Duration matching and bond selection

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READ a book about investment management, particularly on fixed income, and you’ll be baffled If you were an individual willing to actually invest in a bond portfolio. Say it’s your portfolio size, not matching the unlimited cash pools of institutional investors, or the bewildering range of bond options but it’s unlikely you can contact your broker or bank dealer and pass a buy order.

Among the many issues an investor has to face in real-world bond investments is the one of maturity selection. Here’s where another tool comes into play: the yield curve. The relationship between bond maturity and yield on a particular bond class (i.e. sovereign, corporate investment grade, etc.) can be depicted on the media-ubiquitous yield curve. Say you want the highest yield bonds and you’re likely to find them at the higher end of the yield curve, meaning they’re likely to have 20 to 30-year maturities. Say you don’t want to take on the uncertainty (i.e. read “risk”) in such long dated bonds and you can opt for lower maturity and thus lower yield bonds.

This is certainly the case when the yield curve is upward sloping. Sometimes, yields on bonds go upside down. This is when the yield curve is downward sloping meaning that investors are better off selecting lower maturity bonds with higher yields and lower risks of the issuer defaulting on its obligations. Is it easy to invest in lower-maturity/higher-yield bonds when when the yield curve is downward sloping? Nope, especially if your holding period goes over the short term; when investors anticipate an interest rate cut and position themselves in the short run future actual yields on bonds could turn out to be somewhat lower than expected. One solution to the bond selection puzzle is “duration matching” technique.

Duration, an alternative measure of maturity, tells the investor how sensitive is a bond price to market yield changes. For instance, if market yields, on a particular bond class, go down by 1.0% then a bond with a 10-year duration will see its price soar by 10.0% – 1.0% times 10. Vice versa, if yields go up 0.25% on a 6-year duration bond it’s because its price has gone down by 1.5% – 0.25% times 6.

An investor with an investment horizon of 5 years bears reinvestment risk if he or she holds a bond portfolio with a shorter duration. If yields rise the investor will reap a higher yield by reinvesting its proceeds in higher yielding bonds. On the contrary, he or she will be worse off if yields go down for proceeds will be reinvested in lower yielding bonds. An investor holding a portfolio with a longer duration than his or her investment horizon will bear price risk; in fact, no matter what the investor reinvests his or her proceeds in lower or higher yields the bond selling price at the end of the investment horizon will prevail: if yields go down prices will shoot up but if yields rise prices will plummet.

Investors should then know – had they read the investment management book – that reinvestment and price risk offset each other when the bond portfolio duration matches the investor’s holding period. Though some necessary conditions must hold before one can jump to the conclusion of having solved the bond allocation puzzle – and going through some probably unwanted algebra to check out the Fisher-Weil theorem [1] – duration matching offers a simple approach to bond picking. By matching bond portfolio duration and investor’s investment horizon one “immunizes” a bond portfolio from unexpected and unwanted changes in bond yields.

The risk averse investor should thus pick a bond portfolio with a duration matching his or her investment horizon. One question remains unanswered: what’s the investor’s investment horizon?

[1] Financial mathematics for actuaries – Bond management, http://www.mysmu.edu/faculty/yktse/FMA/S_FMA_8.pdf.


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