Paweł Olsza

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The article presents an example of the application of different approaches to the measurement of interest rate risk. Empirical analysis described in the article was carried out using data from the Polish interbank market for the period from September 5th, 2000 to November 19th, 2010. Interest rate risk measurement techniques using principal component analysis (PCA) are presented in the article. These techniques, by giving appropriate economic interpretation of each principal component, can also be used in the sensitivity analysis of the portfolio of debt securities to specific interest rate curve movements. The article also discusses the issue of the appropriate selection of scope and range of market data used in the analysis and its possible impact on values and stability of eigenvectors obtained using PCA. Three different hedging strategies were tested in order to check the effectiveness of interest rate risk measurement using PCA, the first based on PCA, the other based on the measures of effective duration, effective convexity, and BPV, the last considered strategy assumed no hedging at all. The results showed no significant differences in the degree of portfolio value protection in case of hedging strategy using PCA and the one based on the measures of effective duration, effective convexity, and BPV.


hedging, principal component analysis, interest rate risk


[1] Alexander C., (2008a), Market Risk Analysis Volume I: Quantitative Methods in Finance, John Wiley & Sons, Chichester.

[2] Alexander C., (2008b), Market Risk Analysis Volume II: Practical Financial Econometrics, John Wiley & Sons, Chichester.

[3] Baygun B., Showers J., Cherpelis G., (2000), Principle of Principal Components, SalmonSmithBarney Fixed-Income Research January 2000, adres internetowy: (dostep: 20 luty 2011).

[4] Fabozzi F., (2007), Fixed Income Analysis, John Wiley & Sons, Hoboken.

[5] Fabozzi F., Focardi S., (2004), The Mathematics of Financial Modeling and Investment Management, John Wiley & Sons, Hoboken.

[6] Falkenstein E., Hanweck J., (1996), Minimizing Basis Risk from Nonparallel Shifts in the Yield Curve, The Journal of Fixed Income, Vol. 6 No. 1, 60-68.

[7] Falkenstein E., Hanweck J., (1997), Minimizing Basis Risk from Nonparallel Shifts in the Yield Curve Part II: Principal Components, The Journal of Fixed Income, Vol. 7 No. 1, 85-90.

[8] Flavell R., (2010), Swaps and Other Derivatives, John Wiley & Sons, Chichester.

[9] Ho T.S.Y, (1992), Key Rate Durations: Measures of Interest Rate Risks, Journal of Fixed Income, Vol. 2 No. 2, 29-44.

[10] Hotelling H., (1933), Analysis of a complex of statistical variables into principal components, Journal of Educational Psychology, Vol. 24 No. 7, 498-520.

[11] Jolliffe I.T., (2002), Principal Component Analysis Second Edition, Springer, New York.

[12] Litterman R., Scheinkman J., (1991), Common Factors Affecting Bond Returns, Journal of Fixed Income, Vol. 1 No. 1, 54-61.

[13] Macaulay F., (1938), Some Theoretical Problems Suggested by the Movements of Interest Rates, Bond Yields and Stock Prices in the United States since 1856, National Bureau of Economic Research, New York.

[14] Ostasiewicz W. (red.), (1998), Statystyczne metody analizy danych, Wydawnictwo Akademii Ekonomicznej we Wrocławiu, Wrocław.

[15] Phoa W., (2000), Yield Curve Risk Factors: Domestic And Global Contexts, w: The professional’s handbook of financial risk management (red. Borodovsky L., Lore M.), Butterworth-Heinemann, Oxford.

[16] Przybylska-Kapuscinska W. (red.), (2008), Współczesna polityka pieniezna, Difin, Warszawa.

[17] Reitano R., (1991), Multivariate Immunization Theory, Transactions of Society of Actuaries Vol. 43, 393-441.

[18] Reitano R., (1992), Non-Parallel Yield Curve Shifts and Immunization, Journal of Portfolio Management, Vol. 28 No. 3, 36-43.

[19] Ron U., (2000), A Practical Guide to Swap Curve Construction, w: Working Paper 2000-17, Bank of Canada.

[20] Theil H., (1979), Zasady ekonometrii, Wydawnictwo Naukowe PWN, Warszawa.

[21] Trzpiot G. (red.), (2010), Wielowymiarowe metody statystyczne w analizie ryzyka inwestycyjnego, Polskie Wydawnictwo Ekonomiczne, Warszawa.

[22] Tuckman B., (2002), Fixed Income Securities, Wiley Finance, Hoboken.

[23] Jarmołowicz W. (red.), (2010), Podstawy makroekonomii, Wydawnictwo Uniwersytetu Ekonomicznego w Poznaniu, Poznan.

[24] Ziarko-Siwek U., Kaminski M., (2003), Empiryczna weryfikacja teorii oczekiwan terminowej struktury stóp procentowych w Polsce, Materiały i studia nr 159, Narodowy Bank Polski w Warszawie, Warszawa.

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