arXiv subjects

Takaki Hayashi

Publications and source records attributed to Takaki Hayashi.

7 recordsLinked to original sources

arXiv2026

Two-fund separation under hyperbolically distributed returns and concave utility functions

Portfolio selection problems that optimize expected utility are usually difficult to solve. If the number of assets in the portfolio is large, such expected utility maximization problems become even harder to solve numerically. Therefore, analytical expressions for optimal portfolios are always preferred. In our work, we study portfolio optimization problems under the expected utility criterion for a wide range of utility functions, assuming return vectors follow hyperbolic distributions. Our main result demonstrates that under this setup, the two-fund monetary separation holds. Specifically, an individual with any utility function from this broad class will always choose to hold the same portfolio of risky assets, only adjusting the mix between this portfolio and a riskless asset based on their initial wealth and the specific utility function used for decision making. We provide explicit expressions for this mutual fund of risky assets. As a result, in our economic model, an individual's optimal portfolio is expressed in closed form as a linear combination of the riskless asset and the mutual fund of risky assets. Additionally, we discuss expected utility maximization problems under exponential utility functions over any domain of the portfolio set. In this part of our work, we show that the optimal portfolio in any given convex domain of the portfolio set either lies on the boundary of the domain or is the unique globally optimal portfolio within the entire domain.

q-fin.PM↗

arXiv2026

On lead-lag estimation of non-synchronously observed point processes

This paper introduces a new theoretical framework for analyzing lead-lag relationships between point processes, with a special focus on applications to high-frequency financial data. In particular, we are interested in lead-lag relationships between two sequences of order arrival timestamps. The seminal work of Dobrev and Schaumburg proposed model-free measures of cross-market trading activity based on cross-counts of timestamps. While their method is known to yield reliable results, it faces limitations because its original formulation inherently relies on discrete-time observations, an issue we address in this study. Specifically, we formulate the problem of estimating lead-lag relationships in two point processes as that of estimating the shape of the cross-pair correlation function (CPCF) of a bivariate stationary point process, a quantity well-studied in the neuroscience and spatial statistics literature. Within this framework, the prevailing lead-lag time is defined as the location of the CPCF's sharpest peak. Under this interpretation, the peak location in Dobrev and Schaumburg's cross-market activity measure can be viewed as an estimator of the lead-lag time in the aforementioned sense. We further propose an alternative lead-lag time estimator based on kernel density estimation and show that it possesses desirable theoretical properties and delivers superior numerical performance. Empirical evidence from high-frequency financial data demonstrates the effectiveness of our proposed method.

math.ST↗

arXiv2023

A Modelling Framework for Regression with Collinearity

This study addresses a fundamental, yet overlooked, gap between standard theory and empirical modelling practices in the OLS regression model $\boldsymbol{y}=\boldsymbol{Xβ}+\boldsymbol{u}$ with collinearity. In fact, while an estimated model in practice is desired to have stability and efficiency in its "individual OLS estimates", $\boldsymbol{y}$ itself has no capacity to identify and control the collinearity in $\boldsymbol{X}$ and hence no theory including model selection process (MSP) would fill this gap unless $\boldsymbol{X}$ is controlled in view of sampling theory. In this paper, first introducing a new concept of "empirically effective modelling" (EEM), we propose our EEM methodology (EEM-M) as an integrated process of two MSPs with data $(\boldsymbol{y^o,X})$ given. The first MSP uses $\boldsymbol{X}$ only, called the XMSP, and pre-selects a class $\scr{D}$ of models with individually inefficiency-controlled and collinearity-controlled OLS estimates, where the corresponding two controlling variables are chosen from predictive standard error of each estimate. Next, defining an inefficiency-collinearity risk index for each model, a partial ordering is introduced onto the set of models to compare without using $\boldsymbol{y^o}$, where the better-ness and admissibility of models are discussed. The second MSP is a commonly used MSP that uses $(\boldsymbol{y^o,X})$, and evaluates total model performance as a whole by such AIC, BIC, etc. to select an optimal model from $\scr{D}$. Third, to materialize the XMSP, two algorithms are proposed.

stat.ME↗

arXiv2020

Multi-scale analysis of lead-lag relationships in high-frequency financial markets

We propose a novel estimation procedure for scale-by-scale lead-lag relationships of financial assets observed at high-frequency in a non-synchronous manner. The proposed estimation procedure does not require any interpolation processing of original datasets and is applicable to those with highest time resolution available. Consistency of the proposed estimators is shown under the continuous-time framework that has been developed in our previous work Hayashi and Koike (2018). An empirical application to a quote dataset of the NASDAQ-100 assets identifies two types of lead-lag relationships at different time scales.

stat.ME↗

arXiv2018

Wavelet-based methods for high-frequency lead-lag analysis

We propose a novel framework to investigate lead-lag relationships between two financial assets. Our framework bridges a gap between continuous-time modeling based on Brownian motion and the existing wavelet methods for lead-lag analysis based on discrete-time models and enables us to analyze the multi-scale structure of lead-lag effects. We also present a statistical methodology for the scale-by-scale analysis of lead-lag effects in the proposed framework and develop an asymptotic theory applicable to a situation including stochastic volatilities and irregular sampling. Finally, we report several numerical experiments to demonstrate how our framework works in practice.

stat.ME↗

arXiv2017

No arbitrage and lead-lag relationships

The existence of time-lagged cross-correlations between the returns of a pair of assets, which is known as the lead-lag relationship, is a well-known stylized fact in financial econometrics. Recently some continuous-time models have been proposed to take account of the lead-lag relationship. Such a model does not follow a semimartingale as long as the lead-lag relationship is present, so it admits an arbitrage without market frictions. In this paper we show that they are free of arbitrage if we take account of market frictions such as the presence of minimal waiting time on subsequent transactions or transaction costs.

q-fin.MF↗

arXiv2012

Comprehensive Analysis of Market Conditions in the Foreign Exchange Market: Fluctuation Scaling and Variance-Covariance Matrix

We investigate quotation and transaction activities in the foreign exchange market for every week during the period of June 2007 to December 2010. A scaling relationship between the mean values of number of quotations (or number of transactions) for various currency pairs and the corresponding standard deviations holds for a majority of the weeks. However, the scaling breaks in some time intervals, which is related to the emergence of market shocks. There is a monotonous relationship between values of scaling indices and global averages of currency pair cross-correlations when both quantities are observed for various window lengths $Δt$.

q-fin.ST↗