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.

1. 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%)

2. 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.

3. Or should we use 50% US and 50% German Factors in the regression and then regress on the factors of both countries combined.

It really depends on how much work and effort you want to put in.

1. 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%.
2. Can be done and gives you the global exposure of your portfolio.
3. 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!

• Could it be possible to elaborate on the first point. I would have assumed that by regressing on the country specific factors we would have obtained more accurate coefficients and alphas. – Circus_beta Jun 22 '20 at 13:02
• I have edited the answer. – phdstudent Jun 22 '20 at 13:05
• Does the same logic applied to Betas ? B US * 50% + B Ger * 50% will not be equal to the "true" beta because of correlation? – Circus_beta Jun 22 '20 at 13:18
• Definitely. I am clarifying above. – phdstudent Jun 22 '20 at 13:19
• Thank you so much, I just wanted to add a clarification to the last sentence. If we run P1 US stocks against FFUS and P1 DE stocks against FFDE, the alpha will not be 50% of each? – Circus_beta Jun 22 '20 at 13:39