Doc wrote:#Cruncher, can you give us your view of "real duration" and "effective duration".

"Real" and "effective" refer to two different dimensions. Real duration can be either "modified" or "effective" and likewise "nominal" can be either "modified" or "effective".

Code: Select all

```
Real Nominal
--- -------
ME x Modified
x PIMCO Effective
```

Effective duration differs from modified only when the bond has an option like a call option.

Investopedia definition of effective duration:

A duration calculation for bonds with embedded options. Effective duration takes into account that expected cash flows will fluctuate as interest rates change.

Since TIPS have no embedded options, effective duration is the same as modified duration.

So actually both my figure and PIMCO's are modified duration or the indicator of change in price due to a 1% point change in interest rates. They differ in that mine shows the price change per 1% point change in

*real* interest rates. Unfortunately PIMCO gives no definition on its web page. But I assume it is meant to show the price change per 1% point change in

*nominal* interest rates. For example, if the yield on nominal treasuries of comparable maturity rose 1% point PIMCO estimates that the price of its TIPS fund would fall 2.20%.

In my view "nominal duration" is a useless concept when applied to TIPS. It assumes a fairly constant relationship between nominal and real interest rates. Something like:

*If nominal interest rates rise 1% point, then real interest rates will rise 0.7%.* But there is no such stable relationship. In fact it's quite possible for them to move in opposite directions. This happened about six weeks ago when 10-year nominal Treasury rates jumped 0.2% points or so in a week. But at the same time the real rates on 10-year TIPS actually fell. Thus the price of TIPS rose at the same time that those of nominal Treasuries fell. No positive value of duration could express this relation. (See my post,

Re: TIPS fund duration question.)

Regarding PIMCO's "Estimated yield to maturity" of 0.55% and SEC yield of 3.96%: Again PIMCO gives no explanation of either on its web page. But my guess is they reflect CPI change over two different time periods. The YTM seems to reflect an inflation rate of about 1.9%. (0.55% = 1.9% - 1.33%). (1) This is about what the

*annual* change in the CPI has been running the past couple of months. (See 1 Yr change column in

CPI-U since 1961 with annual change for September.)

The SEC yield seems to reflect an inflation rate of about 5.5% (4.16% = 5.5% - 1.33%). (1) (2) It looks like PIMCO is annualizing the latest

*monthly* change in the CPI used for adjusting TIPS' principal (September vs August before seasonal adjustment). 5.5% = (231.407 / 230.379) ^ 12 - 1. If indeed that's what PIMCO is doing, it's improper in my opinion to be extrapolating a one-month change -- especially one that's not seasonally adjusted -- into an annual rate.

1) Negative 1.33% is the real yield I show for the 1 - 5 year index -- see original post.

2) 4.16% is the 3.96% SEC Yield plus the fund's 0.20% expense ratio.