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4.1 Bond pricing and effective maturity
In this section we elaborate on bond pricing relations by discussing Malkiel’s (1962) and Homer & Liebowitz’s (1972) propositions. In order to obtain an excellent understanding of propositions 3 and 4 we introduce effective maturity and contrast this to stated maturity.
Learning Objectives
Explain the relation between bond maturity-change in interest rates and non-proportionality
Explain the relation between change in interest rates and coupon rates
Explain the relation between change in interest rates and YTM
Explain effective maturity and how it differs from stated maturity
In the previous chapters we discussed the inverse relationship between bond prices and interest rates. In this chapter we will further elaborate in that idea. Below we present Malkiel’s (1962) and Homer & Liebowitz (1972) bond pricing propositions:
Malkiel’s proposition 1: There is an inverse convex relation between bond price and interest rates.
Convexity means that an increase in interest rates results in a lower price decrease when compared to a similar decrease in interest rates. Bond Prices decrease less when there is an increase in interest rates and bond prices increase more if there is an interest rate decrease.
Malkiel’s proposition 2: long term bonds are more sensitive to changes in interest rates compared to bonds with shorter maturities; however this relation is not proportional to the length of the life of the bond.
The reason that longer term bonds are more sensitive is because distant cash flows are discounted more heavily. Now, regarding non-proportionality between maturity and price sensitivity, this means that if a bond has twice the maturity of another bond with similar characteristics, its price sensitivity is not going to be twice as much as that of a bond with half its lifetime.
Malkiel’s proposition 3: there is an inverse relation between interest rates and coupon rates. Bonds with higher coupon rates are less...