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I am looking for more details to perform simple and log returns for an entire portfolio. However, I've only been able to find the following semi-reliable source (see Page 9 and Page 19):

Here are my questions

  1. Are the details for calculating portfolio returns described in the PDF correct? I understand the math but don't trust the source.
  2. Are there better resources that can confirm these calculations?
  3. What do I need to do/alter in the calculation if there is a rebalancing of the portfolio (or a set of assets are removed/added/replaced) in between the start and end dates?
  4. When using portfolio log returns, is there a way to attribute increases/decreases in returns to specific assets within the portfolio (i.e., to say that assets A, B, and C increased by 3%, 4%, and 10%, respectively which resulted in an overall portfolio return of +5%)?
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    $\begingroup$ Hi slaw, welcome to Quant.SE! Why don't you trust the source? Eric Zivot is a respected professor. So, in my opinion, these 3 questions are not really worthwhile but I'll let the community decide whether this should be closed. $\endgroup$ – Bob Jansen Nov 2 '15 at 10:01
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    $\begingroup$ I agree I don't understand why you don't trust the source. I'm also hesitating to close this as a basic finance question, but the topic can be more complicated than expected so having a canonical resource could be interesting. $\endgroup$ – SRKX Nov 2 '15 at 10:11
  • $\begingroup$ @BobJansen: I've searched for "portfolio log returns" and couldn't find any other source that showed similar equations. While I understand that Eric may be a respected professor, people can also make mistakes and it is better to have multiple sources stating/reiterating the same thing than to have a single source. If you can direct me to other sources than that would be helpful. Again, I am looking for portfolio return and not just for a single asset. I couldn't find anything to address question #3 so I thought I'd post here. Is there a different/general subgroup that I should post to instead? $\endgroup$ – slaw Nov 2 '15 at 13:27
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    $\begingroup$ As @SRKX says a canonical resource is interesting and getting more than one reference is always good but this question really should be phrased better. Downvoted for now. $\endgroup$ – Bob Jansen Nov 2 '15 at 17:28
  • $\begingroup$ @slaw You haven't made clear what is wrong with the Zivot notes. If you want other sources, any college corporate finance textbook will have the calculation as well. I found it on investopedia also. For rebalancing, you really just need to spend a momentum thinking about it. Log returns are a little trickier. You need to calculate the portfolio arithmetic return first. If you need portfolio log returns you can convert after. $\endgroup$ – John Nov 3 '15 at 14:51
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Computing returns is one of the first things you learn when you start studying finance but I believe it's one the trickiest one once you get to complicated cases.

The source you mentioned seems actually very good to me and it already takes into account different approaches and different subtleties like dividend payment.

But this is in fact only the top of the iceberg, because there are many things that make computing returns of portfolios complicated. For example:

  • Transaction costs which can happened at trade or portfolio level and which can be expressed as a percentage of flat fees.
  • For funds, having investors buying or selling shares makes it more difficult for you to express your portfolio returns.
  • You have might be very illiquid assets for which there are no bid (nobody wants to by it), what the price then?
  • Many more examples I'm sure more experienced community members could be able to highlight.

For examples on how to compute portfolio returns on some these more advanced cases, I'd suggest you to look at the CFA Institute and their material. To be fair it might even be possible that the best book for this would not actually be finance book but some sort of accounting book.

Finally, note that computing returns is something that somehow depends on interpretation. There are many different ways to compute and present past performance and that has be used many times in the past to make products look better than they really are (or at least, has helped to hide some products' weaknesses). This is why some organization exist now to kind of audit the way performance is reported, such as GIPS.

To answer your questions:

  1. The source seems fine to me, although I didn't read it completely so if you have something specific you're worried about you can enhance your question.
  2. Better I'm not sure. But you can have a look at the CFA curriculum books.
  3. You need to take this into account to make sure your comparison "ending price vs initial prices" is apple-to-apple.
  4. This is performance attribution and it's a whole topic on its own.
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