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Long story short... Just think at the risk free rate (which is an essential part of Fama-French factors). It varies across currencies: http://pages.stern.nyu.edu/~adamodar/pdfiles/DSV2/Ch6.pdf You do not get the risk free of another currency just by converting the risk free of a currency. Hence, what are trying to do with converted Fama-French factors?

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Long story short... Just think at the risk free rate (which is an essential part of Fama-French factors). It varies across currencies: http://pages.stern.nyu.edu/~adamodar/pdfiles/DSV2/Ch6.pdf You do not get the risk free of another currency just by converting the risk free of a currency. Hence, what are trying to do with converted Fama-French factors?

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The advantage of the method is that you can use it regardless of whether the factor is traded or non-traded. If the factor is traded, you are correct, you can use time-series tests and test whether the intercept is zero ($\beta_{i0}$) in your case. We are testing whether $\beta_{i0}=$ in: $R_{it} = \beta_{i0} + \sum_{k=1}^K\beta_{ik}F_{kt}+\epsilon_{it}$ ...

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Clarification on the regression coefficients Cochrane (Asset Pricing, rev. edition, 2005) states (p. 247): It it easier to do this in a more standard setup, with left-hand variable $y$ and right-hand variable $x$. Consider a regression $$y_{it} = \beta´x_{it} + \epsilon_{it}$$ $$i = 1,2,..,N$$ $$t = 1,2,...,T$$ [...] In an expected return-beta ...

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Preliminary: I assume from your previous post, that you are using Thomson Reuters Datastream. There are several additional parameters available on your Datatypes. Let's for example look at the Datatype MV, which is the market value of a company: If you are using MV, than you obtain a time-series, where the last available value is repeated, if a stock is (...

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When you handle data of any type you might have the issue of missing elements. You can generally handle it by global ommission or by imputation. Imputation can be feed forward, feed backward, some averaging or interpolation scheme. One such scheme might be to use your existing data to build a machine learning algorithm that predicts market movements ...

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