Chapter_005 - Rui Ro Va Loi Suat
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Transcript of Chapter_005 - Rui Ro Va Loi Suat
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McGraw-Hill/Irwin © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved.
Rủi ro và lợi suât
CHAPTER 5
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5.1 Lợi suất
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Holding Period Return
1 0 1
0
0
1
1
Beginning PricePEnding PriceP
D Cash Dividend
P P DHPRP
− +
===
=
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Rates of Return: Single Period Example
Ending Price =Ending Price = 2424Beginning Price = Beginning Price = 2020Dividend =Dividend = 11
HPR = ( 24 HPR = ( 24 -- 20 + 1 )/ ( 20) = 25%20 + 1 )/ ( 20) = 25%
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Đo lường lợi suất đầu tư trong nhiềukỳ
VD VD CCầầnn bibiếếtt mmộộtt ququỹỹ hohoạạtt đđộộngng nhưnhư ththếếnnààoo trongtrong 5 5 nămnăm vvừừaa quaquaTrongTrong trưtrườờngng hhợợpp nnààyy đođo lưlườờngng llợợii susuấấtthơihơi mơmơ hhồồ
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Rates of Return: Multiple Period Example Text (Page 128)
Data from Table 5.1Data from Table 5.1
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Lợi suất bình quân số học và hình họcArithmetic and Geometric Averaging
SSốố hhọọcc ((Arithmetic)Arithmetic)rra a = (r= (r11 + r+ r22 + r+ r33 + ... r+ ... rnn) / n) / nrra a = (.10 + .25 = (.10 + .25 -- .20 + .25) / 4.20 + .25) / 4
= .10 or 10%= .10 or 10%HHììnhnh hhọọcc ((Geometric)Geometric)rrgg = {[(1+r= {[(1+r11) (1+r) (1+r22) .... (1+r) .... (1+rnn)]} )]} 1/n 1/n -- 11rrgg = {[(1.1) (1.25) (.8) (1.25)]} = {[(1.1) (1.25) (.8) (1.25)]} 1/4 1/4 -- 11
= (1.5150) = (1.5150) 1/4 1/4 --1 = .0829 = 8.29%1 = .0829 = 8.29%
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Lợi suất bình quân theo tỉ trọngDollar Weighted Returns
SuSuấấtt hohoàànn vvốốnn nnộộii bbộộInternal Rate of Return (IRR)Internal Rate of Return (IRR) ––MMứứcc llợợii susuấấtt chichiếếtt khkhấấuu llààmm chocho PV PV ccủủaa ccáácc dòngdòng titiềềnntrongtrong tươngtương lailai bbằằngng ssốố titiềềnn đđầầuu tưtưXemXem xxéétt đđếếnn nhnhữữngng thaythay đđổổii trongtrong ssốố titiềềnn đđầầuu tưtưDòngDòng titiềềnn đđầầuu tưtư ban ban đđầầuu llàà mmộộtt outflowoutflowGiGiáá trtrịị Ending value Ending value đưđượợcc xemxem llàà mmộộtt inflowinflowCCáácc khokhoảảnn đđầầuu tưtư thêmthêm (Additional investment) (Additional investment) llàà dòngdòngtitiềềnn âmâmCCáácc khokhoảảnn gigiảảmm titiềềnn đđầầuu tưtư llàà dòngdòng titiềềnn dươngdương
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Dollar Weighted Average Using Text Example (Page 128)
Net CFsNet CFs 11 2 3 42 3 4$ (mil)$ (mil) -- 0.1 0.1 --0 .5 0.8 1.00 .5 0.8 1.0
2 3 4
0.1 0.5 0.8 1.01.0 4.17%1 (1 ) (1 ) (1 )IRR IRR IRR IRR− −
= + + + =+ + + +
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Cách yết lãi suấtQuoting Conventions
APR = annual percentage rateAPR = annual percentage rateLLợợii susuấấtt thưthườờngng niênniên
(periods in year) X (rate for period)(periods in year) X (rate for period)EAR = effective annual rateEAR = effective annual rateLLợợii susuấấtt thưthườờngng niênniên hihiệệuu ququảả
( 1+ rate for period)( 1+ rate for period)Periods per yrPeriods per yr -- 11Example: monthly return of 1%Example: monthly return of 1%
APR = 1% X 12 = 12%APR = 1% X 12 = 12%EAR = (1.01)EAR = (1.01)1212 -- 1 = 12.68%1 = 12.68%
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5.2 Rủi ro và mức bù rủi ro
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Phân tích kịch bản (Scenario Analysis) và phân bố xác suất
1) 1) GiGiáá trtrịị trungtrung bbììnhnh (Mean): (Mean): GiGiáá trtrịị xxảảyy raranhinhiềềuu nhnhấấtt most likely valuemost likely value
2) 2) PhươngPhương saisai vvàà đđộộ llệệchch chuchuẩẩnn (Variance (Variance or standard deviation)or standard deviation)
3) 3) ĐĐộộ nghiêngnghiêng ((SkewnessSkewness))
* If a distribution is approximately normal, * If a distribution is approximately normal, the distribution is described by the distribution is described by characteristics 1 and 2characteristics 1 and 2
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rrSymmetric distributionSymmetric distribution
Normal Distribution
s.d. s.d.
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rrNegativeNegative PositivePositive
Skewed Distribution: Large Negative Returns Possible
Median
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rrNegativeNegative PositivePositive
Skewed Distribution: Large Positive Returns Possible
Median
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Subjective returnsSubjective returns
p(s) = xác suất xảy ra kịch bảnr(s) = Lợi suất khi xảy ra kịch bản 1 to sp(s) = xác suất xảy ra kịch bảnr(s) = Lợi suất khi xảy ra kịch bản 1 to s
Đo lường lợi suất bình quân: Scenario or Subjective Returns
1( ) ( ) ( )
S
tE r p s r s
=
=∑
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Numerical Example: Subjective or Scenario Distributions
StateState Prob. of StateProb. of State rrinin StateState11 .1.1 --.05.0522 .2.2 .05.0533 .4.4 .15.1544 .2.2 .25.2555 .1.1 .35.35
E(r) = (.1)(E(r) = (.1)(--.05) + (.2)(.05)...+ (.1)(.35).05) + (.2)(.05)...+ (.1)(.35)E(r) = .15 or 15%E(r) = .15 or 15%
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Đo lường phương sai / độ phân tán lợi suấtMeasuring Variance or Dispersion of ReturnsSubjective or ScenarioSubjective or Scenario
[ ]2
1( ) ( ) ( ) ( )
s
tVar r p s r s E r
=
= −∑
( ) ( )SD r Var rσ≡ =
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Measuring Variance or Dispersion of Returns
Using Our Example:Using Our Example:
Var =[(.1)(Var =[(.1)(--.05.05--.15)2+(.2)(.05.15)2+(.2)(.05-- .15)2...+ .1(.35.15)2...+ .1(.35--.15)2].15)2]Var= .01199Var= .01199S.D.= [ .01199]S.D.= [ .01199]1/21/2 = .1095 or 10.95%= .1095 or 10.95%
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Mức bủ rủi ro (Risk Premiums) và sự thận trọng với rủi ro (Risk Aversion)
MMứứcc đđộộ rrủủii roro mmàà nhnhàà đđầầuu tưtư chchấấpp nhnhậậnn đđểể bbỏỏtitiềềnn rara đđầầuu tưtư–– Risk aversionRisk aversion
If TIf T--Bill denotes the riskBill denotes the risk--free rate, free rate, rrff, and , and variance, variance, σσ22 , denotes volatility of returns , denotes volatility of returns then:then:
The risk premium of a portfolio is:The risk premium of a portfolio is:
2Pσ
( )P fE r r−
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Mức bủ rủi ro (Risk Premiums) và sự thận trọng với rủi ro (Risk Aversion)
To quantify the degree of risk aversion with To quantify the degree of risk aversion with parameter A:parameter A:
Or:Or:
21( )2P f PE r r Aσ− =
2
( )12
P f
P
E r rA
σ
−=
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The Sharpe (Reward-to-Volatility) MeasureChỉ số Sharp
portfolio risk premiumstandard deviation of portfolio excess return
( )P f
P
S
E r rσ
=
−=
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5.3 Số liệu trong quá khứ
THE HISTORICAL RECORD
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Annual Holding Period ReturnsLợi suất cho giai đoạn đầu tư tính theo năm
From Table 5.3 of Text
Geom.Geom. Arith.Arith. Stan.Stan.SeriesSeries Mean%Mean% Mean%Mean% Dev.%Dev.%World StkWorld Stk 9.809.80 11.3211.32 18.0518.05US Lg StkUS Lg Stk 10.2310.23 12.1912.19 20.1420.14US Sm StkUS Sm Stk 12.4312.43 18.1418.14 36.9336.93Wor BondsWor Bonds 5.805.80 6.176.17 9.059.05LT Treas.LT Treas. 5.355.35 5.645.64 8.068.06TT--BillsBills 3.723.72 3.773.77 3.113.11InflationInflation 3.04 3.04 3.133.13 4.274.27
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Lợi suất thặng dư trong giai đoạn đầu tư tính theo nămAnnual Holding Period Excess Returns
From Table 5.3 of Text
RiskRisk Stan. Sharpe Stan. Sharpe SeriesSeries Prem. Dev.% MeasurePrem. Dev.% MeasureWorld StkWorld Stk 7.567.56 18.3718.37 0.410.41US Lg StkUS Lg Stk 8.42 20.428.42 20.42 0.410.41US Sm StkUS Sm Stk 14.37 37.5314.37 37.53 0.380.38Wor BondsWor Bonds 2.40 8.922.40 8.92 0.270.27LT TreasLT Treas 1.881.88 7.877.87 0.240.24
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Figure 5.1 Frequency Distributions of Holding Period Returns
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Figure 5.2 Rates of Return on Stocks, Bonds and T-Bills
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Figure 5.3 Normal Distribution with Mean of 12% and St Dev of 20%
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5.4 Lạm phát và lãi suất thực tế
INFLATION AND REAL RATES OF RETURN
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Lãi suất danh nghĩa và lãi suất thực tếReal vs. Nominal Rates
Fisher effect: ApproximationFisher effect: Approximationnominal rate = real rate + inflation premiumnominal rate = real rate + inflation premium
R = r + i or r = R R = r + i or r = R -- ii
Example r = 3%, i = 6%Example r = 3%, i = 6%R = 9% = 3% + 6% or 3% = 9% R = 9% = 3% + 6% or 3% = 9% -- 6%6%
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Lãi suất danh nghĩa và lãi suất thực tếReal vs. Nominal Rates
Fisher effect: Fisher effect:
2.83% = (9%2.83% = (9%--6%) / (1.06)6%) / (1.06)
11 or:1
1
Rri
R iri
++ =
+−
=+
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Figure 5.4 Lãi suất, lạm phát, và lãi suất thực tếInterest, Inflation and Real Rates of Return
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5.5 Phân bổ tài sản cho các danh mục córủi ro và phi rủi ro
ASSET ALLOCATION ACROSS RISKY AND RISK-FREE PORTFOLIOS
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CCáácc nhnhàà đđầầuu tưtư ccóó ththểể phânphân bbổổ vvốốnn đđầầuu tưtưvvààoo ttààii ssảảnn an an totoàànn vvàà ttààii ssảảnn ccóó rrủủii roroTTààii ssảảnn phi phi rrủủii roro:: proxy; T:: proxy; T--billsbillsTTààii ssảảnn ccóó rrủủii roro : : ccổổ phiphiếếuu ((hohoặặcc mmộộtt danhdanhmmụụcc))
Phân bổ vốn
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Phân bổ vốnAllocating Capital
CCáácc vvấấnn đđềề ccầầnn xemxem xxéétt–– MMốốii quanquan hhệệ đđáánhnh đđổổii gigiữữaa llợợii susuấấtt vvàà rrủủii roro–– MôMô ttảả nhnhữữngng mmứứcc đđộộ ththậậnn trtrọọngng vvớớii rrủủii roro
khkháácc nhaunhau ssẽẽ ảảnhnh hưhưởởngng nhưnhư ththếế nnààoo đđếếnnviviệệcc phânphân bbổổ ngunguồồnn llựựcc vvààoo ttààii ssảảnn ccóó rrủủii rorovvàà phi phi rrủủii roro
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Tài sản có rủi roThe Risky Asset:
Text Example (Page 143)
Total portfolio value = $300,000Total portfolio value = $300,000RiskRisk--free value = 90,000free value = 90,000Risky (Vanguard and Fidelity) = 210,000Risky (Vanguard and Fidelity) = 210,000Vanguard (V) = 54% Vanguard (V) = 54% Fidelity (F) = 46%Fidelity (F) = 46%
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The Risky Asset:Text Example (Page 143)
210,000 0.7(risky assets, portfolio )300,000
90,0001 0.3(risk-free assets)300,000
y P
y
= =
− = =
Vanguard 113,400/300,000 = 0.378
Fidelity 96,600/300,000 = 0.322
Portfolio P 210,000/300,000 = 0.700
Risk-Free Assets F 90,000/300,000 = 0.300
Portfolio C 300,000/300,000 = 1.000
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rf = 7%rf = 7% σrf = 0%σrf = 0%
E(rp) = 15%E(rp) = 15% σp = 22%σp = 22%
y = % in py = % in p (1-y) = % in rf(1-y) = % in rf
Calculating the Expected Return Text Example (Page 145)
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E(rc) = yE(rp) + (1 - y)rfE(rc) = yE(rp) + (1 - y)rf
rc = complete or combined portfoliorc = complete or combined portfolio
For example, y = .75For example, y = .75E(rc) = .75(.15) + .25(.07)E(rc) = .75(.15) + .25(.07)
= .13 or 13%= .13 or 13%
Lợi suất kỳ vọng của danh mụcExpected Returns for Combinations
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Figure 5.5 Tập hợp các danh mục đầu tư khi kết hợp vớimột tài sản phi rủi ro
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ppcc ==
SinceSince rfrf
yy
= 0, then= 0, thenσσ
σσσσ
Phương sai của các danh mục có thể được thiết lậpVariance on the Possible Combined Portfolios
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cc = .75(.22) = .165 or 16.5%= .75(.22) = .165 or 16.5%If y = .75, thenIf y = .75, then
cc = 1(.22) = .22 or 22%= 1(.22) = .22 or 22%If y = 1If y = 1
cc = 0(.22) = .00 or 0%= 0(.22) = .00 or 0%If y = 0If y = 0
Khi kết hợp mà không sử dụng đòn bẩy tài chínhCombinations Without Leverage
σσ
σσ
σσ
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Sử dụng đòn bẩy tài chính với đường CALcapital asset line
VayVay titiềềnn ởở mmứứcc lãilãi susuấấtt phi phi rrủủii roro vvàà đđầầuu tưtưvvààoo ccổổ phiphiếếuu
Using 50% LeverageUsing 50% Leveragerrcc = (= (--.5) (.07) + (1.5) (.15) = .19.5) (.07) + (1.5) (.15) = .19
σσcc = (1.5) (.22) = .33= (1.5) (.22) = .33
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Sự thận trọng với rủi ro và việc phân bổ vốnRisk Aversion and Allocation
CCààngng ththậậnn trtrọọngng vvớớii rrủủii roro ththìì đđầầuu tưtư vvààoottààii ssảảnn phi phi rrủủii roro ccààngng nhinhiềềuuCCààngng íítt ththậậnn trtrọọngng vvớớii rrủủii roro ththìì ccààngng đđầầuutưtư nhinhiềềuu vvààoo ccáácc danhdanh mmụụcc ttààii ssảảnn ccóó rrủủiiroroKhiKhi chchấấpp nhnhậậnn rrủủii roro caocao đđểể đđạạtt đưđượợcc llợợiinhunhuậậnn caocao ththìì ddẫẫnn đđếếnn nhnhữữngng ssựự kkếếtt hhợợppccóó ssửử ddụụngng đònđòn bbẩẩyy
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5.6 Các chiến lược đầu tư thụ động vàđường thị trường vốn
PASSIVE STRATEGIES AND THE CAPITAL MARKET LINE
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Table 5.5 Average Rates of Return, Standard Deviation and Reward to
Variability
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Lơi ích và chi phí của việc đầu tư thụ độngCosts and Benefits of Passive Investing
CCáácc chichiếếnn lưlượợcc đđầầuu tưtư chchủủ đđộộngng kkééoo theotheo nhinhiềềuuchi chi phphííLLợợii ííchch ccủủaa ngưngườờii điđi theotheo đđáámm đôngđông–– FreeFree--rider benefitrider benefit
MMộộtt trongtrong ccáácc hhììnhnh ththứứcc đđầầuu tưtư ththụụ đđộộngng llàà ĐĐầầuutưtư vvààoo 2 2 danhdanh mmụụcc ththụụ đđộộngng–– ShortShort--term Tterm T--billsbills–– QuQuỹỹ đđầầuu tưtư vvààoo ccổổ phiphiếếuu thưthườờngng ddựựaa theotheo chchỉỉ ssốố ththịị
trưtrườờngng (Fund of common stocks that mimics a broad (Fund of common stocks that mimics a broad market index)market index)