(L06)CapBudget(f)2

(L06)CapBudget(f)2 - xxx px p x px F x C x C x y F C x C x...

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Primbs/Investment Science 1 Lecture 6: Applied Interest Rate Analysis Reading: Luenberger Chapter 5, Sections 1 – 2, 6
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Primbs/Investment Science 2 Applied Interest Rate Analysis Capital Budgeting Cash Matching Valuation of a firm
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Primbs/Investment Science 3 Cash Matching Problem A series of future obligations must be met. You have various bonds you can invest in. You would like to construct a portfolio to meet the obligations at minimum cost. (Compare and contrast this with immunization)
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Primbs/Investment Science 4 Cash Matching in Pictures Obligation: Bond 1 F 1 Bond 2 F 2 C 2 Bond 3 F 3 C 3 Can invest in these to meet obligation
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Primbs/Investment Science 5 Cash Matching in Pictures Obligation: Bond 1 Bond 2 Bond 3 F 1 F 2 F 3 C 2 C 3 x 1 x 2 x 3 # of bonds Choose portfolio of minimum cost that has enough money to meet the obligation.
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Primbs/Investment Science 6 Cash Matching Assumptions Can solve the cash matching problem under different assumptions: 1) No reinvestment of excess cash is allowed. 2) Excess cash can be held at zero interest rate from one period to the next. 3) Excess cash can be reinvested at the appropriate forward rate.
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Primbs/Investment Science 7 Cash Matching in Pictures Obligation: Bond 1 Bond 2 Bond 3 F 1 F 2 F 3 C 2 C 3 x 1 x 2 x 3 # of bonds y 1 y 2 y 3 1 3 3 2 2 1 1 y x C x C x F + + 1 1 2 3 3 2 2 2 ) ( y x C x C F + + 2 2 3 3 3 3 ) ( y x C F + 3 3 p 1 p 2 p 3 Price of bonds 3 3 2 2 1 1 , , 3 2 1 min x p x p x p x x x + + Without reinvestment C 2 C 3 C 3
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Primbs/Investment Science 8 Cash Matching in Pictures Obligation: Bond 1 Bond 2 Bond 3 F 1 F 2 F 3 C 2 C 3 x 1 x 2 x 3 # of bonds y 1 y 2 y 3 1 1 3 3 2 2 1 1 y z x C x C x F - + + 0 1 z 1 1 2 2 1 3 3 2 2 2 ) ( y z z x C x C F - + + + 0 2 z 2 2 3 2 3 3 3 ) ( y z x C F + + 3 3 p 1 p 2 p 3 Price of bonds 3 3 2 2 1 1 , , 3 2 1 min x p x p x p x x x + + With reinvestment at zero rate C 2 C 3 C 3
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Primbs/Investment Science 9 Cash Matching in Pictures Obligation: Bond 1 Bond 2 Bond 3 F 1 F 2 F 3 C 2 C 3 x 1 x 2 x 3 # of bonds y 1 y 2 y 3 1 1 3 3 2 2 1 1 y z x C x C x F - + + 0 1 z 1 1 2 2 1 2 , 1 3 3 2 2 2 ) 1 ( ) ( y z z f x C x C F - + + + + 0 2 z 2 2 3 2 3 , 2 3 3 3 ) 1 ( ) ( y z f x C F + + + 3 3 p 1 p 2 p 3 Price of bonds 3 3 2 2 1 1 , , 3 2 1 min x p x p x p x x x + + With reinvestment at forward rate C 2 C 3 C 3
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Primbs/Investment Science 10 Bonds 1 2 3 4 Coupon 3% 4% 2% 5% s(0,i) f(i-1,i) d(0,i) Time 1 2 3 4 Amount Obligation 3% 3.0% 0.970446 1 103 4 2 5 10.502406 >= 10 3.50% 4.0% 0.932394 2 104 2 5 200 >= 200 4% 5.0% 0.88692 3 102 5 30 >= 30 4.20% 4.8% 0.845354 4 105 50 >= 50 Price 99.95589 100.8507 94.27156 102.711 Portfolio 0 1.894976 0.270775 0.47619 0 191.1097 25.52638 48.90998 265.54608 Total Price Cash Matching Term Structure Bonds No Reinvestment
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Primbs/Investment Science 11 s(0,i) f(i,i-1) d(0,i) Time 1 2 3 4 Amount Obligation 3% 3.0% 0.970446 1 103 4 2 5 -1 10 >= 10 3.50% 4.0% 0.932394 2 104 2 5 1 -1 200 >= 200 4% 5.0% 0.88692 3 102 5 1 -1 30 >= 30 4.20% 4.8% 0.845354 4 105 1 50 >= 50 Price 99.95589 100.8507 94.27156 102.711 0 0 0 Portfolio 0 1.890324 0.270775 0.47619 0.4837985 0 0 Amount in 0 190.6406 25.52638 48.90998 0 0 0 265.07693 Total Price Reinvest at Zero Interest Reinvest at zero interest Bonds Term Structure
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Primbs/Investment Science 12 s(0,i) f(i,i-1) d(0,i) Time 1 2 3 4 Amount Obligation 3% 3.000% 0.970446 1 103 4 2 5 -1 10 >= 10 3.50% 4.000% 0.932394 2 104 2 5 1.0408108 -1 200 >= 200 4% 5.000% 0.88692 3 102 5 1.05127 -1 30 >= 30 4.20% 4.800% 0.845354 4 105 1.049171 50 >= 50 Price 99.95589 100.8507 94.27156 102.711 0 0 0 Portfolio 0.21037202 1.782777 0.262646 0.384342 21.24643 9.96928 9.192063 Amount in 21.0279227
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(L06)CapBudget(f)2 - xxx px p x px F x C x C x y F C x C x...

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