Oct

25

One underappreciated aspect bond investing is that for long term debt, the reinvestment rate of the coupon stream dominates the total return profile. So there is short-rate risk built-in to long term debt portfolios.

Prof. Ross Miller explains:

I cannot emphasize enough how important this comment of George’s is. In teaching fixed income to students (including my intro MBA class), I make a major distinction between instruments with bullet cash flows and those with multiple cash flows (for example, bonds). I point out, though I doubt students grasp it, that all numbers associated with “bonds” are bogus because of the unrealistic implicit assumptions made about the reinvestment of the coupon payments. I highlight this by pointing out the “future value” of a bullet security is obvious (it’s the amount of the bullet payment), but the future value of a bond a maturity is unknowable because what happens to all the coupon payments before the bond matures is outside the model. Finance textbooks gloss over this because it undermines the use of their most sacred of tools, NPV. They do bring up the reinvestment issue with respect to IRR, which they delight in bashing, but usually fail to note adequately that NPV has a similar problem, because this is much too subtle and disturbing a point for most finance professors.

Let me provide the following example:

Consider a 2-year T-note trading at par on issuance date.

Its PV (under assumptions that are often taken for granted) is 100.

The FV of the embedded principal strips in two years is 100.

The FV of the bond is 100 + last coupon payment + future value of the three coupon payments made prior to maturity.

In a world with no uncertainty about future interest rates (of which the permanently flat yield-curve world that is implicit in most textbook models is a special case) these future values can be readily computed by projecting the coupon payment into the future at the fixed interest rate. In a world with a stochastic yield curve, like the one that we live in, the future value is dependent on how one models the stochasticity and, in any case, the typical result is arguably a meaningless number.


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