What kind of nerd am I? 5’8″, blue eyes, insomniac….
I design and price retail financial products (that are not mortgages). I also initiate opportunistic wholesale purchases of bonds to support a portion of those retail sales. I strongly believe most people should not try to time the bond market for profit. Do it for amusement, but not if you expect to profit from it.
The two rules of thumb I gave for comparing levels of uncertainty about future long bond rates are, unfortunately, about as far as one can go without pulling in far more complex mathematical tools. And the rules of thumb are imperfect simplifications. Sorry.
Where does the square root come from? I said that the amount of unecertainty in a future long bond interest rate roughly varies with the square root of the time from now until that future time, if the time is short enough. Rather than pulling in the general theory, I’ll give a plausibility argument using a simple example. I hope it’s not too mysterious or mathematical. (For those familiar with stats, the key fact is that the standard deviation of the sum of N independent, identically distributed random variables is the square root of N times the standard deviation of one of the random variables.)
Here’s the illustrative example. The change in the long bond rate from now (June 16) to July 16 will be the sum of the daily changes on each of the 20 or so trading days from now until then. We don’t know the change next Monday, but we have some idea from experience how likely an increase or decrease of any amount is. A first approximation to the truth is to assume that the same likelihoods apply to Tuesday and all the other trading days. Another approximation to the truth is that the amount of change that occurs on one day has no impact on the amount of change that occurs on subsequent days (which is clearly not completely true, but look at the results before jumping to conclusions).
Next comes the mysterious math (statistics): The amount of variation in something uncertain that is itself the sum of N other uncertain pieces that all look alike, and that do not depend on each other, is equal to the square root of N times the amount of variation in any one of the pieces. (Read standard deviation for amount of variation, if you like stats)
Applying the math to the daily changes in the long bond rate from now until July 16, a first approximation to the truth is that the amount of possible variation in long bond rates from now until July 16 is the square root of 20 (about 4.5 according to my mental math) times the amount of possible variation we now expect to see on Monday.
So if you are considering a possible 10bp change on Monday, a change of 45bp is about as likely over the next month. I hope that sounds like a reasonable result to you, and it comes in spite of all the imperfections we had to paper over along the way.
How likely is a 10bp move either way on Monday? You can learn more about the likelihood of various amounts of daily change by looking at actual historical daily changes over the last year or longer. (If you’re really interested, a good internet source is the H.15 report updated daily by the Fed.)
OK, that’s probably more than enough technicality for you and 99% of the readers here. Hopefully it shed some light, or at least didn’t give you a headache.
