Lecture Overview:

• Interest rate risk
• Duration
• Convexity
• Bond portfolio management
• Extensions of duration

Interest Rate Risk

A numerical example:

• Suppose a 5-yr treasury coupon bond
• Face value = $100
• Coupon rate = 3% p.a.
• Current zero yield curve is as follows:

$r_{0,1}=1\%,~r_{0,2}=2\%,~r_{0,3}=3\%, ~r_{0,4}=4\%, ~r_{0,5}=5\%$

The current bond price is:

$P=\sum^4_{t=1}\frac{3}{(1+r_{0,t})^4}+\frac{100+3}{(1+r_{0,5})^5}=\$91.8668$

We can also solve for the yield:

$P=\$91.8668=\sum^4_{t=1}\frac{3}{(1+y)^4}+\frac{100+3}{(1+y)^5}~~~~~y=4.87\%$

Now assume that the zero rate increased by 1% suddenly