How to run an asset replication regression?

Question

I am doing extensive research on portfolio replication and was hoping to get some help with some problems I am encountering.

I am running a regression between 2 assets that I believe replicate another asset well. For example, let A be the asset we are replicating and let B and C be the assets we will use to mimic A. I want to run a regression on the returns.

How would I run a regression such that I can include the returns on dividends paid on each of these assets. Would I just add in the amount of the dividend paid to the stock price on the day the dividend is paid? Would I then calculate a return based on those numbers?

Also, how would I use the regression output to find annualized volatility and return on asset A? What about assets B and C?

Finally, what would be the difference between the standard error of each of my variables (B and C) vs. the standard error of the model as a whole?

Answer 1

Regarding the dividends:

In order to avoid jumps on ex-dividend date, you can make the simplifying assumption that dividends are paid continuously and adjust the returns of the assets. The size of dividends could be estimated from historical data or can be set proportionally to the asset price.