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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 ...

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

In your question you do not provide any reference. I believe that we are in front of two possibilities: annualized linear returns and Compound Annual Growth Rate (CAGR). If compounding is not mentioned, I would assume annualized linear returns. $n$-years Annualized linear returns $n$ = number of years $n * r_A = r_*$, where $r_*$ is the return over the ...

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