Bond portfolio duration, cash flow dispersion and convexity

Abstract

Immunization is a well-known fixed-income strategy to lock in a target rate of return over a known investment horizon. This is accomplished by structuring the bonds so that the duration of the portfolio matches the time horizon and then rebalancing the portfolio to maintain the match as time passes and yields change. The structural risk to the strategy can be measured by the cash flow dispersion or by the convexity of the immunizing portfolio. The general relationship between the duration, cash flow dispersion and convexity statistics for any date in the current period is derived in the article. Although both statistics measure the risk, convexity is significantly easier to implement in practice.

Notes

¹The seminal Redington article is available at the Society of Actuaries website: http://library.soa.org. Redington described the basic rule to be equating the ‘mean term’ of the assets to the liabilities. This is mathematically equivalent to what is now named ‘duration’, the original source of which is Macaulay (1938).

²The Fabozzi (2007) use of cash flow dispersion as a measure of the structural risk to immunization is in a sense the ‘industry standard’ in that it is the required reading for the Chartered Financial Analyst® exams.