Interest Rate Risk of Life Insurers: Evidence from Accounting Data

Abstract

Research QuestionLife insurers guarantee their customers fixed interest rates for a long period. However, the duration of their assets typically does not match the duration of their policies which exposes the life insurers to the risk of falling interest rates. Quantitatively, little is known about interest rate risk because these companies do not report it in their financial statements. In recent years, however, interest rate risk taken on in the past has partly materialized. Against this background, this paper examines the interest rate risk of life insurers. ContributionAn important indicator for measuring interest rate risk of insurers is the duration gap, which is the difference in interest rate sensitivity between assets and liabilities. The wider the gap, the greater the risks when interest rates fall, because the value of liabilities grows more strongly than the value of assets. I show how to estimate the duration gap with data from external accounting. The calculation is based on differences between the book and market values. The indicator is calculated for German life insurers. This offers an insight into the distribution and determinants of interest rate risk. This is important for assessing the contribution of the insurance sector to risks to financial stability. ResultsThe calculation at the insurer level yields on average a wide duration gap for German life insurers with pronounced heterogeneity in the cross-section. This indicates that insurers are exposed to quite different degrees of interest rate risk. A wide dispersion implies differences in terms of the management of interest rate risk. Therefore, insurers are likely to respond differently in their investment decisions to falling interest rates. This reduces the degree of alignment in their behavior and, thereby, potential risks to financial stability. Nichttechnische Zusammenfassung FragestellungIhren Kunden garantieren Lebensversicherer für eine lange Laufzeit eine Mindestverzinsung. Hierbei ist jedoch die Laufzeit ihrer Kapitalanlagen typischerweise geringer als die Laufzeit der Versicherungsverträge. Dies setzt Lebensversicherer einem Risiko gegenüber fallenden Zinsen aus. Es ist quantitativ wenig über dieses Zinsänderungsrisiko bekannt, denn diese Unternehmen müssen hierzu in ihren Geschäftsberichten nichts veröffentlichen. In den letzten Jahren hat sich das in der Vergangenheit eingegangene Zinsänderungsrisiko teilweise materialisiert. Vor diesem Hintergrund wird die Höhe des Zinsänderungsrisikos von Lebensversicherern untersucht. Beitrag Eine wichtige Kennzahl zur Messung des Zinsänderungsrisikos von Versicherern ist die Durationslücke, der Unterschied in der Zinssensitivität zwischen Vermögensgegenständen und Verbindlichkeiten. Je höher die Durationslücke, desto größer sind die Risiken aus fallenden Zinsen. Denn in diesem Fall steigt der Barwert der Verbindlichkeiten stärker an als der Barwert der Vermögensgegenstände. Es wird gezeigt, wie man mit Daten aus dem externen Rechnungswesen die Durationslücke abschätzen kann, wobei die Bere...

Macaulay’s theory of duration: 80-year thematic bibliometric review of the literature

“…Insurance companies have much larger duration of their liabilities as compared to their assets that is on the average more than ten years (Schlütter, 2017). Möhlmann (2017) working in the area of insurance risk management proposes an interest risk measure based on accounting data and the concept of duration.…”

“…In order to utilize the function to calculate the possible change in book and market value due to time Möhlmann (2017) develops a single example of valuing a zero-coupon bond at some different time, having a certain face value and time to maturity. In such a case by discounting market value with interest rates after the change and discounting book values with interest rate before the change, and assuming they are not sensitive to interest rates but are sensitive to time passage.…”

“…Furthermore, as changes in market value after change in interest rates, book value before change in interest rates do not involve reinvestment assumption, therefore Möhlmann (2017) in order to incorporate change with respect to earlier payments in coupon bonds introduces a reduction in value change in response to small change in time. It can be interpreted as “the time structure is that interest rates changed from r0 to r0 +Δr just after the item was recognized on the balance sheet and then, from time v0, a time Δv passed while interest rates remained constant”.…”

“…It can be interpreted as “the time structure is that interest rates changed from r0 to r0 +Δr just after the item was recognized on the balance sheet and then, from time v0, a time Δv passed while interest rates remained constant”. However, due to unknown nature of exact time structure, Möhlmann (2017) recommends to include only ½ of Δ v to account for the time insensitive present value of relevant net cash flows. The duration model of such a stream of cash flows can simultaneously be used to calculate the durations of assets and liabilities.…”