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1

You have already answered your question. In Bjork, the $\beta$ terms represent the value in the money market, or deposit, account, while the $\beta$ terms in Andrea Pascucci represent the units in the money market account. Then, the two definitions are basically the same. More specifically, \begin{align*} \beta^{Bjork}_{t+1} = \beta^{Andrea\, ...

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Yes, this is the simple markowitz optimization. Denote $\Sigma$ as the variance-covariance matrix of returns and $\bar{R}$ as a vector of expected returns. The tangency portfolio weights are given by $\omega_{tan}=\frac{\textbf{{1}'}\Sigma^{-1}}{\textbf{{1}'}\Sigma^{-1}\textbf{1}}$. The minimum-variance portfolio is ...

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I agree on Richard. the simpler you choose, the better it is so as to get reliable estimates. What's your data frequency? purpose? For model construction as far as I am concerned, daily data from 2010 is enough. Otherwise, you could use a proxy asset for asset D depending on its nature. To clarify, if D is an ETF let's say CAC 40 ETF, concatenate its return ...

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You can consider old prices for Stocks B, C and D to be "missing data" and apply techniques used by Statisticians to deal with such missing data. One approach, the EM algorithm, suggests you estimate the covariance for the common period, use that covariance matrix and the available data to generate pseudo data for the back period for the third stock and ...

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The short answer: Take all time series starting from 2010 (at most). The covarianc-matrix tells you something about the assets for a certain amount of time. E.g. if I estiamte the covaraince matrix of those 4 assets taking into account data from the last year (!) then I can expect that this matrix remains valid for the coming 1-3 months - if the markets ...

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Computing returns is one of the first things you learn when you start studying finance but I believe it's one the trickiest one once you get to complicated cases. The source you mentioned seems actually very good to me and it already takes into account different approaches and different subtleties like dividend payment. But this is in fact only the top of ...

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