Compounding is great, but is it always the way to go?

I recently discussed why we multiply our returns (plus one) when we compound. And I've written about the challenge with dealing with fees. But today I want to discuss handling "hurdle rates" in our indexes.

Let's say that your mandate is to beat a particular index by 100 basis points; how do you calculate your index to handle this? Many (and perhaps most) firms will take the monthly equivalent (in this case, 0.083%) and add it to that month's index return, and compound as we do with returns. The problem with this approach is that by the end of the year, those 100 basis points are no longer visible; in reality, the annual benchmark will likely be either higher or lower than this hurdle, because we're compounding the monthly hurdle rate by the monthly returns of the benchmark. Here are a few examples:

As you can see, the higher the annual return of the index, the larger the difference between it and the benchmark (which includes the compounded monthly hurdles); and the lower the return, the lower the hurdle. Does this make any sense? I think not.

If your mandate is to beat the index by 100 bps, then the benchmark should reflect this. Of course, if your contract specifically calls for this approach, then you need to be aware that your target will be unknown until the end of the year.

In my opinion, you should compound the index returns but simply add the monthly hurdle. And since we're not compounding the hurdle, it may make sense to simply divide it by 12, rather than compute the amount that you would need to compound it.

I will be addressing this topic in greater detail in our monthly newsletter, and welcome your thoughts.