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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

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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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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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