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712.37 * 15-year bond, 7% coupon, interest paid annually Actual vs. Approximate Bond Prices
6% 8% 10%
YTM 12% Which of the following can have negative convexity?
a callable bond
a noncallable bond
a mortgage-backed security
a and c*
none of the above Properties of Duration
Duration is inversely related to the coupon rate.
Duration is inversely related to the yield to maturity.
Duration generally increases with maturity, but at
a decreasing rate. If the coupon rate is greater than zero, the duration is
less than the maturity.
For zero-coupon bonds, duration equals maturity.
For deep discount bonds, a point is reached at which
duration decreases as maturity increases.
duration Duration vs. Maturity
60 50 M atur ity 40 0 coupon rate
3% coupon rate
6% coupon rate
9% coupon rate
12% coupon rate
15% coupon rate 30 20 10 0
0 10 20 30
Duration 40 50 60 Interest Rate Risk
Interest The yield to maturity calculation assumes
that the yield to maturity (YTM) does not
change over the life of the bond.
– If the YTM does change, you probably won’t
earn your original YTM.
– This is called interest rate risk. Two types of interest rate risk
– Price risk – When interest rates rise, the price of
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- Spring '14