Consider a 30 year, 6% semiannual coupon bond with YTM 6.5% and face value $1000. Compute the following, and report your answers to four decimal places:

(i) the price of the bond (if you use software, specify the inputs)

(ii) modified duration using the formula

(iii) modified duration using the numerical approximation D 1 P+P P/ 2h

with h = 100 basis points

(iv) modified duration using the numerical approximation with h = 1 basis point

2. Suppose a company buys 200 units of Bond A, 300 units of Bond B, and 200 units of Bond C. The bonds attributes are:

Bond Price Duration

A $90 6 B $110 8 C $120 4

Find the approximate value of the portfolio if its yield increases by 0.01.

3. Rank the following bonds in order of decreasing price volatility (modified duration). Explain your reasoning. No computations necessary here!

Bond c(%) Maturity (years) Yield(%)

V 5 5 6

W 0 10 2

Y 5 5 5

Z 4 8 4