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Thursday, October 10, 2013

The World’s Simplest Bond Valuation Model

World's simplest bond valuation model

The chart above shows what I think is the simplest bond valuation model possible (with the added constraint being that the model sort-of works). The low rate environment is taking its toll on the model accuracy recently, but if I attempted to correct for that, it would no longer be the Simplest Bond Model.

The model can be explained in one sentence:
the best prediction for the average Fed Policy rate going forward is the average experienced over recent cycles.

Yes, the model-predicted 10-year yield is the 10-year moving average of the effective Fed Funds rate. The model is implicitly based on the assumption that we are in a stable inflation environment, which I think is a good description of the current situation (see my medium-term inflation outlook). The model does not deal well with regime shifts; it got Volcker-ed from the mid-1970’s to the mid-1980’s.

As my Disclaimer down below notes, this blog does not offer investment advice. This is a very simple model, and I suggest taking it with a big grain of salt. But I want to make the following observations following from this exercise:
  • Realised short rates have been much lower than what the consensus views as neutral for a long time. 
  • This is what I view as a pure bond valuation model, where we attempt to predict the level of yields without using information from long-dated bond yields. You can get a much better fit if you use yields from other maturities, but that turns into the model into a relative value model, which is a very different beast. And if you feed in previous values for the 10-year yield, errors are obviously reduced, since yields move slowly over time (“autocorrelated”). For example, the previous month’s level for the 10-year yield gives a small prediction error, but it offers no guidance whether bonds are over- or under-valued.
  • The real test for a model like this is not statistical tests, but whether it generates profitable trading signals. This has to be done without too extensive data mining. Avoiding data mining is extremely difficult when creating valuation models; analysts need to put a high value on simplicity and robustness.
  • I view this model as a baseline for evaluating other valuation models: does the other model do a better job than this?
  • A more serious model should be forward-based. The level of the 2-year yield (for example) is extremely important component for the path of forward rates. If you disagree with the level of the 2-year by more than 100 basis points, you do not need a model to tell you what to do. So if you assume that the front of the curve is even close to fairly priced, you can get a much better read on where longer maturity yields should be.
  • The model does not take into account the one-way risk facing short rates when they are at zero. With the zero bound hit, that optionality is of increasing importance.

(c) Brian Romanchuk 2013

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