## Thursday, October 27, 2011

### How to make your returns look better

We've discovered a way to enhance performance, at least in the short term: if you have a portfolio begin late in the month, to make the monthly return look better, treat the return as if it was for the full month!

What do we mean by this? Well, consider the Modified Dietz formula for a second:

Let's say that we begin with zero invested, so our beginning value is zero. We have a cash flow of \$100 occur on the 28th of a 30 day month. We end with \$105. It is evident from the numbers that we have a 5% return, yes? But let's see what happens with Modified Dietz, if we calculate the weight for the 30 day period:

Now, let us plug this value into our formula:

Instead of the 5% we know we earned, we will see a 50% return! Quite impressive, yes? And so, what happened?

The problem is, as you hopefully can see, that we are trying to measure a monthly return for an asset that was held for just three days.  The culprit is our weighting formula. Instead of our "CD" (number of calendar days) be three, which we know it is, we're using 30. And therefore, instead of the flow being present for the full time (of three days of a three day period), it is shown as being present but for a mere three days of a thirty day period, or 10% of the time. This causes our denominator to be smaller than it should be, resulting in a return that is much higher than it really is.

Does this mean that Modified Dietz cannot be used in cases like this? Well, no, it can be; you just have to get your weight right.

Now, when we use this weight in our formula, our return is:

Unfortunately, I've seen too many systems that do not test to see the true period an asset is held, and allow distorted returns to be reported. There is no legitimate explanation for allowing this to occur: the return is wrong. You cannot report a one month return for an asset that is held for less than a month; nor can you report a one-year return for an asset held less than a year. We designed a system for a client a few years ago, and made sure it was sensitive to cases like this, to avoid reporting misleading information. If you see very large returns, they may be attributable to this problem, not truly great performance.

Of course, if you have a bad three days, your negative return will be exploded, too, so this practice serves no valid purpose, and should be abandoned.