Going negative

In the past I have occasionally written about the oddity that is a negative yield.  At that time, very short-term yields on Swiss government debt were negative.  Since then the negative-yield phenomenon has only spread further — Table 1 shows that the yields on German government bonds were negative all the way out to 30 years.  Your eyes do not deceive you: you pay €101.42 now for a bond repaying €100 in two years, losing €1.42 if you hold the bond to redemption.

Table 1. Yields on German bunds. Source: Bloomberg, accessed on 12th October 2020.

Price Yield
2 101.42 -0.74%
5 103.79 -0.74%
10 105.53 -0.55%
30 103.62 -0.12%

Short-term government-bond yields in the U.K. are only just negative (-0.04% for two-year bonds), but they may be headed the same way as in Germany.  In a recent letter (Woods, 2020) the Prudential Regulation Authority (PRA) in the U.K. asked chief executives to say what the impact of a zero or negative policy rate would be on their business.  While Woods (2020) was at pains to say that there are no plans for negative interest rates, the opening sentence noted that "some central banks have implemented negative interest rates as a monetary policy tool".  At the time of writing the Bank Rate is 0.1%, so zero and negative interest rates are potentially close.

What would negative interest rates (or negative discount rates) mean for annuity portfolios and pension schemes?  In one sense this is not an entirely new phenomenon for actuaries: if pensions escalate at 2.5% (say), then any interest rate below 2.5% implies a negative real discount rate (the Bank Rate in the U.K. hasn't been above 2% since late 2008, although yields on bonds have been higher).  Some older pension types in the U.K. even have escalation rates of up to 8.5%.

It is well-known that annuity capital requirements depend on the discount rate for both mis-estimation risk and trend risk.  Indeed, the precise shape of the yield curve can lead to some unexpected interactions with the shape of capital requirement by age.  What might negative discount rates throw up?  There are many things that might be impacted:

The above list is by no means exhaustive, and this is just for the annuities business.  I suspect that the PRA will receive plenty of feedback to digest!


Woods, S. (2020) Information request: Operational readiness for a zero or negative Bank Rate, Bank of England Prudential Regulation Authority.

Written by: Stephen Richards
Publication Date:
Last Updated:

Negative discount rates

The Longevitas suite of software tools supports four different approaches to discounting:

  1. Constant discount rates,
  2. Yield curves,
  3. Discount factors, and
  4. Stochastic discount scenarios.

All four approaches support negative discount rates.

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