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No. of Recommendations: 3
By now, you should have seen the news that the SSI COLA for 2012 will be in the neighborhood of 3.5%. If nothing else, that should be a reminder to you that price-increases are a fact of life and that today’s dollars won’t buy as many goods and services next year. Obviously, the same is true of bond yields. A projected, nominal YTM of 5% (or whatever) doesn’t offer a spendable YTM of 5% over the holding-period of the bond, because the purchasing-power the coupons decreases as time passes, as does the purchasing-power of the principal that is eventually returned. Worse, the longer the holding-period, the greater the damage suffered, as will be argued in the following post.

For purposes of this exercise, the issuer doesn’t matter. But prices and broker-calculated YTM’s were accurate as of noon today for these six maturities.

Holding-Period Broker's YTM
1.7 4.70%
5.1 6.83%
6.1 7.20%
6.7 7.41%
9.7 7.71%
26.1 8.62%

Even though the longest-dated bond offers the greatest nominal-yield, I would argue that isn’t the sweet spot on the issuer’s yield-curve. Instead, I’d argue that one of the mid-maturity bonds should be preferred, because one’s holding-period (and, therefore, one’s exposure) has to be massively extended in order to pick up modest gains in basis points. In other word, one of the mid-maturity bonds is a reasonable compromise between the mostest yield and the soonest yield. To see how this might be so, use the holding-period and the YTM for the nearest bond as a benchmark and state the holding-periods and YTMs of the other bonds in terms of it.
Holding-Period Broker's_YTM HP_Index YTM_Index Efficiency (Relative_YTM/Relative_HP)
1.7 4.70% 1.0 1.00 100.00%
5.1 6.83% 3.1 1.45 46.85%
6.1 7.20% 3.7 1.53 41.33%
6.7 7.41% 4.0 1.58 39.11%
9.7 7.71% 5.8 1.64 28.02%
26.1 8.62% 15.8 1.83 11.58%

By my eye, the 4th bond and its 7.41% YTM is the sweet spot. The would-be investor is getting about as much yield as can be obtained without undue exposure. Whether that would be the bond I’d buy would depend on a lot of other factors. But that’s would be where I’d begin digging into the company’s financials, asking this question: “How likely will it be that they can fulfill their promises to the holders of that maturity?”

Now, let’s switch over to considering the impact of inflation. On the basis of next year’s SSI COLA adjustment of 3.5%, one could make the guess that inflation will run about the same. That probably isn’t most people’s experience of inflation in their own daily lives, but it would be a place to begin, and to make the math a bit easier, let’s round that number up to 4%.

Holding_Period Broker's YTM Subtracting_4% Discounting_by_4%
1.7 4.70% 0.70% -0.11%
5.1 6.83% 2.83% 2.03%
6.1 7.20% 3.20% 2.41%
6.7 7.41% 3.41% 2.64%
9.7 7.71% 3.71% 2.95%
26.1 8.62% 4.62% 3.37%

Again, as above, Columns One and Two are the same. If you do a scan using any broker’s bond-search engine and dump the results into a spreadsheet, you can subtract the Settlement Date from the Maturity Date to get the Holding-Period expressed in years, as well as pull the projected YTM directly from the data. If your method of estimating the impact of inflation on bond-yields is based on subtracting the Inflation-rate from the nominal YTM, then you’ll get Column Three. But if your method of estimating the impact of inflation on bond yields is a discounting method, then you’ll end up with something that looks like Column Four. In any case, the relative rankings seen in Columns Two, Three, and Four remain the same: the longer the holding-period, the greater the expected yield. So the investing decision is simply a linear, risk-reward trade-off. Now do this. Bump the inflation-rate to 5% and repeat the exercise. Your expectation should be that order of rankings will be preserved. But a surprise awaits you. Now the longest-dated bond becomes disadvantaged by the impact of inflation.

Holding_Period Broker's YTM Subtracting_5% Discounting_by_5%
1.7 4.70% -0.30% -0.16%
5.1 6.83% 1.83% 1.87%
6.1 7.20% 2.20% 2.21%
6.7 7.41% 2.41% 2.40%
9.7 7.71% 2.71% 2.60%
26.1 8.62% 3.62% 2.54% <<==

What’s going on? Clearly, the repayment of principal is a one-time event. The further away it is, the smaller will be the value of money returned (unless, of course, deflation has prevailed instead of inflation). Just as clearly, the income-stream created by the payment of coupons is more complex. But it can be modeled in a spreadsheet, and discounting factors can be derived for any inflation-rate. That’s why --for me-- the rankings in the fourth column change as I work with different inflation-rates and why, in this instance, the longest-dated bond is not attractive to me on an adjusted-yield basis, never mind the other things that also must be considered.


PS And, "Yes", I'm very aware of the fact that yield-curves typically cannot be described with linear equations (which calls into question use of my "Efficiency Measure"). I've poked around a bit with N-order polynominals, looking for patterns. But I haven't yet come up with anything worth reporting.
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