Contributor
Posts: 44

# Calculating portfolio weights from regression coefficients

Hi,

This topic isn't that much related here, but I'll try anyway..I have made a regression, and based on one financial model the regression coefficients equal the portfolio weights I need. If the coefficients are following, there's no problem obviously in calculations:

coefficients:

b1=4

b2=5

weights:

w1=4/9

w2=5/9

However, if one of the coefficients is negative, how do i calculate the weights? Intuitively calculated as follows:

b1=4

b2=-5

b1+b2=-1

w1=4/-1

w2=-5/-1

More intuitive result obviously would be that w1 is positive and w2 negative..Calculation is simply but can't seem to decide which is the correct approach...

Posts: 5,056

## Re: Calculating portfolio weights from regression coefficients

There's an almost infinite number of ways to combine two coefficients. We need some understanding of the context to make meaningful suggestions. What information do these regression coefficients give about the portfolios? How do you interpret a negative coefficient? What model (equation) do you use to estimate the coefficients?

PG

PG
Contributor
Posts: 44

## Re: Calculating portfolio weights from regression coefficients

I'm using the following regression:

I=b1*HML+b2*MOM /noint

the I represents here an identity vector, i.e. arbitrage profits, expected return of one and standard deviation of zero. This is Britten-Jones's formulation and I can provide more info if it helps.. HML and MOM are long-short equity portfolios formed with two different styles.. The idea of the model is to directly give me the amount of weight to be invested in these two portfolios.. So if I get a negative coefficient for b2, it means I will be shorting the momentum long-short portfolio.. The idea would be just to get the weights into more meaningful figures like in the case of only positive coefficients, where I can easily tell that I for example have to invest 40% to HML and 60% to MOM portfolios.. Hope it helped a bit, let me know if you need more info! Thanks!!

Super User
Posts: 10,214

## Re: Calculating portfolio weights from regression coefficients

What does you sample data look like?

If the coefficients is negative, that means 'MOM' and 'I' have a different direction . So maybe you should exclude it , not include it.

Weight is only allowed for positive . I still don't know what the negative numbers means.

Ksharp

Contributor
Posts: 44

## Re: Calculating portfolio weights from regression coefficients

I attached a pdf file, which is part of the original paper I took the idea from. The author explains more about the regressions and weights there, maybe there's something I haven't understood? Ksharp, the data is similar to that in the other post I have here, where I want to calculate the correlations..However there are only one values for the four variables, since I've combined the countries data using some pre-specified method.. But the four variables data are just returns in the form 0,01 for example (corresponding to1%), nothing else. I really appreciate your help!!

Contributor
Posts: 44

## Re: Calculating portfolio weights from regression coefficients

Solved the problem!

Super User
Posts: 10,214

## Re: Calculating portfolio weights from regression coefficients

Could post the answer You found ?

Thanks.

Ksharp

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