Portfolio analysis duration

Associated with duration is the concept of dollar duration. Dollar duration is invaluable for portfolio managers when analysing the concentration of the portfolio in different buckets adjusted for duration. Mathematically, it is the product of the dollar value of the bond and its duration. For the purpose of portfolio analysis duration contribution (the product of duration and market value percentage) is used. Exhibit 26.3 shows the concentration of a portfolio in duration contribution terms. 

As one might expect the yields on bonds are correlated, in most cases very closely positively correlated. This enables us to analyse interest-rate risk in a portfolio for example, but also to model the term structure in a systematic way. Much of the traditional approach to bond portfolio management assumed a parallel shift in the yield curve, so that if the 5-year bond yield moved upwards by 10 basis points, then the 30-year bond yield would also move up by 10 basis points. This underpins traditional duration and modified duration analysis, and the concept of immunisation. To analyse bonds in this way, we assume therefore that bond yield volatilities are identical and correlations are perfectly positive. Although both types of analysis are still common, it is clear that bond yields do not move in this fashion, and so we must enhance our approach in order to perform more accurate analysis. 

Golub, B. W., and L. M. Tilman, Measuring Yield Curve Risk Using Principal Components Analysis, Value at Risk, and Key Rate Durations, Journal of Portfolio Management (Summer 1997), pp. 72-84. RiskMetrics-09/30/96—Spot ZC 3M-30Y 3 92.8/4.8/1.27... 

Fortunately for the investment community, there are alternatives to calculating tracking error that give an accurate idea of where a portfolio s risks lie. These methods start with understanding the exposures of a portfolio relative to its benchmark, along several dimensions such as duration, term structure, rating, sector, and issuer. They then create interest rate and credit spread scenarios for different future time periods and perform a what-if analysis on the portfolio and the benchmark for these scenarios. These scenarios should encompass both expected and extreme conditions (best and worst case) in order to generate a return profile, both absolute and relative to the index, as well as to identify key thresholds. 

Because of the analysis s assumed restrictions, however, investors applying it must continually adjust their portfolios if they wish to remain immunized. Fabozzi (1996) contains a very accessible discussion of the key issues involved in dynamically managing a portfolio. A number of other considerations also limit the use of duration in portfolio management. For instance, as Blake (1990) 5-8.1 points out, most Treasury bonds have durations of less than twelve years. This makes portfolio immunization difficult when liabilities are very long dated. 

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