Interpreting Regression Coefficients as Stock Hedge Ratios
Summary
The document asks how coefficients from a regression of one stock’s price on two other stock prices can be translated into share quantities for a spread. The example fits a linear model without an intercept, using stock A as the target and stocks B and C as predictors. The response explains that the coefficients describe the quantities of B and C in the fitted linear combination used to estimate A’s price. A negative coefficient corresponds to a short position in that predictor within the fitted combination.
These coefficients are not automatically portfolio weights or a ready-made trading position. Their interpretation depends on the regression target, units, and model specification; regressing raw price levels may produce a relationship that is not stable or useful for trading. The response recommends considering log returns instead of absolute prices. The small illustrative sample does not demonstrate predictive power, cointegration, hedge effectiveness, or profitability, and the original question itself acknowledges the need for further stability checks.
Key ideas
- Regression coefficients specify predictor quantities in the fitted estimate of the target price.
- A negative coefficient implies a short exposure to that predictor in the linear combination.
- Price-regression coefficients are not automatically normalized portfolio weights.
- Raw price relationships may be unstable, so the suggested alternative is to examine log returns.
- The example does not establish a reliable or profitable spread.
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Full text
# How to calculate the weight of the stocks using the linear regression?
# How to calculate the weight of the stocks using the linear regression?
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 by Matt Wolf (score 1, accepted)
https://quant.stackexchange.com/a/3532
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.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.