ACTSC445/845 ASSIGNMENT 1–SOLUTION.
(1) See excel fle
(2) The Following table gives the price at di±erent dates For a threeyear 4% bond that
pays semiannual coupons and has a Face value oF 10
,
000.
i
date
price
1
01/Jan/2007 (issue date)
10,188.40
2
01/July/2007
10,129.22
3
01/Jan/2008
10,129.12
4
01/July/2008
10,119.37
5
01/Jan/2009
10,069.05
6
01/July/2009
10,024.08
(a) (10 points) Compute the yields
y
i
on the bond (expressed on annual rate,
with semi annually compounding) obtained iF the bond is bought at time
i
,
For
i
=1
,
2
,
3
,
4
,
5
,
6.
(b) (10 points) Consider a 6month Tbill on date
i
with a Face value oF $10
,
000,
For
i
,
2
,
3
,
4
,
5
,
6. Let
r
c,i
be the (Canadian) quoted yield on Tbill issued
on day
i
. ²ind the value oF
r
c,i
such that Tbill
i
has the same e±ective annual
yield as the bond in part (a) bought at time
i
.
(c) (10 points) ²or each
i
,
2
,
3
,
4
,
5
,
6 fnd the US quoted yield
r
D,i
equivalent
to the Canadian quoted yield
r
c,i
Found in part (b).
Solution 0.1.
(a)
Let
B
i
be the price of the bond at time
i
(
i
,
2
. . .
6)
. We
have
B
i
= 200
a
7

i

y
i
2
+ 10
,
000(1 +
y
i
2
)

(7

i
)
Using a Fnancial calculator (or Excel), we have
y
1
=3
.
334845%
,y
2
.
456019%
3
.
327327%
,
y
4
.
178770%
5
.
292403%
6
.
509948%
(b)
Let
P
i
be the price for the
T
Bill issued on date
i
,
r
i
be the e±ective annual