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Ideally you'd want to use daily returns and just annualise it, but if you only have monthly returns then calculating the weighted variance in the following way might do it: $$Var = \frac{\sum_{i=0}^{24}(R_i - \mu)^2}{24 + \frac{21}{31}} + \frac{\frac{21}{31} (R_{25}' - \mu)^2}{24 + \frac{21}{31}}$$ $$Vol = \sqrt{Var}$$ Where $R_i$ is the returns of ...

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I think the only valid answer is you can't. The techniques you describe would work of the signal was much stronger than the noise but it seems that with your fund returns this is not the case. You could try to get more data or look at other risk measures like max drawdown to get some idea of the risks involved.

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Effective PA is dependent on the correct description of the investment process. I am not sure, from what you say, what exactly is your investment process. But let me presume that it is the following: You have chosen the S&P500 as your benchmark. You first distributed your money among sectors. (That you gave many sectors zero weight is not relevant to the ...

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If the base ccy of the your portfolio is CAD, then it makes sense to use the asset weights in base too (= CAD) according to your described formula.

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Before prediction you should see which models fit better your data. First before choosing a GARCH model or a GARCH type model with leverage efect you shoud perform the Engle-Ng sign bias test to see if the asset that your are modelling is affected by it, if yes a simple GARCH model won't be a good model. After the estimation and given that all parameters are ...

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If you are interested in evaluating forecasts accuracy, you could compare Value-at-risk forecasts. It has the advantage to take into account the forecast density (via quantile). Then you can compare easily their forecast accuracy via the Kupiec test for instance. Because if you just use points forecasts as it seems you are doing your results won't take the ...

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In theory, stock prices are lognormally distributed. People usually prove lognormality by referring to positivity and right skewness of stock prices. Mathematically (or philosophically if you wish), lognormality follows from the following equation $\frac{S}{dS}={\mu}dt+{\sigma}dW$, which you may see a lot in quantitative finance ("random walk") or in ...

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