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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 ...


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 ...


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 ...


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.


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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