Bonds and Bond Funds

[jk]

Re: Bonds and Bond Funds

Think about it, JK, recalling first semester calculus. The taking of a derivative involves taking differences over an infinitesimal interval. And the operation is only defined on continuous functions. No one (not even me! ;)) actually has continuous data.

The upshot of this is that you have to work with a finite interval. And that means you have to make an arbitrary choice. If your data happen to be (as with the CPI) monthly in frequency, you can in the limit select a month for that choice, but that only means someone else (the BLS) made an arbitrary choice. And for reasons of limiting randomness and noise from your result, you might even choose a longer interval, and perhaps invoke frequency-selective (low pass) filtering. My rate-of-change figures do that, using digital-signal-processing methods.

...

duh me. i forgot we were dealing with real world, sampling errors, measurement methodologies and a few things like that. pure math is so much nicer.

[Jim Nickerson]

Re: Bonds and Bond Funds

I don't recall your having noted the "discrepancy", Jim; sorry I missed it.

Sorry, Finster, I noted it to myself, not publicly.

The "since 1915" is an annual chart meant to give a birds-eye historical view of the level of inflation over nearly a century. The "32 year" is a weekly chart meant to give a much more detailed and accurate close-up of more recent times. Use the annual chart for an overview of how inflation has evolved historically. Use the weekly chart for the most accurate current and recent data.

Keep in mind something I pointed out before - the rate of inflation at any given point in time is not a unique number. It depends over how long an interval you are looking at. The same thing applies to any rate of inflation measure, including the familiar CPI. If you wanted to state the rate of inflation as of the middle of last year, for example, you could start by dividing the CPI as of the end of the year by the CPI as of the beginning of the year. Or you could instead use the CPI figures for June and July. You will get different figures for the rate of inflation. This even though the raw price index data are exactly the same.

Make sense now?

To make things complicateder yet, conventionally the stated rate of inflation is backward-looking - that is, people will state the "current" rate of inflation by comparing the current CPI with that of one year ago. This is commonly done, but misleading - all it really tells you is what CPI inflation has averaged over the past year. To interpret it as a rate of inflation as of some particular date, the best you could infer is that it gives the rate of inflation as of six months ago.

So in order to give a current rate of inflation at all, we actually have to introduce an element of forecasting into the equation. And this is in addition to selecting a time period over which to calculate the change. So in practice the rate of inflation is only finalized once the entire time period has passed. So if you use a one-year time period over which to measure inflation, the last rate that is actually nailed down is the one given for six months ago.

In sum, the rate of inflation charts are inherently "soft" data. If you want only "hard" data, use the raw FDI figures. Then, if desired, you can apply your own time frame preferences to arrive at your own conclusion regarding the rate of inflation.

Finster, I don't know what is happening to my brain, whether it is just tired, or whether it is rather much worn out. All that you wrote does not not suffice to rectify my observation that something seems amiss.

Look at your 32-year chart. It shows inflation at 0323/2001 being right about -10%.

Though one has to "eyeball" 03/23/2001 on the long-term chart, it too suggests that at that time inflation was ~ -10%. At that point the data on both graphs demonstrate the same level of inflation.

Why is this not true for the last data point on each graph?

Look at 2000 on both graphs, both show about 15% inflation.

It seems to me that all data points on the 32-year graph should match the data points for the last 32 years on the longer term graph.

If your explanation suffices to explain everything to yourself, don't fuss with trying to explain it to me again.

Thanks.


P.S. I think something is wrong with the data in the long-term graph near the last data point that shows inflation to be ~1%.

[Finster]

Re: Bonds and Bond Funds

Sorry, Finster, I noted it to myself, not publicly.

Finster, I don't know what is happening to my brain, whether it is just tired, or whether it is rather much worn out. All that you wrote does not not suffice to rectify my observation that something seems amiss.

Look at your 32-year chart. It shows inflation at 0323/2001 being right about -10%.

Though one has to "eyeball" 03/23/2001 on the long-term chart, it too suggests that at that time inflation was ~ -10%. At that point the data on both graphs demonstrate the same level of inflation.

Why is this not true for the last data point on each graph?

Look at 2000 on both graphs, both show about 15% inflation.

It seems to me that all data points on the 32-year graph should match the data points for the last 32 years on the longer term graph.

If your explanation suffices to explain everything to yourself, don't fuss with trying to explain it to me again.

Thanks.

P.S. I think something is wrong with the data in the long-term graph near the last data point that shows inflation to be ~1%.

The details are laid out in full above. But as long as you don’t mind not being totally clear on the details, we can make some simple observations:

1) Since the 32 year plot is more detailed, any difference in very recent values should be resolved in favor of it.

2) For the same reason, do not attempt to eyeball the long term chart too closely.

3) The rate of inflation at any given instant of time does not exist. You must estimate it. You will get different results depending on the method you use to do so.

4) The long term chart and the short term chart use different digital signal processing filters to estimate the current rate of inflation. Because the long term chart is a longer term chart, its filtration algorithm is "slower", i.e. filters out more of the high frequencies. This is somewhat analogous to looking at a long term chart of, say, the Dow Jones Industrials - you wouldn’t use a series of half-hourly samples to plot the entire history since 1896, but if you did, you would get different values for each year if you averaged those values instead of using the monthly closes. Both would be valid long-term representations of the DJIA, but they wouldn’t be exactly the same.

5) Both, the long and short term charts are derived from the same FDI data. This master data is the "hard" data, it doesn’t change. But the rate of inflation is different. You must use at least two different FDI values and compare them, because you’re talking about changes in the FDI. For a given mid-point of those values, you can select the beginning and ending points in an infinite number of ways. You can also (as I do) use more than two points, and, using a digital signal processing algorithm, come up with a rate that represents the current inflation rate in a more sophisticated way than just using two points.

6) If you’re interested in the rate of inflation over any interval and want to be confident of how it’s done, the best approach is to just work from the raw FDI series. If you want to know, for example, what the average rate of inflation was over the past year, divide the year-ago FDI by the current FDI. To do the same over the past half year, divide the half-year-ago FDI by the current FDI and square it. Note that no such method can give you the current rate of inflation. For that, you have to invoke an element of forecasting, and even then, you still have to choose how you are going to extract it from the resultant data.

[Jim Nickerson]

Re: Bonds and Bond Funds

Finster, thanks, and I give you a triple A+ for patience and intelligence, and with that and several bucks you can get a Starbucks of your favorite flavor.

So, the short-term chart is depicting that the rate of inflation is about 5% currently having decreased about 10% from about 09/03. Is that a fair statement?

[Finster]

Re: Bonds and Bond Funds

Finster, thanks, and I give you a triple A+ for patience and intelligence, and with that and several bucks you can get a Starbucks of your favorite flavor.

So, the short-term chart is depicting that the rate of inflation is about 5% currently having decreased about 10% from about 09/03. Is that a fair statement?

Yes it is, Jim. I'd call it 5% and falling.

We could also look at it on a shorter term basis yet and argue it is zero or even negative. That is, we are literally in deflation right now. I am particularly intrigued by the the fact that the FDI is at this moment hovering actually a bit higher than it did at the bottom of that sharp V occuring early last May. (Here) That is the longest stretch since 2002 that we've technically had net deflation.

That illustrates one of the points I was making about teasing an exact rate of inflation out of a price series. That 32-year chart employs some smoothing, and the very recent inflation level according to it also involves some marginal forecasting.

The FDI itself, however, does not. It unequivocally reads net deflation since May 13, 2006.