# Is it correct to define hedge ratio of a mean-reverting portfolio based on the cointegration parameter?

Suppose we have yields time series of 2 bonds, and estimate the following cointegrating relationship:

$$Y_{A} = \alpha + \beta Y_{B} + \epsilon,$$

where where $$Y_{A}$$ and $$Y_{B}$$ are the yields of bonds A and B respectively, $$\alpha$$ is a constant, $$\beta$$ is the coefficient that indicates the long-term relationship (often interpreted as the hedge ratio), and $$\epsilon$$ is the error term.

The $$\beta$$ coefficient represents the relationship between the yields of bonds A and B in the long term. In a classical mean-reversion strategy settings, one typically take positions based on deviations from this long-term relationship. The $$\beta$$ coefficient helps determine the ratio or proportion in which you should take long/short positions. Specifically, for each unit of bond B that you short, you would take $$\beta$$ units of bond A long (because $$\beta$$ represents the number of units of bond A per unit of bond B in the cointegrated relationship); and vice versa.

Question: Is this approach equivalent to constructing mean-reverting portfolio by making positions DV01-neutral? If no, which approach is more robust?

P.S. In my understanding, cointegration coefficient might be misleading when we construct a mean-reverting portfolio. This could happen when the relationship between $$Y_A$$ amd $$Y_B$$ is non-linear, and we model it though linear relationship described above. However, when we use DV01s, which can better approximate non-linear relationship between bonds' yields and the curve, might imply that DV01-netural portfolio might be more accurate. I hope my reasoning is correct, is it?