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An OIS, or Overnight Index Swap, is an interest rate swap whose floating leg payments are calculated as a geometric average of the daily fixings of some underlying O/N or T/N index (these indices are generally volume-weighted averages of reported daily transactions). The annualized floating leg rate is defined as  c_T^{float} = ...

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well they aren't actually log-normal! if you use the terminal measure and test the last forward rate, it is log-normal. The essential point is that the drifts that make the ratio of bond prices to nuemraire a martingale are state-dependent. This state dependence destroys log-normality. You can take the real-world measure rates to be log-normal but the ...

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I do not have access to the exact time-series of the MSCI world, but looking at the returns from the tracking ETF, since 2001 the average return is negative. Thus regardless of the risk-free you use you will get a negative sharpe ratio.

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