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5

The correct answer has some intuition though it doesn't generalize to continuous time very easily: Think about the paper below like this: $Var(X+Y) = Var(X) + Var(Y) + 2Cov(X,Y)$ The generalization is slightly hard because the dynamics of $\mu$ and $\sigma^2$ could be dependent for arbitrary returns. You can use a GMM estimator to derive the asymptotic ...


4

Arithmetic returns allow for easier cross-sectional aggregation and log returns allow for easier time-aggregation. The reason people use log returns (for equities) is that they are approximately invariant and hence easier to work with in estimating distributions. Meucci does better justice in describing invariance here. The basic idea (again, for equities) ...


2

Actually, neither of your two results are quite correct. As explained in the Details for the Return.calculate function, most of the PerformanceAnalytics functions use discrete returns, not log returns. To get the correct results, you will have to convert your data from log returns to simple returns. Compare the charts from the following: ...


2

The answer is that it depends. In addition to the Lo paper above, there are a number of excellent references that go into depth about annualizing or time scaling non-i.i.d. returns, one of which is Roger Kauffman, "Long-Term Risk Management", 2005 which can be found at http://www.rogerkaufmann.ch/all-Budapest.pdf. There are some well known cases where the ...


1

It depends on your investment strategy. The most common approach is to use the close price of $p_t$ and $p_{t+1}$. The volatility you measure using this method implies the "assumption" that your are able to trade at close every day. If you choose to compute the daily returns from open to close, then you assume that you are selling your position every night ...


1

It looks like 1 and 2 are different portfolios of companies. 1 is a portfolio of dual-listed companies, and 2 is a portfolio of everything in the "market". Once you have constructed these these portfolios, let's say you put the returns for every time step into a vector, call it r, then the average return would be mean(r). You need some clarification as ...



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