# How to calculate the ex-ante beta of a portfolio between several rebalancing?

I have a portfolio composed of $$N$$ assets. I know the one-year beta of these assets, I also know the past (ex-post) beta ($$\beta$$) of my portfolio. My portfolio changes allocation every month. So I want to calculate the beta ex-ante at each rebalancing date in order to check if my allocation model chooses to increase the portfolio beta or not compare to the true ex-post beta.

So I have $$N$$ beta 1 year at each rebalancing date and the corresponding weights in my portfolio ($$w_n$$) at each date.

My first approximation is to say that the beta chosen at one rebalancing date $$t$$ is equal to the weighted sum of the 1 year beta at this date.

$$\beta_{p,t} = \sum_{n=1}^{N}w_{n,t}*\beta_{n,t}$$

Is this the right method? I had also imagined to calculate the price series corresponding to the allocation corresponding to the rebalancing on one year (rebalancing every day with the same weights) then calculate the beta of this series in order to say my new allocation corresponds to it beta.

Is there any other method ? What is the most classical method? And realistic/rigorous?

• Ex-ante Beta is usually found by the method you mention: you get the Betas for the individual securities in the current portfolio and you take the weighted average, with the weights equal to the current portfolio weights. Mar 25 at 19:39