How to calculate the weight of the stocks using the linear regression?

Question

I do a simple example with the follow three series(stocks prices):

a = 1, 1.2, 1.8, 1.3, 0.9, 2
b = 56, 58, 63, 61.5, 57.6, 58
c = 105.6, 110, 106.9, 103, 101.2, 107

ok, so let assume those series are the prices of the three stocks, named A, B and C.

Now, I do the linear regression doing:

mod = lm(a ~ b + c + 0)

the result of the linear model is:

Call:
lm(formula = a ~ b + c + 0)

Coefficients:
        b          c  
 0.030570  -0.004095  

> mod$residuals
         1          2          3          4          5          6 
-0.2795238 -0.1226474  0.3118110 -0.1583030 -0.4464512  0.6650691 

Now we know the coefficients of b and c and here I have a doubt regarding, how can I understand reading these coefficients the weight of the stocks I need to buy.

With the weight I mean, example:

A: 10 stocks
B: 2 stocks
C: 16 stocks

I would like to create this spread and calculate the correct number of stocks.

IMPORTANT: This is only an example, I know that I need more tests to check the stability etc etc but with this example I only would like to understand:

How can I calculate the number of the stocks reading the linear regression coefficients?

Thank you!

Answer 1

If I understand correctly then you measure something that you actually do not look out for. Your regression tries to explain prices of stock A by using a linear combination of stocks B and C. The coefficients tell you the fraction of stocks you need to have in stocks B and C in order to arrive at the predicted price of stock A. Thus, 0.031 shares of stock B plus 0.0041 shares SHORT of stock C will output the predicted price of stock A. I doubt that is what you want UNLESS you are convinced that prices of stock B and C OVER TIME are a good predictor for prices in stock A. Generally I advise, however, you work with log returns and not absolute stock prices. Hope this helps.