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By definition, they don't (assuming you're considering something in the vein of APT). The primary benefit of equity factor models in terms of portfolio risk is allowing you to decompose risk to understand what you're actually exposed to aside from simply market risk.


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Technically, say you have $K\gg X$ stocks and $X$ factors. Your (daily) returns can be written as $$dR=\frac{dS}{S}=\mu\,dt + F\,dW$$ where $\mu$ is a $K\times 1$ vector of expected returns (it is not very important since it is deterministic and will play no role in the computation of the covariance) $F$ is a $K\times X$ matrix of loadings of returns on ...


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Hi: If you don't standardize, then each coefficient will have a different meaning. For example, suppose you have a company, ZZZ, that has a 1.5 standard deviation value of "growth" factor exposure and a 2.5 standard deviation value of "liquidity" factor exposure. Then, if the model coefficient for growth is $\beta_{growth}$ and the model coefficient for ...


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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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I think you may be overthinking it. The final relation (3.114) is really the crux of it. In short, that individual assets are exposed to some set of factors (X < K) and can be modeled as such rather than being driven idiosyncratically. As an analog, it's similar to PCA being used to model FI returns, where we can say three factors explain 90%+ of ...


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Simply speaking, author means that dimensionality-reduction can be achieved through factor modelling is because you may need only few factors (equal or less than numbers of variables/stocks) which explain most of the variation in your covariance matrix of variables/stocks. Simple example: Assume you have 3 quantitative subjects: math (M), chemistry (C) and ...


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