# The optimal trade-off between interest rate risk and annual return of bond ladders

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## Abstract

Bond laddering is a popular fixed-income investment strategy. The main purpose of this paper is to develop a methodology for determining private investors’ most interest rate risk (IRR)-return-efficient investment horizon for bond ladders (BLs), which are virtually free of credit risk. Two IRR measures of a continuously rolling and homogenous BL (CRHBL) are analytically derived under the assumption that interest rates are martingales. The first measure is the modified duration, which assumes a flat term structure of interest rates. However, this assumption is not fully supported by the empirical data and, thus, an additional IRR measure is proposed. Under each of these two measures, the ratios between the annual return in excess of the demand deposit rate and IRR of CRHBLs with different investment horizons are calculated. As expected, CRHBLs with rather low IRR are most risk-return-efficient. The results for the theoretical CRHBLs also apply to “real-world” discrete BLs. Thus, the proposed methodology can help private investors construct IRR-return-efficient discrete BLs.

## Keywords

Bond ladder Fixed-income instrument Interest rate risk Modified duration Time deposit## Abbreviations

- BL
Bond ladder

- CF
Cash flow

- CR
Credit risk

- CRHBL
Continuously rolling and homogenous bond ladder

- DGS
Deposit guarantee scheme

- DPS
Deposit protection scheme

- IR
Interest rate

- IRR
Interest rate risk

- LtV
Loan to value

- MD
Modified duration

- HPB
Hypothekenpfandbrief

- PV
Present value

- TD
Time deposit

## JEL Classification

G11## Notes

### Acknowledgements

First, I would like to thank three anonymous referees and the editor for providing very valuable comments on and suggestions for earlier versions of this paper. A very early version of the paper also benefited from discussions with participants at the World Finance Conference 2014 (Venice, Italy). Last, but not least, I thank the German Academic Exchange Service for funding my trip to this conference.

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