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This answer depends on the $X^i$ Before jumping on to the solution it should be answered that are $X^i$ traded in the market? i.e. are the returns on these available in the market (Size/Momentum portfolios, ETF returns) or are these economic variables like CPI, Inflation etc. If it is the former i.e. traded assets then we can do the time series regression ...

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Are you sure the return for two years is 0.7214? It should be 0.3422 per year if you are using 31/12/2011, and 0.3416 if you are using 01/01/2012 as the end date. Assuming the last number (because it makes for two full years, therefore easier to calculate), yes, there is a formula to derive it from the return of the individual years. It's the geometric ...

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It depends on what makes more economic sense: If you are calculating CAGR for FX (which is traded effectively 24/7) strategy returns for instance, it would seem fair to use 365.25 calendar days. If you are calculating CAGR for internal reporting of trading strategy returns on a product with 5 market sessions per week, it would seem fair to use 252 calendar ...

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You can use both standards, but when you apply or compare this rate the standards must be equal, and it should be noted which convention you used. Note that 300/365 yeardays would in percentage be equal to 205/250 tradingdays, so its really just a convention that would make no difference in actual time.

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One could use a GARCH of his choice to estimate the volatility. A mean over your period would be a good indicator, otherwise the instant conditional sd is as good as it gets. Another way could be via an exponential smoothing of the risk-metrics type. Your question is not so clear is to be honest.

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