A Canadian's random thoughts on personal finance

Aug 29, 2008

Log points

Ok, you may all think I'm crazy for this one, but I find the easiest way to get a quick picture of the performance of my investments is through the formula 100×ln(x), a metric I refer to as log points (though its technical name is the rather unfortunate "centinepers"). "Log points" columns crop up in most of my financial spreadsheets.

Why on Earth would I use this formula? It makes the spreadsheet do the hard math, so that whenever I want to compare two numbers, I only need to do simple mental subtraction of relatively small quantities.

Suppose you have an asset worth $36316 one day and $35596 the next day. Quick: what percentage did you lose? Well, you need to subtract them, then divide by an unwieldy 5-digit number. That's ok if you program your spreadsheet to do it, but if you have a large amount of financial numbers and you want to compare them all to get the gist of them, you'll have a lot of pairwise formulas to enter into your spreadsheet. Instead, suppose we convert these two numbers to log points, using the above formula. So what?

Here's the trick: the difference between two log-point amounts equals the percentage difference between the original two dollar amounts. This works whenever the difference is small; anything less than about 10% works just fine. In our example, the first number comes out to 1050, and the second is 1048, so we've lost 2 log points, which indicates that we've lost very nearly 2%.

If we let the spreadsheet compute each number's log-point equivalent, we can pick any pair of dollar quantities and compare the percentage difference just by mental subtraction. This greatly aids visual scanning to find patterns.

Log points have a number of other interesting properties with regards to compounding and amortization that I may describe in a future article if anyone's interested.

(Nobody was interested, but I wrote another article anyway. Part 2 is here.)

No comments: