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Testing for the best alternative with an application to performance measurement

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  • Frahm, Gabriel

Abstract

Suppose that we are searching for the maximum of many unknown and analytically untractable quantities or, say, the 'best alternative' among several candidates. If our decision is based on historical or simulated data there is some sort of selection bias and it is not evident if our choice is significantly better than any other. In the present work a large sample test for the best alternative is derived in a rather general setting. The test is demonstrated by an application to financial data and compared with the Jobson-Korkie test for the Sharpe ratios of two asset portfolios. We find that ignoring conditional heteroscedasticity and non-normality of asset returns can lead to misleading decisions. In contrast, the presented test for the best alternative accounts for these kinds of phenomena.

Suggested Citation

  • Frahm, Gabriel, 2007. "Testing for the best alternative with an application to performance measurement," Discussion Papers in Econometrics and Statistics 7/07, University of Cologne, Institute of Econometrics and Statistics.
    • Handle: RePEc:zbw:ucdpse:707
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    References listed on IDEAS

    as
    1. Jorion, Philippe, 1985. "International Portfolio Diversification with Estimation Risk," The Journal of Business, University of Chicago Press, vol. 58(3), pages 259-278, July.
    2. Jobson, J D & Korkie, Bob M, 1981. "Performance Hypothesis Testing with the Sharpe and Treynor Measures," Journal of Finance, American Finance Association, vol. 36(4), pages 889-908, September.
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    Cited by:

    1. Gabriel Frahm & Tobias Wickern & Christof Wiechers, 2012. "Multiple tests for the performance of different investment strategies," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 96(3), pages 343-383, July.
    2. Gabriel Frahm, 2010. "Linear statistical inference for global and local minimum variance portfolios," Statistical Papers, Springer, vol. 51(4), pages 789-812, December.

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    More about this item

    Keywords

    Ergodicity; Gordin's condition; heteroscedasticity; Jobson-Korkie test; Monte Carlo simulation; performance measurement; Sharpe ratio;
    All these keywords.

    JEL classification:

    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • B20 - Schools of Economic Thought and Methodology - - History of Economic Thought since 1925 - - - General

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