Price Risk An investor has a one-year time horizon (H=1) He can invest in three
ID: 2669244 • Letter: P
Question
Price Risk
An investor has a one-year time horizon (H=1)
He can invest in three different zero coupon bonds:
1) 1-year-zero-coupon bond
2) 5-year-zero-coupon bond
3) 10-year zero-coupon bond
The current level of the interest rate is equal to 5% per year. During the first year, the interest rate rises from 5 to 10% per year (stays constant afterwards)
What is the annual realized return of the three bonds?
Present Value Coefficients
Year 1 2 3 4 5 6 7 8 9 10
5% 0,95 0,91 0,86 0,82 0,78 0,74 0,71 0,68 0,64 0,61
10% 0,91 0,83 0,75 0,68 0,62 0,56 0,51 0,47 0,42 0,38
Explanation / Answer
Here, annual realised return = (Vt/V0)^1/t - 1
V0 face value of the bond, take the face value of the bond is $1,000.
Time period is 10 years.
For the first year the interest rate is 5%, after that it is 10%.
For the first year annual payment is = 0.05*1000
= $50
Then after, it is 10%. Coupon payment is $100.
For finding annual realized return, here we have to calculate the Vt.
Vt is must be account for reinvestment of annual coupon $50 and $100.
These reinvestments are as follows.
year1
Year2
Year3
Year4
Year5
…
Year9
Reinvest
Year10
1st coupon
$50
*0.61
$ 30.5
5th year coupon
$100
*0.62
$62
10th year coupon + Principal
$100
*0.91
$91
1000
$1091
$ 1.183.5
Therefore Vt is - $1,183.5
Annual realized return = (1,183.5/1000)^(1/10) - 1
=(1.1895)^(1/10) - 1
=1.0175- 1
=0.0175 or 1.75%
Therefore Annual realized return is 1.75%
year1
Year2
Year3
Year4
Year5
…
Year9
Reinvest
Year10
1st coupon
$50
*0.61
$ 30.5
5th year coupon
$100
*0.62
$62
10th year coupon + Principal
$100
*0.91
$91
1000
$1091
$ 1.183.5
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