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The Hunt for Duration: Not Waving but Drowning?


Long-term interest rates in Europe fell sharply in 2014 to historically low levels. This development is often attributed to yield-chasing in anticipation of quantitative easing by the European Central Bank. We examine how portfolio adjustments by long-term investors aimed at containing duration mismatches may have acted as an amplification mechanism in this process. Declining long-term interest rates tend to widen the negative duration gap between the assets and liabilities of insurers and pension funds, and any attempted rebalancing by increasing asset duration results in further downward pressure on interest rates. Evidence from the German insurance sector is consistent with such an amplification mechanism.

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  1. Another source of convexity, relevant for steeply rising rates and not discussed in this paper, arises from policyholders' surrender option. As interest rates rise, policyholders may choose to exercise their surrender option, which allows to them terminate their policies at predetermined surrender values. Yet, the declining values of insurers' bond holdings, amid rising rates, could render life insurer assets insufficient to cover the aggregate surrender values of policyholder claims, possibly causing a run. Feodoria and Foerstemann (2015) document that German life insurance companies have become less resilient to such a shock, with the associated critical interest rate level declining from 6.3 to 3.8 percent between 2007 and 2011.

  2. Stevie Smith, Not Waving but Drowning, see

  3. See, for example, Bernanke (2013) on how imperfect substitutability provides a mechanism for quantitative easing policies by the central bank to affect asset prices. See also IMF (2015) for a discussion of the pension fund and insurance sectors' portfolio rebalancing in the context of central bank QE in Japan and the euro area. Chodorow-Reich (2014) finds a positive impact of monetary easing on equity values of life insurers in the US, suggesting that this was due to the positive impact on life insurers' legacy assets which were largely held in MBS. Joyce et al (2014) finds that portfolio rebalancing by UK insurance firms in response to Bank of England's purchases of Gilts was more pronounced for insurance firms less constrained by fixed rate liabilities (eg those with unit-linked products).

  4. These are typically shares in funds owned by insurance firms, set up, in particular, because indirect investments through funds provide greater flexibility for portfolio management and, in some cases, tax advantages.

  5. Market swap rates are used up to about 20-year maturities, or the last liquid point of the interest rate term structure. After this point, discount rates are extrapolated towards the so-called ultimate forward rate, an ultra-long rate based on broad assumptions about long-term growth and inflation (e.g. future real rates), see EIOPA (2015).

  6. Short-term solvency pressures arising from the asymmetric effects of low yields on mark-to-market values of assets and liabilities are distinct from long-term pressures on solvency that may arise if yields stay low for a prolonged time period; for the empirical analysis of the latter, see, for example, Kablau and Weiss (2014).

  7. Indeed, US investors exposed to negative convexity, such as MBS holders, have been largely relying on interest rate swaps rather than US Treasuries for dynamic hedging.

  8. Buying duration through swaps does, however, increase exposure to margin payments throughout the life of the swap contract.

  9. For the use of interest rate swaps by US life insurance firms, see, for example, Berends and others (2013).

  10. In principle, the institution could also increase asset duration through interest rate swaps. Economically, this is equivalent to buying bonds, and the cash market can be expected to react as if bonds were purchased through arbitrage.

  11. When interest rate term structure is variable, an alternative measure is the Fisher–Weil duration, which is a generalisation of the Macaulay duration that computes the present values of the coupon payments using a non-flat term structure. Since we do not have individual bond data or information on their coupon payment structure, such as measure is beyond the scope of this paper.

  12. We take the 25-year zero-coupon swap rate because this is the longest approximate maturity for which the euro swap market is still considered liquid. Above the approximately 20–25-year range, EIOPA extrapolates forward rates using the ultimate forward rate assumptions based on long-term expectations of broad macroeconomic fundamentals, see EIOPA (2015).

  13. While our estimates of the insurance sector liability duration are calibrated to match the 2013 number reported in EIOPA (2014a, b), the Bundesbank (2016) has published an alternative estimate of the mean duration gap of 6.0 (compared to 10.7 published by EIOPA) in the German insurance sector, by taking smaller insures into account and using a different methodology.

  14. See item: Liabilities/Insurance corporations (ICs)/Insurance technical reserves/World/Total economy including non-residents (all sectors)/Outstanding amounts at the end of the period (stocks), available via

  15. We use the index computed by Thomson Reuters DataStream, mnemonic LFINSBD.

  16. Bundesbank (2015) also reports that the rise in the maturity of life insurance companies’ assets has worked to alleviate the duration mismatch, reducing the sector’s vulnerability to long-term capital market risk. At the same time, it has made the insurance companies more sensitive to a sharp rise in interest rates. In addition, falling net return on investment was found to threaten the capital adequacy from one in 83 firms in the mild scenario to up to one in every four firms in the most severe scenario, by 2015.

  17. The results are also robust to running simple OLS regressions on stacked data rather than random-effects panel regressions, and these are shown in Appendix Table 5. The main result for the interaction term also holds when we run fixed- rather than random-effects panel regression, Appendix 6. However, since the Hausman test fails to reject the null that the difference in coefficients between fixed- and random-effects specification is not systematic at the 5 percent level (p value = 0.0820), and moreover, since economically it makes little sense to assign individual intercepts to each cross-sectional unit because this is already done by controlling for duration and sector (sector group) of issuance, we focus on random-effects panel regression results. Replacing duration with bond maturity also yields qualitatively similar results, as one would expect, and these are shown in Appendix Table 7.

  18. We use the Nelson–Siegel four-factor model for German zero-coupon rate curve and a spline method for zero-coupon rate curve derived from euro swap rates.

  19. In the long run, life insurers can reduce, or eliminate, negative duration gaps by adjusting insurance contracts, e.g. through lower contractually guaranteed returns or move away from products with fixed guaranteed rates altogether. Such an adjustment may raise different policy issues.

  20. See BIS (b, c) for the discussion of market positioning and volatility during the bund tantrum.


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Correspondence to Vladyslav Sushko.

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*Dietrich Domanski at the Bank for International Settlements; his email address is: Hyun Song Shin at the Bank for International Settlements; his email address is: Vladyslav Sushko at the Bank for International Settlements; his email address is: The views expressed here are those of the authors, and not necessarily those of the Bank for International Settlements. This paper was prepared for the Sixteenth Jacques Polak Annual Research Conference hosted by the International Monetary Fund. We are grateful to the Deutsche Bundesbank for making available the portfolio information for the German insurance sector and to Stefanie von Martinez for compiling the data used in this study. We also thank Claudio Borio, Anna Maria D’Hulster, Ingo Fender, Anastasia Kartasheva, Aytek Malkhozov, Sergio Schmukler, Suresh Sundaresan, Nikola Tarashev, two anonymous referees, the participants at the BIS Research Seminar, and the BIS insurance workshop for their comments. Participants at the Bank of France conference on Financial Regulation—Stability versus Uniformity: a focus on non-bank actors, Deutsche Bundesbank banking and finance seminar, and Research Institute of Economy, Trade and Industry (RIETI) seminar (Tokyo, Japan), are also thanked for their comments.

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In this appendix, we present supplementary scatter plots contrasting the demand response from end-2013 to end-2014 and contrasting it with the demand responses in the previous 3 years (Figures 13, 14, 15, 16, 17; Tables 6, 7, 8).

Figure 13
figure 13

Demand elasticity, Long-Term Government Bond Holdings of German Insurance Sector; OECD Government Bonds, >10-Year Maturities. percent Change in Prices, dP/P, Proxied Using Market Data Rather Than Yields Imputed from Insurer Portfolio Holdings. Generic Government Bond Yields Obtained from Bloomberg are Matched with Holdings in each Maturity Bucket for German Bunds, Euro Area Government Bonds and Non-euro OECD Government Bonds: GDBR10 Index, GDBR15 Index, GDBR20 Index, GDBR30 Index; GECU10YR Index, GECU15YR Index, GECU20YR Index, GECU30YR Index; USGG10YR Index, USGG2YR Index; GUKG10 Index, GUKG15 Index, GUKG20 Index, GUKG30 Index, US Treasury and UK Gilt Generic Yields are Weighted by 0.8 and 0.2, Respectively, in the Non-euro Area OECD Composite, Except Where US Treasury Yield Benchmark not Available

Figure 14
figure 14

Demand Elasticity, Long-Term Government Bond Holdings of German Insurance Sector; OECD Government Bonds, >10-Year Maturities

Figure 15
figure 15

Demand Elasticity, Long-Term Government Bond Holdings of German Insurance Sector; OECD Government Bonds, <10-Year Maturities

Figure 16
figure 16

Demand Elasticity (Maturity Weighted), Long-Term Government Bond Holdings of German Insurance Sector; OECD Government Bonds, >10-Year Maturities

Figure 17
figure 17

Demand Elasticity (Maturity Weighted), Short- and Medium-Term Government Bond Holdings of German Insurance Sector; OECD Government Bonds, <10-Year Maturities

Table 6 Relationship Between Bond Demand and Bond Price, Conditional on Bond Duration; Stacked OLS Regression Results, Dependent Variable: pct Change in Bond Nominal Value
Table 7 Relationship Between Bond Demand and Bond Price, Conditional on Bond Maturity; Fixed-Effects Panel Regression Results, Dependent Variable: pct Change in Bond Nominal Value
Table 8 Relationship Between Bond Demand and Bond Price, Conditional on Bond Duration; Panel Regression Results, Dependent Variable: pct Change in Bond Nominal Value

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Domanski, D., Shin, H.S. & Sushko, V. The Hunt for Duration: Not Waving but Drowning?. IMF Econ Rev 65, 113–153 (2017).

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