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3#
发表于 2011-7-13 16:57
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If you think of interest rates as the discount factor applied to bond coupons and principal payments in order to get today's price, then the effect of coupons is easier to understand.
Let's imagine that you have a $1000 bond that pays 5% once annually and matures in 2 years. So there is just a single coupon payment of $50 in one year, plus a second coupon of $50 and the principal payment of $1000 in two years ($1050 total).
The price of the bond should be = PV($50 in one year) + PV($1050 in two years).
To make it easy to calculate, let's suppose that interest rates for similar bonds is 10%. Therefore the bond's value is:
$50*(0.90) + $1050*(0.90)^2 = $895.50
[ 0.90 is the discount factor for a 10% interest rate = (1-10%) ]
What's important here is the (0.90)^2 vs the (0.90). The payments that come later down the line are much more sensitive to interest rate changes because the discount factor compounds over time. Their contribution to the price of the bond today is much more sensitive to interest rate changes than the payments that come earlier, where the compounding is less. The coupon payments thus have a smaller duration, because they are less sensitive to the price.
A bond's duration can be thought of a the weighted average of the durations of all the payments. Since the payments that come earlier have smaller durations, bonds with more coupons (and larger coupons) will tend to have smaller durations. |
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