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Empirical Economics

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30-04-2020

Evaluation of performance of stock and real estate investment trust markets in Japan

Author: Jiro Hodoshima

Published in: Empirical Economics | Issue 1/2021

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Abstract

We evaluate three stock markets and one real estate investment trust market in Japan by using four performance measures: the inner rate of risk aversion (IRRA) proposed by Miyahara (Evaluation of the scale risk, 2014), Sharpe ratio, Sortino ratio, and Calmar ratio. When compared to other performance measures, the IRRA responds more sensitively to the underlying risk and is more relevant for risk-averse investors. We reveal the characteristics of the markets through the IRRA and three alternative performance measures. One stock market index, i.e., the second section of the Tokyo Stock Exchange, is found to perform considerably better than the DOW and NASDAQ when evaluated by the IRRA.

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${\varvec{C}}^2$-class is the class of functions that possess continuous second derivatives.

The several desirable properties that a suitable evaluation function must satisfy are explained in the next section.

When we are revising the paper, we find the IRRA is equivalent to another performance measure studied by Kadan and Liu (2014). The performance measure of ${\varvec{X}}$ studied by Kadan and Liu (2014) is defined to be the solution $\alpha _0$ to the implicit equation given by

$$\begin{aligned} E[e^{- \alpha _0 {\varvec{X}}}] = 1. \end{aligned}$$

This performance measure is based on the economic index of riskiness, a risk measure, proposed by Aumann and Serrano (2008). In other words, the performance measure studied by Kadan and Liu (2014) is the reciprocal of the riskiness index of Aumann and Serrano (2008), which is given by $\frac{1}{\alpha _0}$.

Use of the Sortino ratio and Calmar ratio in addition to the Sharpe ratio was suggested by one of the referees.

In the first version of the paper, we included the TSE JASDAQ Securities Exchange. However, we do not include the TSE JASDAQ Exchange in the present version since dividend data for the index of the TSE JASDAQ Exchange are not available in the TSE. We remark, in the data without dividends, the index of the TSE JASDAQ performs, as in the index of the second section of the TSE in this paper, superiorly by the IRRA compared to the US indexes of the DOW and NASDAQ.

There are currently three other stock markets in Japan, namely the Nagoya Stock Exchange, Sapporo Securities Exchange, and Fukuoka Stock Exchange. They are local stock markets, when compared to the TSE, and the market capitalization of companies listed in the three exchanges is small when compared to that in the TSE.

Inclusion of dividends in the index data was suggested by one of the referees.

Use of annualized mean and annualized standard deviation was suggested by one of the referees.

The US risk-free rate observations are downloaded from Ken French home page. We are very grateful to Ken French for making his database available for everyone.

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Title: Evaluation of performance of stock and real estate investment trust markets in Japan
Author: Jiro Hodoshima
Publication date: 30-04-2020
Publisher: Springer Berlin Heidelberg
Published in: Empirical Economics / Issue 1/2021
Print ISSN: 0377-7332
Electronic ISSN: 1435-8921
DOI: https://doi.org/10.1007/s00181-020-01869-5

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