Abstract
We evaluate stock market indexes by the Aumann–Serrano (AS) performance index for multi-period gambles and one-period gambles and the Sharpe ratio. Our results show the AS performance index is more distinct for multi-period gambles than for one-period gambles in evaluation of the Japanese stock market indexes. In other words, a favorable evaluation score as compared to the Sharpe ratio becomes even better in multi-period gambles than in one-period gambles while an unfavorable evaluation score compared to the Sharpe ratio becomes even worse in multi-period gambles than in one-period gambles.
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Notes
Kadan and Liu (2014) proposed two performance measures based on risk measures proposed by Aumann and Serrano (2008) and Foster and Hart (2009). However, we only consider the performance measure based on the risk measure by Aumann and Serrano (2008) in this paper. We remark the performance and risk measures by Foster and Hart (2009) do not exist for many common distributions (cf. Riedel and Hellmann 2015). Therefore, the performance measure by Foster and Hart (2009) is limited in its applications.
There are currently three other stock exchanges in Japan, namely, the Nagoya Stock Exchange, Sapporo Securities Exchange, and Fukuoka Stock Exchange. They are local stock exchanges, 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.
The Nikkei 225 and TOPIX are, more specifically, respectively an equal weighted average of stock prices of the 225 companies and a value weighted average of stock prices of all the companies listed in the first section of the TSE compared to that at certain time point. The difference between the two indexes is similar to that between DOW and S&P500 in the U.S. stock market.
It is well-known that the EM algorithm works well in estimation of normal mixture processes or normal mixture distributions. See, e.g., Hastie et al. (2001).
The Ljung-Box statistics we use here are modified ones by Diebold (1988) who corrected the original Ljung-Box statistic which is known to reject the null hypothesis too often.
A market with low mean may not necessarily imply investors in that market unprofitable. Investors can earn profits by various strategies using options and futures. Foreign investors in the Japanese stock market are well-known to use derivatives of options and futures.
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J. Hodoshima: This research was financially supported by JSPS KAKENHI Grant Number JP17K03667.
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Hodoshima, J., Yamawake, T. Comparing Dynamic and Static Performance Indexes in the Stock Market: Evidence From Japan. Asia-Pac Financ Markets 29, 171–193 (2022). https://doi.org/10.1007/s10690-021-09343-7
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DOI: https://doi.org/10.1007/s10690-021-09343-7