Calculating Simple Portfolio Returns with Rebalancing or Adding/Removing Securities

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:

1. There is a portfolio rebalance
2. A new security is added
3. 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?

• are you calculating the return as IRR? Nov 6 '15 at 14:07
• I'm not familiar with IRR but from what I can gather, no "decision" (accept/reject) is made based on the percent portfolio being calculated. Does that answer your question or would you care to elaborate? There really is no further context behind my question besides calculating the simple portfolio return when given a start and end date. The challenge for me is understanding how to correctly handle things when there are changes in the portfolio during that time period (i.e., rebalancing, adding a security, removing a security, etc)
– slaw
Nov 6 '15 at 14:15
• I'm new to this group. Is this the right place to ask this sort of question?
– slaw
Nov 6 '15 at 14:25
• IRR is the rate of return that makes the NPV of all of the considered cashflows 0 so its simple to calculate the returns with intra-period rebalancing just by calculating the IRR intra-period rather than full period. i.e. change the final cashflow date to the date of sale. Nov 6 '15 at 14:26
• I could make an answer in which I discuss using IRR if you like? Nov 6 '15 at 15:05