Quick Proxies for Long-Term Bond Term Premia

Summary

The document asks how to roughly estimate term premia at the long end of a bond curve, including for a market such as Brazil. It presents two approaches: regress the ACM ten-year term premium on several US yields, or use differences between distant forward short rates as a proxy. The regression is reported to fit the US ACM series closely, while the forward-rate idea rests on the view that far-ahead rate expectations may contribute less to the curve's slope.

The main caveat is transferability. Applying coefficients estimated from US rate dynamics to another country may produce a poor estimate if that market behaves differently. The forward-rate proxy is also only an approximation, since the curve's slope can reflect both term compensation and expectations. The note gives no local calibration, validation, or method for separating those components, so it offers exploratory heuristics rather than a robust estimate for a specific market.

Key ideas

• A linear regression on selected US yields is presented as a proxy for the ACM ten-year term premium.
• The reported fit is strong for the US data used in that regression.
• Applying US coefficients to another country's curve may perform poorly when rate dynamics differ.
• The slope between distant forward short rates is suggested as another rough term-premium proxy.
• Both approaches are approximate and require market-specific validation.

Tags

# How to roughly estimate long term term premia?


# How to roughly estimate long term term premia?












Is there a way to crudely estimate term premia in long term bonds? I understand there is a well developed and widely available model from the NY Fed (ACM Model) but I'm wondering if there is a 'quick and dirty' method which can be applied to any curve, as I am trying to estimate the term premium in the long end of the Brazilian curve (e.g. 10y - 3m rates?)

## Answer by Helin (score 2)

https://quant.stackexchange.com/a/35655

The ACM term premium can be replicated very well with a simple linear regression:

$$\text{10-Year ACM TP} = -1.84 - 0.0579\times\text{3M Rate} - 0.6922\times\text{2Y Yield} - 0.4329\times\text{5Y Yield} + 1.6159\times\text{10Y Yield}. $$

Adjusted $R^2$ of this regression is 0.96. You can perhaps apply these coefficients to Brazilian rates to get some crude estimate. How well will it work? Probably not very well, unless the Brazilian interest rate dynamics happen to be the same as the US, which seems highly unlikely.

Other easy ways to measure term premium is to look at forwards. For example, the difference between 7y forward 3m rate and 10 year forward 3m rate can be used as a proxy (that far out into the future, people are unlikely to have strong views about rate direction, so the slope of the curve mostly likely can be attributed to term premium, rather than changing rate expectations).

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.