3-year bond, coupon rate 4%, yield 3.5%, compute the price? Estimate the price using duration
n
3
r
4.00%
N
1
y
3.50%
P
unknown
exact computation
t
cashflow
D
unknown
0
1
0.04
2
0.04
3
1.04
approximate computation
with 3 years to go and at a yield o
its duration can then be computed
t
cashflow
0
1
0.04
2
0.04
3
1.04
the approximate price is given by
In your portfolio you have €10.000 nominal in 2-year bonds, coupon 4.25%, and €10.000 nom
from 4.95% to 4.85%. Using duration, estimate the change in value of your portfolio.
First
n
2
r
4.25%
N
10,000.00
y
4.05%
price or
P
unknown
t
cashflow
value
duration
D
unknown
0
10,037.69
1.96
new yield
4.15%
1
425.00
408.46
0.04
2 10,425.00
9,629.24
1.92
Second
n
4
r
4.75%
N
10,000.00
y
4.95%
price or
P
unknown
t
cashflow
value
duration
D
unknown
0
9,929.00
3.73
new yield
4.85%
1
475.00
452.60
0.05
2
475.00
431.25
0.09
3
475.00
410.91
0.12
4 10,475.00
8,634.24
3.48

price
101.40%
0.039
0.037
0.938
of 4%, a 4% bond has a price of 100%
d from
weight
duration
100.00%
2.8861
0.038
0.0385
0.037
0.0740
0.925
2.7737
1-duration / (1+yield) * yield differential i.e.
101.39%
quite close to the exact price
minal in 4-year bonds, coupon 4.75%. The 2-year ytm goes from 4.05% to 4.15%, the 4-year ytm
estimated value change
-18.90
estimated value change
35.34
total value change
16.43

m goes

Q. 04 Suppose someone promises you JPY 12.500 in sixteen months time in return for the JPY 12
the compounded one, or the simple one?
t
0.00
-12,175.00
1.33
12,500.00
1.976%
continuous return
1.995%
compound return
2.002%
simple return

2.175 you give him today. Which rate of return implied in this transaction is highest: the contin

nuously one,

Q. 05 What is worth most to you if you require a compound rate of return of 3% on a sixmonth
return
3%
per sixmonthly period
t in sixmonthly periods
cash flow
present value
0
1000
1000
2
1060
999.1517
3.5
1115
1005.413
so the 1115 in 21 months is worth most

hly basis: EUR 1.000 now, EUR 1.060 in one year time or EUR 1.115 in 21 months time?

Q. 06 Suppose you require a continuous rate of return of 4% on a yearly basis. Someone borro
him the money?
return
4%
t
cash flow
present value
0
-1,200.00
-1,200.00
3.0031
1,350.00
1,200.00
0.0000
sum of present values must be set to zero by changing time of seco

ows USD 1.200 from you and is prepared to pay you back as much as USD 1.350. How long wi
ond cashflow

ill you lend

Q. 07 What is your compound rate of return if in exchange for a sum of GBP 18.500 invested toda
return
2.644%
t
cash flow
present value
0 -18,500.00
-18,500.00
2
10,000.00
9,491.38
4
10,000.00
9,008.62
0.000000
sum of present values must be set to zero by changing return

ay you will receive GBP 10.000 in two years time and GBP 10.000 in four years time?

Q. 08 Someone lends you ZAR 100.000
today in return for which you are supposed to pay back ZA
replace the two payments of ZAR 60.000 and ZAR 65.000 by a single – equivalent – payment of ZA
return (continuous or compounded)?
Compound case
return
15.552%
t
cash flow
present value
0
100,000.00
100,000.00
0.25
-60,000.00
-57,870.51
3
-65,000.00
-42,129.49
0.00
sum of present values must be set to zero by changing return
replace this by
t
cash flow
present value
0
100,000.00
100,000.00
1.261335 -120,000.00
-100,000.00
0.00000
sum of present values must be set to zero by changing time of seco
Continuous case
return
14.455%
t
cash flow
present value
0
100,000.00
100,000.00
0.25
-60,000.00
-57,870.51
3
-65,000.00
-42,129.49
0.00
sum of present values must be set to zero by changing return
replace this by
t
cash flow
present value
0
100,000.00
100,000.00
1.261335 -120,000.00
-100,000.00
0.00000
sum of present values must be set to zero by changing time of seco

AR 60.000 in three months time and another ZAR 65.000 in three years time. Suppose you wan
AR 120.000. When do you have to pay this single sum? Does your answer depend on the way y
ond cashflow
ond cashflow: EXACTLY the SAME!

nt to
you compute rates of

Q. 09 You will lend someone HKD 45.800 five months from now in return for which he is suppose

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- Fall '10
- Bart Vinck
- Exchange Rate, Net Present Value, Forward contract, USD