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5 . , , . 457 (Wall Street Journal)

yield to maturity based on asked price( )

2003 1 22 1: 2003 4 =

Treasurysof 2003 1,000 1000 62.5

= 100: 02 = = 100.0625 58 vs. : (bid price) (asked price) . . Treasury Bond ( = )Treasury Bill ( ; ) Treasury Note ( ; ) Treasury Bond ( ; ): 1 : 1 10: 10 30 60 vs. (Rate of Return) : 1) 2) , , : ( + ) RET = Pt+1 - Pt Pt = C C + Pt+1 - Pt Pt Pt +(g) (ic)62 1 $800 ?

(, : paper loss) . 1 $1,200 , ? 6

( ) i EX)7 : . . EX) . , (preemptive interest rate policy) . : ( ) .8 vs. (Time Value of Money) 1,000 . 1,000 10 1000 ? 1,000 1,000 . ? , .75 (e) . 1: , .( ) (2) .

77 2: . 3) , .

( ) . .

78 (Stylized Facts) . 1) , . 2) , .3) , . vs. 79 2 . . TIPS (Treasury Inflation Protection Securities; ) : .80 vs. : .( ) 50s & 60s: 70s : (70 ) 80s: 80 , 90s: Early 00s: . Mid to late 00s: , (-) . . 8283 . (Infinite Geometric Series) A . a, ar, ar2, ar3, ar4 (a = , r = ) r 1 ( ) . () a r . 84

: 1) 2) 3) (1) (2) , (1-r)S = a ? Let S = a + ar + ar2 + ar3 + (1) Then rS = ar + ar2 + ar3 + ar4 + (2)8570 B A n A(1+i) A(1+ i)n = 2A (, A n = 2) n n , , 2A . i X 100% A (n) ? 5% P 2P . 2 P(1+0.05) + P(1+0.05)X0.05 = P(1+0.05)2 . P 2 . 86 i = 4% n = 0.693/ln1.04 = 0.693/0.039 = 17.67 . , nln(1+i) = ln2 n = 0.693/ln(1+i) . : A (1+ i)n = 2 . 2 . 2 (n) (%) 70 . 70 % ( ) 2 . 87 (log/logarithm) (natural logarithm) logax = m am = x 10 . 103 = 1000 10 (base number), 3 (exponent) . 3 = log101000 1000 10 . 10 10000 log1010000 = log10104 = 4 . , . 88 (, ) 2.718. e . 5 (1+ i)n = 2 ln(1+ i)n = ln2 nln(1+ i) = ln2 . ln2 0.693 ( ) . lnxy = lnx + lny lnxn = nlnx . ( ) e loge ln . 93EX 1) 10% 7 .EX 2) 2% 35 .EX 3) 1990 20% 3 .EX 4) 14% 5,000 5 10,000 . EX5) 24% 3 .94 C , ? ( .) ? : O.K.! O.K. 1) 2) .95 D ? , . , . . : . . 24

$39,509.54 * (?) *

5 4.5% 5 ? 3) . 1) $200,000 .2) 5 $200,000 .25

38 . 40 $250,000 ? , 10% . 26() 4 (Simple Loan) EX) ( 1) EX) (mortgage), , , (Fixed Payment Loan)27 (Coupon Bond) (, ) () (par value = face value): (annuity) (coupon payment) , (coupon rate) ip = C F28 EX) ( , ) () EX) (T-bills), , , , . ? (discount bond / zero-coupon bond)29 = (Yield to Maturity) (YTM) = ( ) 30 1) ? = YTM 2) ? (Internal Rate of Return: IRR)? () () . . , . .31 R1 , R2 , Rn . P NPV( = ; Net Present Value) . (NPV) .

0 i . 32 , i . : :

--- (1) 33 (, ) . . : (1) P i . , . . > 34 (Simple Loan) () = $100, FV = $110

(Single Period Simple Loan) $100 1 $110 . ? = $100, = $110/(1+i) 35 , , = =

(, ) = $1,000 3 = $1,000(1+0.1)3 = $1,331 $1,000 = $1,331/(1+i) 3 i , YTM = 10% . (Multi-Period Simple Loan) 10% 3 $1,000 . ? $100 = $110/(1+i) i i = 10% = YTM = 36 (Fixed Payment Loan) ( ) = $1,000 . 0 (fully amortized loan) . , $126 25 $1,000 . ?37 LV (; the loan value) = , FP (fixed payments) = n =

, .

i 11.83% . ( )38 LV, i, n FP . FP .

39

LV = $15,000 n = 60 (5 x 12) i = 1% (0.12 / 12 = 0.01) Note) , n = i = , n = i = 12% 5 , $15,000 ?40--------------------------------------------------------------------------------- --------------------------------------------------------------------------------- 1. $59.40 $7.12 $52.27 $947.72 2. $59.40 $6.75 $52.65 $895.08 3. $59.40 $6.38 $53.02 $842.05 4. $59.40 $5.00 $53.40 $788.65 5. $59.40 $5.62 $53.78 $734.87 6. $59.40 $5.23 $54.16 $680.71 7. $59.40 $4.85 $54.55 $626.16

= 8.55%/12 = 0.7125% 8. 55% 18 $1,000 ? : $1,000 18 8.55% 41--------------------------------------------------------------------------------- --------------------------------------------------------------------------------- 8. $59.40 $4.46 $54.94 $571.22 9. $59.40 $4.07 $55.33 $515.89 10. $59.40 $3.67 $55.72 $460.17 11. $59.40 $3.28 $56.12 $404.04 12. $59.40 $2.88 $56.52 $347.52 13. $59.40 $2.48 $56.92 $290.60 14. $59.40 $2.07 $57.33 $233.27 15. $59.40 $1.66 $57.74 $175.53 16. $59.40 $1.25 $58.15 $117.38 17. $59.40 $0.84 $58.56 $58.82 18. $59.24 $0.42 $58.82 $0.00----------------------------------------------------------------------------------Note) . . ----------------------------------------------------------------------------------- : $1,000 18 8.55% 42 (Discount Bond)

= $900, FV () = $1,000 = $1,000/(1+i) (, ) . 1 F = , P =

$1000 12 $900 ?43 ? When P = $1,000,

P = $900,

P = $850, P = $800, . .44 (Coupon Bond) P, C, F n , YTM i . P = C = F = n =

45 C, F, n P i . P () i (). i () , P(). i , P . i , ( ) P . ( ) . ( )46

.When P = $800, i = 13.81% $900, i = 11.75% $1,000, i = 10.00%

$1,000 (C/F) = 10% 10 . Note) (P) (F) = (coupon rate) = (current yield) 47 ($) (%) 200 53.05 300 37.17 400 28.74 500 23.27 600 19.32 700 16.27 800 13.81 900 11.75 1,000 10.00 1,100 8.48 1,200 7.13 1,300 5.94 1,400 4.86 1,500 3.87 10 10% ( = $1,000)48

(%) ($) 10 , 10% ( =$1,000) = , = 49 (consol) (perpetuity) . (, ) . : 1) . ( , ) 2) , . 3) , , , .50

(, ) . , , . 51 ( ) . . (Current Yield) ic = C P = (, P = F), = = 52 , . : 1) a) b) . 2) a) b) . 3) . 4) . 53 (yield on a discount basis) 1 . (T-bills) (discount yield) . $1000 90 $970 ? ? idb = F - P F X 36054

= $970, =

i . i = 90 =

55

< . () .

, i P .3) , . 2) 0. 1) . 69 :

1 :

( ) ( ) . ( ) ? $M 1 . = , = i, = P , 1 M(1+i) P(1+ ) . 71 i . i r r = 0 1/(1+ ) = 1 .

( = - )

( = + )72 100% r . A, A+Ar (A+Ar) . A + Ar + (A+Ar) = A(1+r)(1+) . A(1+i) : A(1+i) = A(1+r)(1+), 1+i = (1+r)(1+) i : 73 . = A+Ar

(1) .

A(1+i) =

: 76Source: Expected inflation calculated using procedures outlined in Frederic S. Mishkin, The Real Interest Rate: An Empirical Investigation, Carnegie-Rochester Conference Series on Public Policy 15 (1981): 151200. These procedures involve estimating expected inflation as a function of past interest rates, inflation, and time trends. ) . ()

81 vs. (3 : 1943-2011)

Sources: Nominal rates from www.federalreserve.gov/releases/H15 and inflation from ftp://ftp.bis.gov/special.requests/cpi/cpia.txt. The real rate is constructed using the procedure outlined in Frederic S. Mishkin, The Real Interest Rate: An Empirical Investigation, Carnegie-Rochester Conference Series on Public Policy 15 (1981): 151200. This procedure involves estimating expected inflation as a function of past interest rates, inflation, and time trends and then subtracting the expected inflation measure from the nominal interest rate.89 , 70 ( 72 ) 70 ( 72) . 2% 70 8% 72 .

90 i(%) n i nN(70/i) 2% 35.0 70.0 35.0 3% 23.45 70.3 23.3 4% 17.67 70.7 17.5 5% 14.21 71.0 14.4 6% 11.90 71.4 11.7 7% 10.24 71.7 10.3 8% 9.01 72.1 8.8 9% 8.04 72.4 7.8 10% 7.27 72.7 7.0 12% 6.12 73.4 5.8 15% 4.96 74.4 4.7 20% 3.80 76.0 3.5 2 9170

1292

12

96 (period) : (periodic interest) : i 1 m (, ) = i/m (Frequency of compounding: m) : 1 (, ) 0 (continuous) . E97mIf i = 12%1i12%2i/26%4i/43%12i/121%365i/3650.033% 98 1 m . 1 . .

m=1 (APY) i x 100 . (APY; Annual Percentage Yield)99(P)(I) (P+I)6 A12

i $A ? 1 2 , 6 1 . .

100 , A

.

(APY)

101(P)(I)(P+I) 4 A 8 12

1 3 (APY):

. 102

1 m ? :

.

A, m 103 m ? , ( ) ? APY?

. m () . , () .

?

104

. m , h . m = h x i .

h ?

.105

h 2.718 .

e .

, . 106

.

. : A i 1 .

107

APY . APY m .

, APY =

108 : e 1 100% 1 . 1 100 1 ? A i 1 Aei . Aei = 1x e1 = e 2.718 . 109Im (APY) 5% 1 5%2 5%4 5%12 5%365 5%

5% 110 7-31 day 0.85 0.85 , $20,000 91 day 0.90 0.90 , $2,500 6 month 1.00 1.00 , $2,500 1 year 1.10 1.095 , $500 18 month 1.20 1.195 , $1,000 2 year 1.30 1.293 , $500 3 year 1.75 1.739 , $500 4 year 2.00 1.985 , $500 5 year 2.25 2.233 , $500 (CD) (2004 9)111 12% , ? ? . APR 1 . , . 112 1 ( 2 , 4 ) ? n =

14 = $81.92 28 = $1.34 million = x 365 = 100% x 365 = 36,500% APY =

=

=

113

A 1 3 2 ? A 1 m n ?

114128A424 20 16 (P+I)(I)(P)

3 A 2 115 . APR . Mortgage APR: (The Federal Truth in Lending law) APR . APR . : , APR . (APR; Annual Percentage Rate)116 600 16000 1 5 1% C 2004 3 17 . F 1% = 30% = 360% 117 = 66%( 5.5%) . 2002 10 (= ) ( 3 ) 2007 9 49% . 2010 7 44% . 2011 6 39% . . 118 : 400% - 800% . ( risk premium .) , 119

600 ( 1% )

(: ) 30%() 12 600 1 4 120 600 ( 1% )

(:)345584759449()3 600 759 . 121 , 600 . 1% 36 759 . 6,000 100% 3 7590 . 40 3 .. (, , ) . , . 122 / :

: : , , , , . : . . Chart13.8715004.8614005.9413007.1312008.48110010100011.7590013.8180016.2770019.3260023.2750028.7440037.1730053.05200

Yield to Maturity(%)Price of Bond($)

Chart23.874.865.947.138.481011.7513.8116.2719.3223.2728.7437.1753.05

Yield to Maturity(%)53.0537.173.874.865.947.138.481011.7513.8116.2719.3223.2728.74

Sheet1Price of Bond($)Yield to Maturity(%)15003.8714004.8613005.9412007.1311008.4810001090011.7580013.8170016.2760019.3250023.2740028.7430037.1720053.05100100.85

Sheet2

Sheet3

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5 26 74732 36243 99257801 397913184894

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Chart20.0780.10140.131820.1713660.22277580.289608540.3764911020.4894384330.6362699620.8271509511.0752962361.3978851071.817250642.3624258313.0711535813.9924996555.1902495526.747324417

5 26 74732 36243 99257801 397913184894

Sheet110.07878020.1014101430.131821318.240.1713661713.6650.22277582227.75860.289608542896.085470.3764911023764.9110280.48943843264894.38432690.63626996246362.6996238100.82715095118271.50951094111.075296236410752.962364222121.397885107313978.8510734886131.817250639618172.5063955352142.362425831423624.2583141958153.071153580830711.5358084545163.992499655139924.9965509908175.190249551651902.4955162881186.747324417167473.2441711745198.771521742387715.21742252692011.4029782649114029.7826492852114.8238717444148238.717444072219.2710332677192710.3326772922325.052343248250523.4324804792432.5680462225325680.4622246232542.3384600892423384.6008920092655.039998116550399.9811596122771.5519975507715519.9755074962893.017596816930175.96815974529120.92287586081209228.7586076730157.1997386191571997.3861899731204.35966020472043596.6020469632265.66755826612656675.5826610533345.36782574593453678.2574593634448.97817346974489781.7346971735583.67162551065836716.2551063236758.77311316387587731.13163822

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