Question 1: (Bonds, 15 points)
a)
Find the price of a 10% Government coupon bond that pays annual coupons, matures
in exactly 2 years, and has a face value of $1,000. The yield to maturity is 4.09% p.a.
compounded annually. The bond has just paid its annual coupon, hence you need to price
it assuming that the first coupon that you will receive is due in exactly one year. (5
points)
Answer: The value of this bond is:
=
+
⎥
⎦
⎤
⎢
⎣
⎡ −
=
−
2
2
0
)
0409
.
1
(
000
,
1
0409
.
)
0409
.
1
(
1
100
P
$1,111.3
b)
You have the following data on spot and forward rates on US treasury securities:
Time horizon
Rates
r
0
,
1
4.12%
f
1,2
4.06%
f
2,3
4.36%
f
3,5
4.18%
For example, the one-year spot interest rate, r
0
,
1,
is 4.12%. The one-year forward rate
starting in one year for one year, f
1,2
, is 4.06%. All rates compound annually.
Construct the term structure of interest rates from the data above. That is, calculate the
implied yields on a 1, 2, 3, and 5-year zero coupon bonds using the information about the
forward rates. (6 points)
Answer: the yield on a one-year zero coupon bond is given as 4.12%. The yield on the 2-
year zero coupon bond is obtained by noting that:
(1+ r
0,2
)
2
= (1+ r
0,1
)*(1+ f
1,2
) so r
0,2
=
4.09%. The rest of the yields are calculated similarly and given in the next table:
Time horizon
Rates
r
0,1
4.12%
4.12%
f
1,2
4.06%
r
0,2
= 4.09%
f
2,3
4.36%
r
0,3
= 4.18%
f
3,5
4.18%
r
0,5
= 4.18%
2