第二篇微观金融运行

interestinterest rate

(market interest rate) (controlled interest rate)

(fixed interest rate)(floating interest rate)

(nominal interest rate)(real interest rate )(6-4)

Time Value of Money

(Simple Interest)(Principal) 6-5

SIPin

(Compound Interest)compounding

Future Value:6-6FVnnnPV

(Future Value Interest Factor)6-4

1

1.021.041.061.081.11.121.14

1.04041.08161.12361.16641.211.25441.2996

1.0612081.1248641.1910161.2597121.3311.4049281.481544

1.082432161.169858561.262476961.360488961.46411.573519361.68896016

1.10408080321.21665290241.33822557761.46932807681.610511.76234168321.9254145824

1.12616241931.26531901851.41851911231.58687432291.7715611.97382268522.1949726239

1.14868566761.31593177921.5036302591.71382426881.94871712.21068140742.5022687913

1.1716593811.36856905041.59384807451.85093021032.143588812.47596317632.8525864221

1.19509256861.42331181241.6894789591.99900462712.3579476912.77307875753.2519485212

1.218994421.48024428491.79084769652.15892499732.59374246013.10584820833.7072213141

1.24337430841.53945405631.89829855832.33163899712.85311670613.47854999334.2262322981

1.26824179461.60103221862.01219647182.51817011683.13842837673.89597599254.8179048198

1.29360663051.66507350732.13292826012.71962372623.45227121444.36349311175.4924114946

1.31947876311.73167644762.26090395582.93719362433.79749833584.88711228516.2613491038

1.34586833831.80094350552.39655819313.17216911424.17724816945.47356575937.1379379784

1.37278570511.87298124572.54035168473.42594264334.59497298646.13039365048.1372492954

1.40024141921.94790049562.69277278583.70001805485.0544702856.86604088849.2764641967

1.42824624762.02581651542.85433915293.99601949925.55991731357.68996579510.5751691843

1.45681117252.1068491763.02559950214.31570105916.11590904488.612761690412.05569287

1.4859473962.1911231433.20713547224.66095714386.72749994939.646293093313.7434898719

2%

4%

6%

8%

10%

12%

14%

Sheet1

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

11.0201.0401.0601.0801.1001.1201.140

21.0401.0821.1241.1661.2101.2541.300

31.0611.1251.1911.2601.3311.4051.482

41.0821.1701.2621.3601.4641.5741.689

51.1041.2171.3381.4691.6111.7621.925

61.1261.2651.4191.5871.7721.9742.195

71.1491.3161.5041.7141.9492.2112.502

81.1721.3691.5941.8512.1442.4762.853

91.1951.4231.6891.9992.3582.7733.252

101.2191.4801.7912.1592.5943.1063.707

111.2431.5391.8982.3322.8533.4794.226

121.2681.6012.0122.5183.1383.8964.818

131.2941.6652.1332.7203.4524.3635.492

141.3191.7322.2612.9373.7974.8876.261

151.3461.8012.3973.1724.1775.4747.138

161.3731.8732.5403.4264.5956.1308.137

171.4001.9482.6933.7005.0546.8669.276

181.4282.0262.8543.9965.5607.69010.575

191.4572.1073.0264.3166.1168.61312.056

201.4862.1913.2074.6616.7279.64613.743

21

22

23

24

25

26

27

Sheet1

0000000

0000000

0000000

0000000

0000000

0000000

0000000

0000000

0000000

0000000

0000000

0000000

0000000

0000000

0000000

0000000

0000000

0000000

0000000

0000000

2%

4%

6%

8%

10%

12%

14%

Sheet2

Sheet3

Annual Percentage RateAPREffective Annual Rate , EFF

Effective Annual Rate , EFF

meAPRe=2.71828(5)

6-1 10%

6%53 1

=59834.03

(Present Value)(6-6)PVFVin

(Present Value Interest Factor)1/(1+i)n(i)(n)11

6-7im1n

(Annuity)Ordinary Annuity, Immediate Annuity,

(Perpetuity)

C i

Net Present Value, NPV

CItCOtt

NPVOpportunity Cost of Fund, , Market Capitalization Rate

15100007258.8%16.5% 10000*0.7=7000PVO=7000510000PVI=[1/(1+0.065)5]*10000=7298.81NPV1=7298.81-7000=298.81>0PVO=7000570000.088*5*7000=3080PVI==[1/(1+0.065)5]*1080=7357.20NPV2=7357.20-7000=357.20NPV2NPV1

(Internal Rate of Return, IRR)

6-67.275%

x=0.065% IRR=7.3%+0.065%=7.365%

6-22 =1

(Law of One Price)

1:1.021:1.01(1.02-1.01)/1.01=1%

1:1.02, 1:1201:1241001:1241240012400120:1103.33103.331:1.02101.301.301.3%

(Zero-Coupon Bond)(Pure Discount Bond)

(Yield to Maturity) 110095%95=100-95=5=-/=(100-95)/95=5.26% 210090%90=100-90=10 5.41%i=(100/90)1/2-1=5.41% 51007%100=100*(1+0.07*5)=1356.19%i=(135/100)1/5-1=6.19%

Yield Curve 7-2

7-2

1

4.94929312463.37181464312.91125356792.91125356792.81932634692.81932634691.0172099666

7.32965.47294.1828494.1828493.9992043.357722251.0189893025

9.187.475.675.224.773.781.0198

9.45318634017.62899237665.77334257745.43244282484.74731500143.88455130581.022252415

9.80682348617.67575360415.85990749115.85990749114.7233837783.97953246131.0245903578

9.89721948877.71435877935.9170874565.9170874564.74734342524.14231266811.0264619755

1996-5-1

1996-8-23

1997-10-23

1998-3-25

1998-7-1

1998-12-7

2002-5-1

Sheet1

36123567-121-3(3)3-5(5)520361

5/15/932.169.188.829.3612.0612.247.567.568.468.648.829

7/11/933.1510.98910.9813.8614.049.189.1810.0810.2610.4410.62

1/1/953.1510.98910.9814.5814.769.189.1810.2610.4410.7110.89

7/1/953.1510.9810.0812.0615.1215.39.189.1810.4410.6210.9811.16

5/1/962.974.867.29.189.910.812.069.7210.9814.9415.128.828.82910.0810.1710.98

8/23/961.983.335.47.477.928.2899.1810.0811.712.428.287.9299.7210.1710.62

10/23/971.712.884.145.675.946.216.667.658.649.910.537.567.028.558.829.099.36

3/25/981.712.884.145.225.586.216.66

7/1/981.442.793.964.774.864.955.22

12/7/981.442.793.333.783.964.144.56.126.396.667.27.563.244.594.865.045.133.96

5/1/020.721.711.891.982.252.522.79

20%0.5761.3681.5121.5841.8002.0162.232

1.006975

0.250.51235

5/1/964.957.339.189.459.819.90

8/23/963.375.477.477.637.687.71

10/23/972.914.185.675.775.865.92

3/25/982.914.185.225.435.865.92

7/1/982.824.004.774.754.724.75

12/7/982.823.363.783.883.984.14

5/1/021.0171.0191.0201.0221.0251.026

20%1.0141.0151.0161.0181.0201.021

Sheet1

0000000

0000000

0000000

0000000

0000000

0000000

1996-5-1

1996-8-23

1997-10-23

1998-3-25

1998-7-1

1998-12-7

2002-5-1

Sheet2

Sheet3

10056% PV=100/(1+0.06)5= 74.73 236%PV=100/(1+0.06)3=83.96 7%PV=100/(1+0.07)3=81.63 5%PV=100/(1+0.05)3=86.38

7-3 7-4

(Coupon Bond)

PVnPMTiFV

(Par Bond)

(Premium Bond)100105%554%7-4PV=[1/0.04-1/(1+0.04)5*0.04]*(0.05*100)+[1/(1+0.04)5]*100=104.46104.46(Current Yield)=/=5/104.46=4.787%

100105%556%7-4PV=[1/0.06-1/(1+0.06)5*0.06]*(0.05*100)+[1/(1+0.06)5]*100=95.7995.79=/=5/95.79=5.22%

7-4 5%106102 =5/102=4.9%4.5 %102.24.5%4.6% PV=101.75

7-6knhc

kIChin

1010%100057%=+17-6i9.74%10%0.26%i=9.74%

PVttP0g N

1005%101:107%8/108%

DDM (D)P1-P0P0k 7-9

7-10

(7-10)

7-11 (7-11)(7-10)

(7-12)

D1=D2=Dt(7-12) (7-13)

(7-14) 0.102%P0=0.1/0.02=5

D 0g(7-15) (7-15)(7-12)

(7-16) g

0.205%6%P0=0.2(1+0.05)/(0.05-0.04)=21 P1=0.2(1+0.05)2/(0.05-0.04)=22.05 g =(22.05-21)/ 21=5%

(D)(E)(I)Dt=Et-It7-127-18

12

7-19 NPVI

A0.305%P0=0.3/0.05=6BA0.3055%8% h: I ie =0.044 =22.50

BA =22.50-6.00=12.50 C5%g=0.550.05=0.028, P0=(0.30.45)/(0.05-0.028)=6 D4%:g=0.550.04=0.022, P0=(0.30.45)/(0.05-0.022)=4.82 BA8%5%

MER t = Pt / Et MERPE(k)(NPVI)

20024920010.34 220010.2920024813.6013.60/0.29= 46.89720010.44120024816.93=16.93/0.441=38.392(38.39+46.897)/2=42.644

38.39 A63%25%8.67% 20-30%20%31.99230%29.563%8.0120024910.5130.9110.8832.008.5225.06

7-1 32001

1961MM

8-1

8-1

(credit risk)(price risk)

(interest rite risk)exchange rate risk(liquidity risk)

(purchasing power risk)(inflation risk)(business risk)

(national risk)solvency riskperformance risk

1550%30%10%-10%-30%0.10.20.40.20.15E(R)=0.1*50%+0.2*30%+0.4*10%+0.2*(-10%)+0.1*(-30%)=10%(expected yield)(8-1)RiPin

3 Var(R)(8-2) Var(R)=0.1*(50%-10%)2+0.2*(30%-10%)2 +0.4*(10%-10%)2+ 0.2*(-10% -10%)2+0.1*(-30% -10%)2 =480%

(8-3)

=22%

2 rating()48-13AAA3B8-2AB

potential losses

8-1 J4801998

8-2AB1970-1997Moodys Investors Sevvice,1997

Sheet1

(%)(%)

Aaa0.000.00

Aa0.050.12

A0.080.05

Baa0.200.29

Ba1.801.40

B8.305.03

3 4 5 8-2

(hedge)A

( insuring)A diversify

B10001:8.2568.2551000 B168.255

61:8.2768.27B8.25561:8.2068.20B8.255

C10001:8.2568.2551000 B16

61:8.2068.20B8.255 61:8.2768.27B8.255

D5100C1001:8.20 DC51:8.20100

1:8.10CD(8.20-8.10)X100=101:8.25DC(8.25-8.20)X100=51:8.20

BA10005B512%A510%8% BABA100010%AB10002% A8%-2%=6%2%B8%+2%=10%512%212%-10%5

D5%100ELIBOR+0.25%DE

gap managementA

LG(8-4)GALG>0G

Insuring

Insuring Contracts

7%A1000.5%8%80%

10%(10%-8%)80%100=1.61000.5%=0.51.6-0.5=1.1 5%(7%-5%)100=20.52-0.5=1.5

Financial OptionsStrike Price

Put Option

B5010 5%100B501100100B100100-1=991100110B110110-100-1=9

Call OptionAA55%5%10011053%112.43[1]A105

112.43 [1] 15%PV=[1/0.05-1/(1+0.05)4*0.05]*(0.05*100)+[1/(1+0.05)4]*100+0.05*100=105 3%PV=[1/0.031/(1+0.03)4*0.03]*(0.05*100)+[1/(1+0.03)4]*100+0.05*100=112.4315%PV=[1/0.051/(1+0.05)4*0.05]*(0.05*100)+[1/(1+0.05)4]*100+0.05*100=105 3%PV=[1/0.031/(1+0.03)4*0.03]*(0.05*100)+[1/(1+0.03)4]*100+0.05*100=112.43112.43-105-1=6.43

[1]

8.4

(efficient portfolio)(Markowitz Efficient Frontier)12 15%015%0.20 20 8384

w 1-w

(8-5) B0.05+0.25[0.15-0.05]=0.075

(8-6) B 0.20.25=0.05

8-68-5

(8-7) (8-4)RF,

12%8-512%=5%+(15%-5%)w, w=(10%-5%)/12%=83%

1w21-w,

8-8

8-9 E(R )E(R1) 1E(R2) 2Var(R)Var(R1)1Var(R2)2Com(R1,R2)

1

115%0.20210%0.1508-4

8-4

8-6

CC136%

8-78-58-6TT

8-108-11

8-7 CBE(rp)

8-7

8-12

Capital Asset Pricing Model CAPM

Capital Market Theory

112Market Portfolio

2 MMCapital Market Line, CML, 9.1

(9.1)E(rP)rfE(rM)MMarket Price of Risk

3MMMMarket Portfolio

(9.2)RbRM e`

(9.2)(9.3)(9.3)9.2

=M=p=pMpWi

1std(RM)

CML(9.4)(Security Market Line, SML),

(9.5)(9.5)(9.4) (9.6)

=0=1>1

1 (9.7)r,9.4

(passive invest strategy)122/3

21 kCAPMg(9.8)k (9.8)A0.35%AkkA4%A1.28%SMLkA=4%+1.2*(8%-4%)=8.8%(9.8)P0=0.3/(8.8%-5%)=9.09

2CC1.5, 5%10%SMLkA=5%+1.5*(10%-5%)=13%C13%

CAPM3 CAPM

CAPMCAPMMultifactor CAPM9.9

RFF1,F2,.Fk1KbpfkkE(RFK)k

9.109.9CAPMCAPMCAPM

CAPM (9.11)

CAPM

1976[3](arbitrage pricing theory, APT)CAPMCAPMAPTnmn>mn

APTi 9.12

E(Ri) ibij Fjj;eiiVii

(9.13)

(9.14)

(9.19)APTCAPMCAPMCAPMAPT

APTCAPMCAPMAPTCAPM[4]

(1)2000100 (2)20006%3(3) 20003(4)34%20001051 4%1003210020001310520001

31006%/4=1.5 105 106.5 100+1004%/4=101.0 5.5 20002000

2000105951 95200012 100200013 4%10033 100+1004%/4=101.0 95 1006%/4=1.5 96.5 4.5

(theoretic price of futures)

1rPPF9.20FPyr9.209.21

2PFrP9.229.229.219.219.21F=100+100(0.04-0.06)=9898r-y(r-y)net financing cost, NFCcost of carry9-1

1c9.230.2%, F=100+100[0.04-(0.06-0.002)]=98.2

2borrowing ratelending rate1rBPPFH9.24A2PFLrLP 9.24B9.24A9.24B3.5%4.5% FH=100+100[0.045-(0.06-0.002)]=98.7FL=100+100[0.035-(0.06-0.002)]= 97.7

call option

1$20$22$18$21$22$1$1809-6 =$22 =$1=$20 =$18 =$0 9-6

$20$2222$122-1$20$181818 22-1=18, =0.250.25 $22 22 0.25 1=4.5$18 18 0.25 = 4.5$4.5

12%$4.5 f $20 20 0.25 f = 5 f 5 f = 4.367 f = 0.633$ 0.633$ 0.633$ 4.367$ 0.633

2 STfTSS (u > 1 , d < 1)u-11-dTSd9-7

9-7 Su,fuSSd,fd

SSu x - fuSSd, x - fdSu x - fu = Sd, x - fd 9-25

x r Sx-f

9-25(9-26)(9-27)

(9-26)(9-27) = 1.1 , d = 0.9 , r = 0.12 , T = 0.25 , =1=0(9-27)p = (e0.03-0.9)/(1.1-0.9) = 0.65239-26 = e0.03( 0.6523 * 1 + 0.3477 * 0 = 0.633

3 9-260.50.99-26p1-p [pfu+(1-p)fd] 9-26

T9-279-28

risk-neutral world9-28:9-26

$20$22$18$2112%12%22p +18(1 p)= 20e0.12*0.25p=0.6523$10.65230.3477 0.6523 1 + 0.3477 0 = $0.6523: 0.6523e0.12*0.25=0.633

303031terminal stock prices23010

Black-ScholesBlackScholescTXSsrT 9-31

9-31a

9-31bN(x)01x

S=100 r=0.1010%X=95 T=0.25(3)s=0.50(50%)

N(0.43)=0.664 N(0.18)=0.5714

Black-ScholesBlack-ScholesBlack-ScholesFinance EngineeringMathematic FinanceReal options

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第二篇 微观金融运行

第二篇微观金融运行