Asset–Liability Management of Life Insurers in the Negative Interest Rate Environment

Abstract

This study investigates the asset–liability management (ALM) of life insurers in markets with negative interest rates. Using a sample of Japanese life insurers between 2000 and 2020, we provide initial evidence that the negative interest rate environment produces a much more serious consequence on insurers than the positive interest rate environment. Given that duration and convexity are two common measures widely used by insurers to manage their assets and liabilities, we highlight that the assumption of a flat yield curve underlying the traditional measures (e.g., the Macaulay and modified durations and convexities) is problematic when interest rates turn negative. To address this issue, we propose an ALM framework using the duration and convexity based on the Vasicek stochastic model. Results show that the strategy based on the Vasicek model outperforms the strategy using the modified duration and convexity in the negative interest rate environment.

ACKNOWLEDGEMENTS

We are grateful to the Co-Editor Patrick Brockett and the two anonymous referees for their constructive comments.

Disclosure Statement

No potential conflict of interest was reported by the author(s).

Notes

1 In addition to the studies examining the relation between a change in interest rates and a life insurer’s performance, some research focuses on other perspectives and impacts of interest rates. For example, Killins and Chen (2022) used the change in yield spreads (instead of yield level) to demonstrate the negative effect of a rising yield curve on insurers. Liu, Chang, and Shiu (2020) examined joint determination of interest rate exposures and the usage of interest rate derivatives for hedging and found a positive relation between them. Möhlmann (2021) showed that life insurers assume interest rate risk by adopting alternative investment strategies such as asset insulation rather than pursue a strict duration-matching strategy.

2 Some extensions have been proposed to rectify some of these issues. For example, the generalized duration and convexity developed by Fisher and Weil (1971) take into account the term structure of interest rates. The partial duration and the key rate duration proposed by Reitano (1991) and Ho (1992) provide a remedy for non-parallel yield curve shifts. Although these extensions improve the classical immunization model, all of them implicitly assume positive interest rates.

3 The Financial Services Agency in Japan (https://www.fsa.go.jp) publishes the list of Japanese life insurance companies every year and we followed their list to identify life insurers in Japan and include them in our sample. If multiple life insurers were under common ownership, we aggregated them at the group level. According to Japan’s Insurance Business Act, life insurers in Japan sell insurance related to a person’s life and death (e.g., term life insurance, whole life insurance, and annuity insurance). Some also sell accident and sickness insurance (Naito 2002; T&D Holdings 2018). Life insurance and annuity businesses account for more than 50% of all premiums written by all life insurers except four life insurers in some years in our sample. As a robustness check, we excluded these four life insurers from our sample and reran all regressions. Our inferences remained unchanged.

4 To obtain unbiased estimates in finite samples, the clustered standard error is adjusted by $(N-1)/(N-P)\times G/(G-1),$ where N is the sample size, P is the number of independent variables, and G is the number of clusters.

5 The Trading Economics Application Programming Interface (https://tradingeconomics.com/api) shows that Japanese government bonds have low default risk and were rated A + or better by Standard & Poor’s during our sample period from 2000 to 2020. The corporate bonds invested by Japanese life insurers are also investment grade with low default risk. For example, 93% of Dai-ichi Life Holdings’ fixed income investments were rated BBB or above in 2019 (Dai-ichi Life Holdings 2020).

6 Browne, Carson, and Hoyt (2001), Brewer et al. (2007), Berends et al. (2013), and Hartley, Paulson, and Rosen (2016) suggested using long-term interest rates to measure insurers’ sensitivities to interest rate changes. In our study, we relied on 7-year Japanese government bond rates, which were the longest-term rates with negative rates for at least 2 years during our sample period, to examine the impacts of interest rates, especially negative interest rates, on Japanese life insurers’ performance.

7 As a robustness check, we replaced 7-year $\mathit{\text{YT}}{M}_t$ with 2-, 3-, and 5-year $\mathit{\text{YT}}{M}_t$ and re-estimated all regression specifications. Our inferences remained unchanged, which strongly supports Hypotheses 1 and 2.

8 Another commonly used performance measure in the literature is stock return. However, public firms only account for a small percentage of all Japanese life insurers. Among 29 groups of Japanese life insurers under common ownership and unaffiliated single life insurers in our sample, only 4 are public life insurers. They are T & D Holdings, Dai-ichi Life Holdings, Japan Post Insurance Company, and Lifenet Insurance Company. As a robustness check, we conducted an additional analysis on the basis of these 4 public life insurers. We replaced the 4 public insurers’ annual ROAs with their daily stock returns ${\mathit{\text{Stockreturn}}}_{t,d}$ as the dependent variable. We also replaced the annual observations of YTM and Nikkei 225 return with ${\mathit{\text{YTM}}}_{t,d}$ of the 7-year Japanese government bond and the Nikkei 225 return, $\mathit{\text{Nikkei}}225r\mathit{\text{etur}}{n}_{t,d},$ in day d of year t as the independent variables and then reran all regressions. Our inferences from the results based on this setting remained unchanged.

9 Several Japanese life insurers have become insolvent since the 1990s as an effect of low interest rates. Surviving firms might be more experienced or more strongly regulated in dealing with low interest rates. In this sense, our empirical results may be subject to survival bias. Indeed, our sample includes firms that have survived since the 1990s, firms founded after 2000, and firms exiting the market. Specifically, 12 affiliated or unaffiliated Japanese life insurers were founded after 2000 and one exited the market before 2020 in our sample. Thus, survival bias may not be an issue. Moreover, if we only include surviving firms in our regressions, our estimates will be biased toward zero (i.e., experienced life insurers are not sensitive to interest rate changes). Yet, we still have the significant coefficients that support our hypotheses, which suggests that our results are strong.

10 The question of whether negative interest rates would persist has prompted considerable discussions. In fact, the debate regarding negative interest rates can be traced back to the 19th century (Ilgmann and Menner 2011). It is largely an economic policy debate. For example, Brandao-Marques et al. (2021) argued that NIRP would likely be temporary, whereas the European Parliament (2021) and Altavilla et al. (2022) discussed the effect of prolonged negative interest rates. In a normal economic environment, the real interest rate is positive and so is the nominal interest rate. Although some economic models advocate the use of negative interest rates to stimulate economic growth, those models are not mainstream and largely ignored in economics. In this article, we leave the question of whether interest rates should be low or high to the monetary policy research, which is a hot topic in economics today. Instead, on the basis of the assumption that interest rates will return to the long-term mean (i.e., positive interest rates in the long run), we focus on the effect of negative interest rates and point out that the Macaulay duration exaggerates the interest rate sensitivity when the interest rate is zero or negative.

11 We do not use other stock index durations in the literature (e.g., Leibowitz 1986; Nawalkha 1996) owing to their limitations. For example, Leibowitz (1986) proposed calculating the stock index duration as a function of the bond index duration, the standard deviations of the stock index and bond index returns, and the correlation of returns between stock and bond indices. To obtain a reasonable stock index duration, a positive relationship should exist between the returns of stock and bond indices. However, such a relationship can be positive or negative because the correlation of returns of stock and bond indices reflects more than interest rate risk. This approach also relies on the parallel shift of yield assumption. Finally, Leibowitz’s (1986) stock index duration fails to capture the sensitivity of dividend growth and stock risk premium to a change in interest rates. Similarly, the stock duration proposed by Nawalkha (1996) is subject to the same limitations. Therefore, we do not adopt their approaches.

12 Note that there are many other possible choices of stochastic mortality models including Cairns, Blake, and Dowd (2006). See Janssen (2018) for a comprehensive review of mortality models and their variants. In this article, we adopt the Lee-Carter model simply because it has been widely applied in the mortality modeling literature and often used as the benchmark for various studies.

13 To show the robustness of our approach, we conduct an additional analysis to show how excess deaths caused by a pandemic affect our results. To capture pandemic risk, we use the stochastic mortality model with a temporary adverse mortality jump process proposed by Cox, Lin, and Pedersen (2010) to account for excess deaths caused by a pandemic (e.g., COVID-19). Then we solve the ALM optimization problem (54) in Section 5.2 with the new mortality rates. The results are qualitatively similar to those without mortality jumps. The details are available upon request.

14 In practice, life insurers invest a very small portion of their assets in common stocks but invest a notable portion of their funds in securities with volatility similar to (or higher than) common stocks. These high-risk exposures account for around 30% of life insurers’ total invested assets. Notably, non-agency mortgage-backed securities (MBS) and mortgage loans comprise around 20% of all assets invested by U.S. life insurers (McMenamin 2013). Similar to non-agency MBS and mortgage loans, the S&P 500 Index has a long duration and high volatility. Because we do not have specific information on the maturities of different risky asset classes held by life insurers, we use the S&P 500 Index as a proxy for U.S. life insurers’ risky investments.

15 $r_0$ is the risk-free rate at $t=0$ and it can be proxied by the 3-month Treasury bill. Thus, we use the yield of 3-month Treasury bills on August 31, 2020, obtained from the Eikon Datastream database as the initial interest rate $r_0=0.0011$ for our simulation. Our inferences remain unchanged when we use a Treasury bill with a different duration and/or on a different date.

16 Life insurers in the United States primarily hold high-quality corporate debt. In recent years, they have been increasing the holdings of investment-grade bonds and decreasing the weights in lower rating bonds. According to Standard & Poor’s Financial Services LLC, 59% of the U.S. life insurers’ bond portfolios were in the “A–AAA” quality category and 35% in the “BBB” category in 2020 (Maheshwari et al. 2020). Thus, in the numerical illustration, we use the ICE BofA 1-5 Year AAA U.S. Corporate Bond Index as the proxy for corporate bonds whose credit spreads are generally small. Based on the data of the ICE BofA AAA US Corporate Index of all maturities effective yield and the market yield on U.S. Treasury securities at 10-year constant maturity from St. Louis Fed (https://fred.stlouisfed.org), we calculate the average credit spread of the ICE BofA AAA U.S. Corporate Bond Index. The average credit spread of this corporate bond index is only about 0.5% from January 2006 to August 2020 (i.e., the same sample period as that of the ICE BofA 1-5 Year AAA U.S. Corporate Bond Index in our numerical example), suggesting that the effect of credit risk on our results will be small. Thus, we expect our results will be qualitatively similar if we consider credit risk of corporate bonds. Our inferences remain unchanged when we use a different investment-grade bond index. Because U.S. life insurers only invest in a very small percentage of bonds with lower qualities (e.g., less than 4.2% of total invested assets in BB or lower bonds in 2020) and tend to further reduce this percentage, default risk is negligible. Moreover, insurers can transfer default risk with, for example, credit default swap, but this is outside the scope of this article. Therefore, we do not adjust duration for credit risk.

17 Solvency II is for European insurers. The National Association of Insurance Commissioners (NAIC), the insurance regulator in the United States, uses the risk-based capital formula to determine insurers’ capital requirements. However, the risk-based capital formula does not specify time horizon, risk metrics, or confidence levels. Thus, we follow Solvency II to set the values of $\alpha$ and $S_{\mathrm{\text{min}}}.$ The NAIC’s Life and Health Actuarial Task Force has endorsed a conditional tail expectation methodology that looks at the expected value past the VaR loss. Based on the estimate of Insurance Europe (known as Comité Européen des Assurances until March 2012), a 99.5% VaR is approximately equivalent to a 98.7% TVaR (Comité Européen des Assurances 2006).

18 Authors’ calculation based on table 2.1 in American Council of Life Insurers (2021).

Additional information

Funding

XZ gratefully acknowledges financial support from the China Scholarship Council (CSC201906490023).