What’s in a number? If a picture is worth a thousand words can a number be worth an exponential amount of that thousand? Dare I answer with a resounding “yep!”. I’m still going to try to knock this out in 500 words or so…
You open an account with $1,000.
The account promptly doubles in value the first year to $2,000 – a gain of 100%.
Then the account is subsequently cut in half the second year, back to $1,000 – a drop of 50%.
What is the annual return/gain at the end of year 2, as a percentage?
……………..fight amongst yourselves……………..
………….ok… you have the answer yet? ………….
• For those of you who say the annual return is 0% - you are right.
o If you start with $1,000 and it grows to $2,000 before getting cut in half – you are right back at $1,000 where you started.
• For those of you who say the annual return is 25% - you are also right!
o If you start with a 100% return and then have a -50% return – the sum of these is 50% and divided by 2 years you get 25% per year.
How can this be?
Well, arithmetic doesn’t care much for what humans think should or shouldn’t be. Arithmetic just is. And it either answers your question or it doesn’t.
In the above example, the first answer (0%) is based on the Geometric Mean, or Time-Weighted Return formula. The second answer is from the basic Arithmetic Mean. The important thing to note is that neither are wrong – but they answer very different questions.
• The Geometric Mean answers the question “how has the portfolio manager done, regardless of contributions to, and distributions from the portfolio?”
• The Arithmetic Mean answers the questions “what is the next period return likely to be?”, albeit in a rather rudimentary way.
Interestingly – neither of these tell you how your portfolio performed inclusive of contributions and distributions. Meaning – how you are actually doing as it relates toward your goals.
Many investors ask their advisors (our clients ask us too) “what was my return last year?,” and without providing any context around that question these folks expose themselves a response that doesn’t answer the question they asked. It gives the advisor the ability to be selective.
For example, imagine you had the return structure described above and you called to ask your advisor how the account performed, and they said, “the account was up 25% on average over the past couple years”.
1. You asked the wrong question.
2. The advisor didn’t lie, even if they weren’t totally forthcoming.
3. You didn’t get the decision useful information that you really needed to be able to make a decision.
We like to think that we go above and beyond to first understand what our clients are asking before attempting an answer. This is imperative to be able to know how to answer such questions professionally and provide decision-useful information.
1. Is the client trying to determine how their advisor is doing?
a. If so, we use the Time-Weighted Rate of Return calculation to answer the question.
2. Is the client trying to determine how their advisor and portfolio might do, next year?
a. If so, we may use some form of the arithmetic mean.
3. Is the client trying to determine how their portfolio is doing?
a. If so, we use a different measure not yet mentioned – called the Money-Weighted Rate of Return, or IRR calculation to answer the question.
b. More on this in the next blog.
One is not better or worse than another – they simply provide different information – all of which is totally accurate when used in the appropriate context.
At Elevate, we always provide both time-weighted and money-weighted returns. We think it is important for our clients to know both how they are doing and how we are doing. And from there, we have candid discussions about how to proceed together.
Ended up at 656 words… if you don’t count the next blog!
Chief Investment Officer
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