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Author: trptrade Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: of 35387  
Subject: Re: Bond Shopping & Yield-Curve Trade-offs Date: 1/24/2010 2:27 PM
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I still struggle with your use of linear data to drive yield curve assertions. Yield curves are not linear, and neither empirical data nor theory should lead anyone to believe they should be.

So here's an alternate analysis:

As a note, and not to suggest you've asserted otherwise, but at least for clarity, I'd note this differs from the CD discussion because non-marketable CDs can return the principal at any time with a penalty of some interest. Bonds (and to the point you made in that thread about their similarity to bonds - marketable CDs) inherently have maturity risk to them that makes one's personal situation potentially more important than the yield.

Now, let's look at a few methods that are non-linear. First would be looking at the forward implied rates. Assuming that these bonds are attempting to be zero real return (a bad assumption, but let's try it for a moment), we get this as the forward rates:

  0  0.00%
1 0.03%
3 0.07%
6 0.24%
12 0.58%
24 1.23%
36 2.67%
60 4.05%
84 5.08%
120 5.00%
240 5.32%
360 4.82%


I will assert (without proof, simply because doing the research to empirically prove this isn't worth the time) that predicting interest rates out in longer periods (say 5+ years) cannot be done better than a random guess. In forecasting, if you can't outperform (measured in accuracy) what is a "random walk" (meaning you assume the future = today), you shouldn't be using the forecasting method.

The reason that assertion is important is that when the forward rate falls, that would indicate (to me anyway) that either (1) there is an assertion that inflation will decrease [violates the assertion in a way that is negative to the purchaser] or (2) there is a lower required real rate of return [violates at least my common sense and basic bond theory]

Therefore, with this test, I would assert the efficient point is somewhere between 60 and 120 months (the treasury data is not granular enough to figure out if the 5.08% is the exact peak in the market, but if these were the only choices, then I might define the efficient point as 84 months)

Another test that can be run, since we're talking treasuries, is to compare with real rates, http://www.ustreas.gov/offices/domestic-finance/debt-managem... I know you aren't a fan of TIPS, but the accuracy of the CPI-U isn't the point, so don't lose the forest for the trees. What it does is it provides a universal basis for carrying on a discussion of a required return above the CPI-U (even if this isn't your personal rate of price increases)

If we use real rates from 01/22/10:
 5 Yr  0.42%
7 Yr 0.84%
10 Yr 1.31%
20 Yr 1.96%


We get the following forward implied CPI-U estimates:
 5 Yr  3.63%
7 Yr 4.24%
10 Yr 3.69%
20 Yr 3.36%


Now I don't know about you, but I think the rise and fall of forward implied CPI-U rates would lead me to a strong conclusion that the 7 year would be deemed more "efficient" than the 10 or 20 year, because the forecasting risk associated with the 10 year is compounded by both a lower forecast, and a longer time period for inaccuracy.

Tom
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