Immunization Using Principal Component Analysis

Barber, Joel R.; Copper, Mark L.

doi:10.3905/jpm.1996.409574

Cited by 48 publications

(22 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…consideration. Similar results were also obtained for the yield curve data analyzed in [1] and for more recent data. We can't use this calculation to support a claim that the shape of the first principal persists over time, not without some more work at any rate, but it does show once again how our statistics aren't lining up with our intuition.…”

Section: Shape Of First Principal Componentsupporting

confidence: 77%

“…The 90% confidence interval for the first component alone includes neither the 80% proportion found in [1] nor any of the proportions for the various maturities found through factor analysis by Litterman and Scheinkman in [20], Table 2. These earlier studies were conducted using different data; we may be seeing evidence of non-stationarity.…”

Section: -Jk=l Aimentioning

confidence: 99%

“…The first approach centers around the principal component analysis of sample covariance matri ces derived from the history of the term structure of interest rates. This approach was first used in [1] and is closely related to the use of common factor analysis by Litterman and Scheinkman in [20]. Moreover, this approach has continued to be of interest to researchers, both as a simple model for term structure evolution [8] In the second approach term structure shifts are decomposed into atoms called "wavelets".…”

mentioning

confidence: 99%

See 2 more Smart Citations

Principal component and second generation wavelet analysis of treasury yield curve evolution

Copper¹

Self Cite

View full text Add to dashboard Cite

Copper, Mark L., "Principal component and second generation wavelet analysis of treasury yield curve evolution" (2004). This dissertation studies aspects of this evolution.There are two complementary approaches to the study of yield curve evolution here. The first is principal components analysis; the second is wavelet analysis. In both approaches both the time and maturity variables are discretized. In principal components analysis the vectors of yield curve shifts are viewed as observations of a multivariate normal distribution.The resulting covariance matrix is diagonalized; the resulting eigenvalues and eigenvectors (the principal components) are used to draw inferences about the yield curve evolution.In wavelet analysis, the vectors of shifts are resolved into hierarchies of localized fun damental shifts (wavelets) that leave specified global properties invariant (average change and duration change). The hierarchies relate to the degree of localization with movements restricted to a single maturity at the base and general movements at the apex. Second generation wavelet techniques allow better adaptation of the model to economic observ ables. Statistically, the wavelet approach is inherently nonparametric while the wavelets themselves are better adapted to describing a complete market.Principal components analysis provides information on the dimension of the yield curve process. While there is no clear demarkation between operative factors and noise, the top six principal components pick up 99% of total interest rate variation 95% of the time.An economically justified basis of this process is hard to find; for example a simple linear model will not suffice for the first principal component and the shape of this component is nonstationary.Wavelet analysis works more directly with yield curve observations than principal com ponents analysis. In fact the complete process from bond data to multiresolution is pre sented, including the dedicated Perl programs and the details of the portfolio metrics and specially adapted wavelet construction. The result is more robust statistics which provide balance to the more fragile principal components analysis.

show abstract

Section: Shape Of First Principal Componentsupporting

confidence: 77%

Section: -Jk=l Aimentioning

confidence: 99%

mentioning

confidence: 99%

See 1 more Smart Citation

Principal component and second generation wavelet analysis of treasury yield curve evolution

Copper¹

Self Cite

View full text Add to dashboard Cite

show abstract

“…We find this correlation pattern quite acceptable. In view of these findings, and to have a better understanding of the way that spot rates for different maturities change, we followed Garbade (1986), Litterman and Scheinkman (1991), Barber and Copper (1996), Knez et al (1994) and DÕEcclesia and Zenios (1994) and carried out a Principal Component Analysis (PCA). 8 In Table 2, we use the results produced by the PCA (over eight representative interest rates) to show the relative importance of factors.…”

Section: Term Structure Behaviormentioning

confidence: 99%

Immunization using a stochastic-process independent multi-factor model: The Portuguese experience

Bravo

Silva

2006

Journal of Banking & Finance

View full text Add to dashboard Cite

“…Since Litterman and Scheinkman (1991) found that essentially three factors were enough to describe the movements of the U.S. treasury term structure, PCA has been applied to many problems in financial engineering: risk management as in Singh (1997), portfolio immunization as in Barber and Copper (1996), identification of main driving forces of term structures as in Heidari and Wu (2003), Collin and Goldstein (2002), and Almeida et al (2003), besides being a benchmark used to define the number of factors in dynamic models. Whenever PCA is applied to yield levels, 2 principal components inherit the qualitative characteristics of yields, including autoregressive behavior with near-unit roots (see Backus et al (1999) or Diebold and Li (2003) for a discussion on stylized facts of the term structure of interest rates).…”

Section: Introductionmentioning

confidence: 99%

A Note on the Relation Between Principal Components and Dynamic Factors in Affine Term Structure Models

Ibsen

Almeida²

2005

Brazilian Review of Econometrics

View full text Add to dashboard Cite

In econometric applications of the term structure, affine models are among the most used ones. Nevertheless, even presenting a closed form characteristic function, its estimation procedure still presents many points to be understood and difficulties to be removed. In this note, we address one of these points. Suppose we estimate an affine dynamic term structure model, and also apply principal component analysis to the interest rate database available. A very plausible question would inquire about the relation (if any) between the principal components obtained assuming no dynamic restrictions, and the dynamic factors estimated using the proposed term structure model. We answer this question when estimating a standard affine model using zero coupon data. We show that each principal component can be approximated by a linear transformation of the dynamic factors. Although simple, this is an important step to the understanding of the mechanics of dynamic affine term structure models. A numerical example using U.S. zero data illustrates the result.

show abstract

Immunization Using Principal Component Analysis

Cited by 48 publications

References 5 publications

Principal component and second generation wavelet analysis of treasury yield curve evolution

Principal component and second generation wavelet analysis of treasury yield curve evolution

Immunization using a stochastic-process independent multi-factor model: The Portuguese experience

A Note on the Relation Between Principal Components and Dynamic Factors in Affine Term Structure Models

Contact Info

Product

Resources

About