## Are Rates Low?

Above all else, the mark-to-market value of long-term liabilities is determined by long-term interest rates. The relentless fall in interest rates over the last few years has hit pension funds hard. However, many argue that such valuations are misleading because interest rates are artificially low, and will rise back up soon.

To say interest rates are low, compared to history, seems eminently fair. Using data on US 10yr rates from Professor Robert Shiller, current rates are just above the 10th percentile; so for nearly 90% of the last 144 years US 10y rates were higher than they are today. But are they artificially low or is this just the new normal? With low earnings growth and a global shift in policy, low short-term rates - and therefore low long-term rates - may be here to stay^{1}. We might not be able to resolve the qualitative argument at all. One thing we can do though is to look for quantitative evidence as to whether we should expect rates to go up again anytime soon.

## Do Interest Rates Mean Revert?

A glance at figure 1 suggests if anything that rates move in broad, long-term eras, rather than reverting quickly; indeed, the obvious take-away message from the last 2 decades has been that rates can just keep going down. But it is worth a deeper look.

*Figure 1 – Long-Term history of US 10y Rates; Source data: Professor Shiller (http://www.econ.yale.edu/~shiller)*

## What would Mean-Reversion Mean?

Previously I blogged about mean-reversion in equities^{2}, and showed some of the problems that arise when you try to define precisely what mean-reversion might mean. Using a consistent approach, we look at how the volatility changes over longer time periods. The idea is that, if there is any “pull to parity”, then long-term changes should be proportionately more stable than shorter-term changes^{3}.

As we did for equities, we took the average volatility over a number of “runs”; that is, for ten year periods, we defined run 1 as the changes over the periods 1870-1880, 1880-1890..., and run 2 as changes over 1871-1881, 1881-1891... etc. We then took the average volatility over all the “runs” for each time period. We did this to make as much use of the data as possible while limiting the bias that comes from re-using data^{4}.

## The Evidence

Initially, it seems as though there might be some mean reversion. The annualized volatilities^{5} for longer tenors are lower than for annual rates, albeit marginally- see figure 2

*Figure 2 – How annualized interest rate volatility changes when measuring over different length intervals; Source data: Professor Shiller; Calculations: Redington*

Years | Average Vol |
---|---|

1 | 0.74% |

2 | 0.69% |

3 | 0.64% |

4 | 0.65% |

5 | 0.66% |

6 | 0.66% |

7 | 0.66% |

8 | 0.68% |

9 | 0.66% |

10 | 0.66% |

However we need to be careful, not least because the differences are fairly small. There also seems to be no further reduction after 2 years, whereas we should expect some reduction if there were a consistent “pull to parity” in interest rates. On closer inspection, the whole effect vanishes if we strip out just 2 data points, 1986 and 1994 - see figure 3.

*Figure 3– How annualized interest rate volatility changes when measuring over different length intervals, with two data points changed. Source data: Professor Shiller; Calculations: Redington*

Years | Average Vol |
---|---|

1 | 0.66% |

2 | 0.63% |

3 | 0.61% |

4 | 0.62% |

5 | 0.64% |

6 | 0.665% |

7 | 0.66% |

8 | 0.67% |

9 | 0.67% |

10 | 0.68% |

Now there is nothing wrong with these data points, and we can’t just ignore them. What we can say, though, is that the evidence for mean-reversion in interest rates over the last 144 years ultimately comes down to 2 data points. 144 years seems like a lot of data; but if we conclude from figure 2 that interest rates mean revert, we are effectively basing our conclusion on just two events, 8 years apart. Interest rates might mean-revert but the evidence is weak, and if they do the effect is small.

## Conclusions

Interest rates are lower than they have been for most of the last 144 years, but there is scant evidence for any significant mean-reversion. That means that whether interest rates are high or low doesn’t tell you much about where they’ll be over the next few years. On the other hand, interest rates can keep moving in the same direction for several decades, and they’ve done so several times in the past. All in all, relying on rates to rise is a significant gamble, and should be sized accordingly.

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^{1 }As they have done in Japan And concluded that it probably didn’t exist [read blog]

^{2}In ten years, more can change than in one year, so we annualize the volatilities of t-year moves by dividing by √t.

^{3}If there is no “pull to parity”, then the annualized volatilities should be very similar across different values of t; if there is, longer-term volatilities should be lower

^{4}If we compared, say, changes in rates from 1870-1880 with those from 1871-1881, then we should not be surprised if they were similar

^{5}Gaussian volatilities- i.e. the changes in rates are just calculated by subtraction

*Please note that all opinions expressed in this blog are the author’s own and do not constitute financial legal or investment advice. Click here for full disclaimer*