes using transactions data from the New York Stock Exchange. The motivation lies on the fact that asymmetric information models of market microstructures predict that the Markov property does not hold for the bid–ask spread. We robustly reject the Markov assumption for two out of the five stocks under scrutiny. Finally, it is reassuring that our results are consistent with two alternative measures of asymmetric information.     

On loss functions and ranking forecasting performances of multivariate volatility models

The ranking of multivariate volatility models is inherently problematic because when the unobservable volatility is substituted by a proxy, the ordering implied by a loss function may be biased with respect to the intended one. We point out that the size of the distortion is strictly tied to the level of the accuracy of the volatility proxy. We propose a generalized necessary and sufficient functional form for a class of non-metric distance measures of the Bregman type which ensure consistency of the ordering when the target is observed with noise. An application to three foreign exchange rates is provided.     

How do “gatekeepers” affect credit risk?

This study investigates the relationship between auditor tenure and credit default swap (CDS) spreads of U.S. firms based on quantile regression. After allowing for common determinants of CDS spreads, auditor tenure exerts both statistically and economically significant additional impacts on the CDS market. Furthermore, there are differential effects of common CDS spread determinants and auditor tenure. While common determinants of CDS spreads (e.g., leverage, volatility, risk free rate, credit ratings, and earnings) have monotonically increasing impacts when CDS spreads (and their changes) are increasingly higher, auditor tenure primarily has the impact when CDS spreads are of low or median levels for less risky firms.     

Options and efficiency in spaces of bounded claims

In a seminal contribution, Ross (1976) showed that a static finite state-space market can be completed by supplementing the primitive securities with ordinary call and put options. Galvani (2009) extends this result to norm separable _Lp$L_p$-spaces, with 1≤p<∞$1\le p<\infty$. This study concludes that options maintain the same spanning power in the space of bounded payoffs topologized by the duality with the space of the state price densities. In particular, under mild assumptions on the probability space, options written on a claim that is a.s. equal to an injective function complete the market.     

Edgeworth expansions and normalizing transforms for inequality measures

Finite sample distributions of studentized inequality measures differ substantially from their asymptotic normal distribution in terms of location and skewness. We study these aspects formally by deriving the second-order expansion of the first and third cumulant of the studentized inequality measure. We state distribution-free expressions for the bias and skewness coefficients. In the second part we improve over first-order theory by deriving Edgeworth expansions and normalizing transforms. These normalizing transforms are designed to eliminate the second-order term in the distributional expansion of the studentized transform and converge to the Gaussian limit at rate O(n⁻¹)$O\left(n^{-1}\right)$. This leads to improved confidence intervals and applying a subsequent bootstrap leads to a further improvement to order O(n^−3/2)$O\left(n^{-3/2}\right)$. We illustrate our procedure with an application to regional inequality measurement in Côte d’Ivoire.     

Extreme-quantile tracking for financial time series

Time series of financial asset values exhibit well-known statistical features such as heavy tails and volatility clustering. We propose a nonparametric extension of the classical Peaks-Over-Threshold method from extreme value theory to fit the time varying volatility in situations where the stationarity assumption may be violated by erratic changes of regime, say. As a result, we provide a method for estimating conditional risk measures applicable to both stationary and nonstationary series. A backtesting study for the UBS share price over the subprime crisis exemplifies our approach.