Given a set of portfolio weights, w, and historical security prices, I am looking to calculate a simple portfolio return via:
where R is the simple return for a given security from time t to t+1:
This is pretty straight forward. However, I can't seem to wrap my head around how the portfolio return calculation changes if:
- There is a portfolio rebalance
- A new security is added
- An existing security is removed
For example, if my portfolio only contains two securities, A and B:
And, so, the simple portfolio return is:
What happens now if I want to rebalance the portfolio? How would that alter the return calculation or how would my portfolio return be different? Does "time" matter? Say, the portfolio from time t to t+1 was one year but the portfolio was then balanced for only one day. Then, the return period that I am interested would be for time t to (t+1+one day).
Similarly, instead of rebalancing, what if I wanted to add a new security C at time t+1 and the calculate the return from time t to (t+1+one day). In other words, security C did not exist in the portfolio from time t to t+1. How do I get the portfolio return now?
What if I want to remove security A at some later time t+2?