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I'm puzzled about certain parameters in calculating the annualized Sharpe Ratio using monthly return data.

  1. Average excess return: Does this mean the arithmetic average of all the monthly excess returns? Or should I calculate the rate of monthly return that, if compounded, will result in the overall excess return of the portfolio?

  2. Risk-free rate: The debate of this being 0, the T-bill rate, or a baseline porfolio aside, if I were to use a T-bill rate as risk-free rate, then should the selected time period correspond to the rebalancing period of my portfolio or the entire duration of the portfolio's return?

Thank you in advance!

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    $\begingroup$ (1) Yes, by definition it is the arithmetic average that is used (2) the T-bill rate is being compared to the portfolio returns so both have to be compatible in terms of period and unit (eg. monthly returns expressed in percent per month. If you have Tbill annual returns divide it by 12). Note: The original article by Sharpe is online and I think would address these questions. $\endgroup$
    – noob2
    Jul 26 '20 at 6:11