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Internet Bubble Examination with Mean-Variance Ratio

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Handbook of Financial Econometrics and Statistics

Abstract

To evaluate the performance of the prospects X and Y, financial professionals are interested in testing the equality of their Sharpe ratios (SRs), the ratios of the excess expected returns to their standard deviations. Bai et al. (Statistics and Probability Letters 81, 1078–1085, 2011d) have developed the mean-variance-ratio (MVR) statistic to test the equality of their MVRs, the ratios of the excess expected returns to its variances. They have also provided theoretical reasoning to use MVR and proved that their proposed statistic is uniformly most powerful unbiased. Rejecting the null hypothesis infers that X will have either smaller variance or larger excess mean return or both leading to the conclusion that X is the better investment. In this paper, we illustrate the superiority of the MVR test over the traditional SR test by applying both tests to analyze the performance of the S&P 500 index and the NASDAQ 100 index after the bursting of the Internet bubble in the 2000s. Our findings show that while the traditional SR test concludes the two indices being analyzed to be indistinguishable in their performance, the MVR test statistic shows that the NASDAQ 100 index underperformed the S&P 500 index, which is the real situation after the bursting of the Internet bubble in the 2000s. This shows the superiority of the MVR test statistic in revealing short-term performance and, in turn, enables investors to make better decisions in their investments.

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Notes

  1. 1.

    We note that Bai et al. (2009a, b, 2011c) have also used the same framework as in 53.5.

  2. 2.

    The results of the one-sided test which draw a similar conclusion are available on request.

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Acknowledgment

We would like to thank the editor C.-F. Lee for his substantive comments that have significantly improved this manuscript. The third author would also like to thank Professors Robert B. Miller and Howard E. Thompson for their continuous guidance and encouragement. The research is partially supported by grants from North East Normal University, National University of Singapore, Hong Kong Baptist University and the Research Grants Council of Hong Kong. The first author thanks the financial support from NSF China grant 11171057, Program for Changjiang Scholars and Innovative Research Team in University, and the Fundamental Research Funds for the Central Universities and NUS grant R-155-000-141-112.

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Authors and Affiliations

  1. KLAS MOE & School of Mathematics and Statistics, Northeast Normal University, Changchun, China

    Zhidong D. Bai

  2. Department of Statistics and Applied Probability, National University of Singapore, Singapore, Singapore

    Zhidong D. Bai

  3. Department of Economics, Hong Kong Baptist University, Kowloon, Hong Kong

    Wing-Keung Wong

  4. School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, China

    Yongchang C. Hui

Authors
  1. Zhidong D. Bai
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  2. Yongchang C. Hui
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  3. Wing-Keung Wong
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Correspondence to Zhidong D. Bai .

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Editors and Affiliations

  1. Department of Finance and Economics, Rutgers Business School, Rutgers, The State University of New Jersey, Piscataway, New Jersey, USA

    Cheng-Few Lee

  2. Center for PBBEF Research, North Brunswick, New Jersey, USA

    John C. Lee

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Bai, Z.D., Hui, Y.C., Wong, WK. (2015). Internet Bubble Examination with Mean-Variance Ratio. In: Lee, CF., Lee, J. (eds) Handbook of Financial Econometrics and Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-7750-1_53

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  • DOI: https://doi.org/10.1007/978-1-4614-7750-1_53

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