FM4 Ch21 - Immunization - Template.xlsx

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UN-16C

1

2

34567

891011121314151617181920212223

2425262728

2930

31323334

 A B C D E F

Basic Immunization Example with One of 3 Bonds

Future Obligation $1,790.85Yield to maturity 6%Maturith 10Present Value of the Obligation <-- =B3/(1+B4)^B5, The amount of investment

Bond 1 Bond 2 Bond 3Coupon rate 6.70% 6.988% 5.90%Maturity 10 15 30Face value $1,000 $1,000 $1,000

Bond price <-- =PV($B$4,D10,-D9*D11,-D11)Units of Bond bought <-- =$B$6/D13Face value of $1,000 investment <-- =D14*D11Settlement date <-- =DATE(2014,11,3)Maturity date <-- =DATE(YEAR(D16)+D10,MONTH(D16),DAY(D16))

Right After Investing in the Bond

New yield to maturity 6%

Bond 1 Bond 2 Bond 3

Bond price at Year 10 <-- =PV($B$21,D10-$B$5,-D9*D11,-D11)Reinvested coupons <-- =FV($B$21,$B$5,-D9*D11)Total <-- =D24+D25

Terminal Value <-- =D14*D26

Data Table: Bond Value

Sensitivity

to Interest Rate

Bond 1 Bond 2 Bond 3

<-- =D28 , data table header (hidden)0%1%

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UN-16C

353637383940414243444546474849505152535455565758596061626364656667686970

 A B C D E F

2%3%4%5%6%7%8%9%

10%11%12%13%14%15%

$200.00

$300.00

$400.00

$500.00

$600.00

$700.00

$800.00

$900.00

$1,000.00

$1,100.00

$1,200.00

$1,300.00

$1,400.00

$1,500.00

$1,600.00

$1,700.00

$1,800.00

$1,900.00

$2,000.00

   T   e   r   m   i   n   a    l   V   a    l   u   e

Immunization Properties of the Three Bonds

Bond 1

Bond 2

Bond 3

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UN-16C

71727374

 A B C D E F

$0.00

.

0% 2% 4% 6% 8% 10% 12% 14% 16%Interest Rate

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Pages 545, 546

1

23456

789101112131415

1617

1819202122

2324252627

2829

3031323334

353637

38

394041424344454647

 A B C D E

Immunization with Convexity Maximization

Future Obligation $1,790.85Yield to maturity (YTM) 6%Maturity 10Present Value of the Obligation <-- =B3/(1+B4)^B5, The amount of invest

Bond 1 Bond 2 Bond 3

Coupon rate 6.70% 6.988% 5.90%Maturity 10 15 30Face value $1,000 $1,000 $1,000

Bond priceUnits of Bond boughtFace value of $1,000 investment

Beginning date 2014-Nov-03 2014-Nov-03 2014-Nov-03Ending date

Duration <-- =DURATI

New YTM 6%

Bond 1 Bond 2 Bond 3

Bond

Portfolio (1

& 3)

Bond priceReinvested coupons

Total

Terminal Value

Portfolio of Bonds 1 and 3

  Proportion of Bond 1 <-- =(B5-D19)/(B19-D19)  Proportion of Bond 3 <-- =1-B31

Bond 1 Bond 2 Bond 3Bond

portfolioInterest Rate

0%

1%

2%3%4%5%6%7%8%9%10%

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23456

789101112131415

1617

1819202122

2324252627

2829

3031323334

353637

38

394041424344454647

F G

  ent

  ON(D16,D17,D9,$B$4,1)

<-- =B31*B28+(1-B31)*D28

<-- =E26, Data Table Header 

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4849505152

535455

565758596061626364

656667686970717273

F G

nd 2

nd Portfolio

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Immunization with Matching the 2nd

 Derivatives

Future Obligation $1,790.85

Yield to maturity 6%Maturity 10 years

Present Value of the Obligation $1,000

Bond 1 Bond 2 Bond 3 Bond 4

Coupon rate 4.50% 6.988% 3.50% 11.00%Maturity 20 15 14 10Face value $1,000 $1,000 $1,000 $1,000

Bond priceUnits of Bond boughtFace value equal to $1,000 of market value

Beginning date 2014-Nov-03 2014-Nov-03 2014-Nov-03 2014-Nov-03Ending date

DurationSecond derivative of duration

New yield to maturity 6%

Bond 1 Bond 2 Bond 3 Bond 4

Bond price

Reinvested coupons

Total

Product

Data Table: Sensitivity of Bond 2 and Bond

Portfolio terminal values to interest rate

Bond 2Bond

Portfolio

<-- =I31*B30+I0%

1%

2%

3%

4%

5%

6%7%8%9%

10%11%

12%13%14%15%

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<-- =PV($B$4,E10,-E9*E11,-E11)<-- =$B$6/E13<-- =E14*E11

<-- =DATE(2014,11,3)<-- =DATE(YEAR(E17)+E10,MONTH(E17),DAY(E17))

<-- =DURATION(E17,E18,E9,$B$4,1)<-- =W24

Weights of the Bond Portfolio

Matrix of coefficients

<-- =PV($B$23,E10-$B$5,-E9*E11,-E11) 1 1 1

<-- =FV($B$23,$B$5,-E9*E11)<-- =E26+E27

<-- =E14*E28 Solution

<-- =MMULT(MINVER

32*D30+I33*E30Explanation of the above: We wa

x1, x3, and x4 in bonds 1, 3 and 4 r

that: a) The total investment is $1

b) Portfolio duration is matched to

that x1*D1+x3*D3+x4*D4 = D2, wher

of bond I.

c) The weighted average durationto that of bond 2.

These three conditions give us thecells I26:K28 and the correspondicells I31:I33 .

0

0

0

1

1

1

1

0% 2% 4% 6% 8% 10% 12% 14% 16%

Immunization Using 2nd Derivative

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Bond 2 Portfolio

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Calculating the 2nd Derivative of Duration

t C1,t C2,t C3,t C4,t t(t+1)PV(C1,t)

12

3

456789101112

13141516

171819 <-- =B$9*B$1120 <-- =(1+B$9)*B$11

Vector of Second derivative of duration -->

constants

1

<-- =B5<-- =B5*(B5+1)

E(I26:K28),M26:M28)

t to invest proportions

espectively, in order 

  000; this means x1+x2+x4=1

that of bond 2; this means

e Di is the duration

derivatives are equal

matrix system ing solution in

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t(t+1)PV(C2,t) t(t+1)PV(C3,t) t(t+1)PV(C4,t)

<-- =$O23*($O23+1)*P23/(1+$B$4)^$O23<-- =SUM(W4:W23)/E13