# Principal Component Value at Risk: Application Measuring Interest Rate Risk

Mark Tracey1

Financial Stability Department Research & Economic Programming Division Bank of Jamaica

Abstract This paper develops an effective value at risk (VaR) methodology to complement existing Bank of Jamaica financial stability assessment tools. This methodology employs principal component analysis and key rate durations for assessing interest rate risk of the Jamaican banking sectors’ holdings of both local and global Government of Jamaica (GOJ) bonds. Principal Components Analysis (PCA) is proposed as a tractable and simple-to-implement method for extracting market risk factors from observed data. This approach, which is informationally efficient, quantifies the risk associated with portfolios using three principal factors that affect yield curves. Due to the orthogonal nature of the factors, correlation and covariance between the yields do not have to be explored, simplifying the calculation of VaR for the portfolios. Results of this paper indicate that the PC VaR outturn for the Jamaican banking system is higher relative to both parametric and historical VaR outturns suggesting that the PC VaR holds more information as it relates to the risks impacting banking system portfolios.

JEL Classification: G11, G28, G32 Keywords: Key Rate Duration, Principal Component Analysis, Value at Risk

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The views expressed are those of the author and do not necessarily reflect those of the Bank of Jamaica.

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Table of Contents 1. Introduction.................................................................................................................... 3 2. Data Set .......................................................................................................................... 6 3. Methodology ................................................................................................................... 7 3.1 Statistical Analysis of data .................................................................................................. 7 3.2 Determining the key rate duration..................................................................................... 7 3.3 Determining the Principal Components and Principal Components Duration ............. 7 3.4 Determining VaR Using Principal Component Duration.............................................. 11

4. Results........................................................................................................................... 11 4.1 Statistical Analysis............................................................................................................. 11 4.2 Examination of Maturity/Re-pricing Gap....................................................................... 13 4.3 Sensitivity Factors of Instruments ................................................................................... 14 4.4 Principal Component Analysis ......................................................................................... 15 4.5 Value at Risk Outturn....................................................................................................... 18

5. Discussion..................................................................................................................... 20 6. Conclusion.................................................................................................................... 21 Reference.......................................................................................................................... 23 Appendix 1: ...................................................................................................................... 25 Summary Statistics .................................................................................................................. 25

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