If Duration is given as 5, but effective duration is given as -2.5…does this mean the bond is callable? Doesn’t this mean that is the sign of duration is negative then the P would be increasing as rates increase (positive relationship)? Why does a negative effective duration imply a callable bond?

Thanks,

Negative effective duration doesn’t imply that the bond is callable. Callable bonds have positive effective duration, but when interest rates are very low, the effective duration is very low (but still positive).

Think about what negative effective duration means: as interest rates *decrease*, the price of the bond _ **decreases** _, and as interest rates *increase*, the price of the bond _ **increrases** _: exactly the opposite of the behavir of a normal bond.

The most common example of bonds that have negative effective duration are I/O strips from mortgage-backed securities; these are bonds that receive only the interest payments from mortgages (I/O means *interest only*). When interest rates are low, these bonds will have negative effective durations: as interest rates *decrease*, more people refinance their mortgages, so the interest payments stop, and the value of I/O strips _ **decreases** _; as interest rates *increase*, fewer people refinance their mortgages, so the interest payments don’t stop (as fast as they would have), and the value of I/O strips _ **increases** _;