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8/10/2019 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 $1,000 investment
Beginning date 2014-Nov-03 2014-Nov-03 2014-Nov-03Ending date
Duration <-- =DURATI
New YTM 6%
Bond 1 Bond 2 Bond 3
Bond
Portfolio (1
& 3)
Bond priceReinvested coupons
Total
Terminal Value
Portfolio of Bonds 1 and 3
Proportion of Bond 1 <-- =(B5-D19)/(B19-D19) Proportion of Bond 3 <-- =1-B31
Bond 1 Bond 2 Bond 3Bond
portfolioInterest Rate
0%
1%
2%3%4%5%6%7%8%9%10%
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Pages 545, 546
1
23456
789101112131415
1617
1819202122
2324252627
2829
3031323334
353637
38
394041424344454647
F G
ent
ON(D16,D17,D9,$B$4,1)
<-- =B31*B28+(1-B31)*D28
<-- =E26, Data Table Header
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Pages 545, 546
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