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Time aggregation of the Sharpe ratio

Author

Listed:
  • Ziemowit Bednarek

    (Orfalea College of Business, California Polytechnic State University)

  • Pratish Patel

    (Orfalea College of Business, California Polytechnic State University)

  • Cyrus A. Ramezani

    (Orfalea College of Business, California Polytechnic State University)

Abstract

The Sharpe ratio (SR) is the most widely used risk-adjusted performance index. The building blocks of the SR – the expected return and the volatility – depend on the investment horizon. This raises a natural question: how does the SR vary with investment horizon? To address this question, we derive an explicit expression for the SR as a function of the investment horizon for both simple and log-returns. Assuming independent normal returns distribution, we show that for simple returns, the SR is humped shaped – it rises and then falls with the investment horizon. This finding suggests that time aggregation of the SR using the square-root-t rule will lead to significant errors in ranking portfolios. For log-returns, we show that the SR monotonically rises with the horizon and the square-root-t rule holds true. Using robust bootstrap sampling methods, we empirically corroborate our theory with annual data for a large number of important style portfolios, based on size, book-to-market, and other investment criteria. Our empirical analysis provides robust benchmark SRs for these portfolios over investment horizons that span from one to twenty-five years. Our findings have important implications for investors and portfolio managers who rely on SR for asset-allocation and performance-evaluation decisions.

Suggested Citation

  • Ziemowit Bednarek & Pratish Patel & Cyrus A. Ramezani, 2016. "Time aggregation of the Sharpe ratio," Journal of Asset Management, Palgrave Macmillan, vol. 17(7), pages 540-555, December.
  • Handle: RePEc:pal:assmgt:v:17:y:2016:i:7:d:10.1057_s41260-016-0003-x
    DOI: 10.1057/s41260-016-0003-x
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    References listed on IDEAS

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    1. Jonathan Ingersoll & Ivo Welch, 2007. "Portfolio Performance Manipulation and Manipulation-proof Performance Measures," The Review of Financial Studies, Society for Financial Studies, vol. 20(5), pages 1503-1546, 2007 17.
    2. Campbell, John Y., 2003. "Consumption-based asset pricing," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, edition 1, volume 1, chapter 13, pages 803-887, Elsevier.
    3. Haim Levy, 1972. "Portfolio Performance and the Investment Horizon," Management Science, INFORMS, vol. 18(12), pages 645-653, August.
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    More about this item

    Keywords

    Sharpe ratio; performance evaluation;

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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