Estimating Alpha for Portfolios Across Multiple Countries
Summary
The note considers how to estimate the alpha of a portfolio split across US and German equities using Fama–French factors. It compares estimating separate country-level regressions and averaging their alphas, using global factors, or constructing a combined set of country factors. The central methodological point is that alphas estimated against different factor sets cannot generally be combined by weighting them, because correlations between the factors affect the joint regression.
A global factor regression can describe exposure to broad global risks. A more tailored combined model requires constructing the factors consistently from the underlying stocks across both markets, rather than simply averaging precomputed national factors. The discussion gives conceptual guidance, not empirical results or a prescribed universal model. The appropriate factor set depends on the portfolio and the exposure question; comparisons across separately specified regressions may not yield a meaningful portfolio alpha.
Key ideas
- Alphas from regressions using different factor sets are not generally additive.
- Factor correlations across markets affect the alpha estimated for a combined portfolio.
- Global factors can be used to describe broad global exposures.
- A combined country model requires consistently constructed factors that account for cross-market relationships.
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Full text
# Global portfolio alpha
# Global portfolio alpha
How does one compute the alpha of a global portfolio. Let's say we are using the Fama French 3 factor model and we have a portfolio of 50% US stocks and 50% German stocks.
- Should the regression be applied on every country by using the country specific factors? And then reconstruct the portfolio? (Alpha Us * 50% + Alpha Germany *50%)
- Should the regression be done on the World Fama French factors? I assume that since we are not exposed to every country that it might not be the correct factors.
- Or should we use 50% US and 50% German Factors in the regression and then regress on the factors of both countries combined.
## Answer by phdstudent (score 1, accepted)
https://quant.stackexchange.com/a/55125
It really depends on how much work and effort you want to put in.
- Is definitely not correct. Alphas regressed to different factors are not additive because you are not taking into account the correlation across factors in the two markets. Let's you have a 5% alpha against US factors and a 10% alpha against German factors. The combined alpha is not 50%. If you had run the model with a jointly estimated alpha (as in point 3 below) e could well be that the actual alpha would be < 5%.
- Can be done and gives you the global exposure of your portfolio.
- Can be done, but you need to make it correctly. You can't pick the german factors, and the US factors and average them out (you are missing correlations). You need to get the actual individual stocks for US and Germany and then sort portfolios into book-to-market and size, and then create the factors.
Clarification:
Let's assume you have two portfolios $P_1$ and $P_2$.
Let's assume you also have two sets of factors $\mathbf{FF}^{US}$, $\mathbf{FF}^{DE}$.
Now if you run let's say $P_1$ and $P_2$ agains US factors, then yes, the alpha of a 50% portfolio of each portolio (1 and 2) is the the sum of 50% of each alpha.
Now, if you run $P_1$ against $FF^{US}$ and against $FF^{DE}$ it is no longer true that the alpha will be 50% of each alpha because this does not take into account the correlation between the factors!Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.