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Q-1:
Given the (yearly) spot rate curve s = (4.8, 5.1, 5.4, 5.6, 5.8, 5.9), fnd the spot
!ear (i) 1 " #
4.8$% 5.1$% 5.4$%
&pot rate ( 1, i) 5.4$1% 5.'$1%
Using formula= f1,2 = (( 1+s2)^2/(1+s1)) - 1
Using formula= f1,2 = (( 1+s3)^3/(1+s1))^(1/2) - 2
Q-2:
Consider two 6-year bonds: one has a 10% coupon and sells for 108.00; the other has a 5% coupo
1$ 5 y = $y =1
1$ 1$ y = 1$
5 y =1$ y = "
= 1
1$8 "*(85.$6) = +
+ = 6".1"
Q-3: ( oo- +ro. 4.11)
Year Cash Flo !"o# $a#e
1 4$ 5 $.95"#8$95"4 $.95"#8$95"4
" 1$ 5.# $.9$18685815 $.94696"$1$6
# 1$ 5.6 $.84919659'5 $.9415968#$1
4 1$ 5.8 $.'981$$$##8 $.9#98"95"#'
5 1$ 6 $.'4'"581'"9 $.9#6"96#8$4
6 1$ 6.1 $.'$$98##4$# $.9#8$'#8#55' 1$
Q-%: Problem 4.13
&trea/ 0//uniation
&pot rate (&)
+2- = 3ash lo d-,-1
* ( +2-1)
&is'oun# ra#e
,*
&is'oun# ra#e
*, *+1
8/16/2019 Homework 2 Ashish Vishnoi Revised
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Year !"o# 1 1
1 '.6'% $.9# 6 5.5'#
" 8."'% $.85 6 5.118
# 8.81% $.'8 6 4.65'
4 9.#1% $.'$ 6 4."$#
5 9.'5% $.6# 6 #.'68
6 1$.16% $.56 6 #.#5'' 1$.5"% $.5$ 6 ".9'9
8 1$.85% $.44 6 ".6#"
9 11.15% $.#9 6 ".#1'
1$ 11.4"% $.#4 6 ".$#5
11 11.6'% $.#$ 6 1.'8"
1" 11.89% $."6 1$6 "'.5#$
.o#al: 001
&ura#ion:
+1 65.95 1" !ear 6% ond+" 1$1.66 5 !ear 1$% ond
4liga#ion:
Year Cash Flo !"o# $a#e -15
1 5$$ '.6'% %%361761 4#1.#$1
" 9$$ 8."'% 77713336 1418."#5
# 6$$ 8.81% %07%137337 1"84.$95
4 5$$ 9.#1% 3021101%23 1"81.5#5
5 1$$ 9.'5% 262012%% "86.116
6 1$$ 1$.16% 000720%00 #$4.''8
' 1$$ 1$.5"% %%36%12 #14.4648 5$ 1$.85% 2132312%736 158."85
!um 2236%3701 0%766
7uasi /odifed duration o oliation ".44'6$4"4"4
0//uniation esult
$% 1%
ond1
&hares -1%3 -1%3
+rice 65.95 61.512alue 9"5.1$ 86".8'
ond"
&hare 3112 3112
+rice 1$1.66 9'.9$
2alue #16#.#" #$46.4"
:liation 2alue ""#8.44 "184.'$
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onds :liation $."" 1.16
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rate curve or net year
4 5 6
5.6$% 5.8$% 5.9$%
5.868% 6.$51% 6.1"1%
n and sells for 85.06. Find the price of a 6 year ero-coupon bond
e; 1e; "
%76776%2unnin +2- = 9.49'
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-15 2 2 -25
5.1'6 1$ 9."8'6#8 8.6"6$""
9.455 1$ 8.5#$681 15.'5816
1".841 1$ '.'6"#56 "1.4$159
15.#'8 1$ '.$$4"# "5.6#$'
1'.16' 11$ 69.$8"8" #14.'"81
18."8' $ $18.868 $ $
18.994 $ $
18.'6#
18."6"
1'.551
"95."5'
%0 116 361%0
7 3761
.
.
65.951 * 1 1$1.668 *" = ""#8.4#8
466.$ *1 #86.1446 *" = 54'8.8$9
1= 14.$"'#1"= #1.11665
Year ash Flo!"o# $a#
1 5$$ 8.6'%
" 9$$ 9."'%
# 6$$ 9.81%
1% 4 5$$ 1$.#1%
5 1$$ 1$.'5%
-1%3 6 1$$ 11.16%
'$.84 ' 1$$ 11.5"%99#.69 8 5$ 11.85%
!um
3112 !"o# 1
1$5.6" 1 8.6'% $.9" 6
#"86.54 " 9."'% $.84 6
# 9.81% $.'6 6
""94.#$ 4 1$.#1% $.68 6
+1*1 +"*" = +2
+1*>1*1 +"*>"*" = +2*>
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1.45 5 1$.'5% $.6$ 6
6 11.16% $.5# 6
' 11.5"% $.4' 6
8 11.85% $.41 6
9 1".15% $.#6 6
1$ 1".4"% $.#1 6
11 1".6'% $."' 61" 1".89% $."# 1$6
!"o# 1
1 6.6'% $.94 6
" '."'% $.8' 6
# '.81% $.8$ 6
4 8.#1% $.'# 6
5 8.'5% $.66 66 9.16% $.59 6
' 9.5"% $.5# 6
8 9.85% $.4' 6
9 1$.15% $.4" 6
1$ 1$.4"% $.#' 6
11 1$.6'% $.## 6
1" 1$.89% $."9 1$6
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8/16/2019 Homework 2 Ashish Vishnoi Revised
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e;1 65.951 1$1.668 ""#8.4#8
e;" 466.$ #86.1446 54'8.8$9
Year ash Flo!"o# $a#
%1 1 5$$ 6.6'% %6730
703773 " 9$$ '."'% 7621%3
%03133 # 6$$ '.81% %76622
3376% 4 5$$ 8.#1% 33320
16 5 1$$ 8.'5% 07%3
03% 6 1$$ 9.16% 01%3
%100 ' 1$$ 9.5"% 02112%116 8 5$ 9.85% 23061%
216%70 !um 22%37
1 2 2
5.5"1 1$ 9."$"1'"
5.$"5 1$ 8.#'5"56
4.5#1 1$ '.55""15
4.$5" 1$ 6.'5#68
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#.6$1 11$ 66.$19''
#.18$ $
".'9' $
".449 $
".1#8
1.861
1.615"4.'4"
101% 73
1 2 2
5.6"5 1$ 9.#'4'$'
5."14 1$ 8.69$4'#
4.'88 1$ '.98$#6'
4.#6$ 1$ '."665$8
#.945 11$ '".#1'99#.546 $
#.1'5 $
".8#$ $
".514
".""'
1.96'
#$.66"
7602 103
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5."
2 8ne"enen# goals an 1 ro9e'#s
.o#al nnual uge# ;0,,
.a4le 02
&es'ri"#ion Cos# (;1)1 3oncrete, " lanes "
" 3oncrete, 4 lanes #
#
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H $H indicates no c
H'H indicates '$ p
H1$H indicates po
H"$H indicates po
0nterest rate ##%
>iscount actor $.'5188
Jihest cash Io eneratin path ro/ ends
( "8, $, $) K ( 14, 14, $)
2alue (2) = E
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Using A
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onsu/ption as cash Io
ercent fshes etracted ro/ the pond as cash Io
ulation reaches to the initial level in net season
ulation doules in net season i no fsh is etracted ro/ the pond.
@ode values :pti/u/ Hunnin +2H$
'
$ $
$$
14 "8
14
'
'
$
26
1%
7
2
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$
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