Ризик и принос - utms.cc fakultet/II godina...Required rate of return = Risk-free rate...
Transcript of Ризик и принос - utms.cc fakultet/II godina...Required rate of return = Risk-free rate...
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Ризик и принос
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Rizik i stapki na prinosRisk and Rates of Return
Return
Risk
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RIZIK
• Kako da go izmerime rizikot -varijansa, standardna devijacija,
beta (variance, standard deviation, beta)• Kako da se reducira rizikot
(diverzifikacija)• Kako da se vrednuva rizikot (How to price risk)(security market line, CAPM)
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Za dr`avna hartija od vrednost (Treasury security), koja e baranata stapka na
prinos (required rate of return)?
Requiredrate of return
=
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Requiredrate of return
=Risk-free
rate ofreturn
Za dr`avna hartija od vrednost (Treasury security), koja e o~ekuvana stapka na prinos
(required rate of return)?
Poradi toa {to Treasury’s se vo osnovaoslobodeni od kreditniot rizik (default risk),baranata stapka na prinos na dr`avnitehartii od vrednost e ednakva na bezrizi~nastapka na prinos ( “risk‐free” rate of return).
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Requiredrate of return
=
Za korporativni akcii i obvrznici, koja e baranata stapka na prinos?
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Requiredrate of return
=Risk-free
rate ofreturn
Za korporativni akcii i obvrznici, koja e baranata stapka na prinos?
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Requiredrate of return
=Risk-free
rate ofreturn
+Risk
Premium
Za korporativni akcii i obvrznici, koja e baranata stapka na prinos
Pra{aweto e: Kolku treba da bide golema premijata za rizik koja ja barame (risk premium) za da kupime
korporativni obvrznici?
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Definicija za prinos (Return)
Ostvaren prihod od investicijata plus promena na pazarnata cena, izrazena
kako procent od po~etnata pazarna cena od investicijata.
Dt + (Pt - Pt-1 )Pt-1
R =
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Primer
Cenata na akcijata A iznesuva{e $10 po akcija (per share) pred 1 godina. Akcijata momentalno se trguva za $9.50 per share, a akcionerite dobija $1 dividenda. Koj prinos e zaraboten vo tekot na minatata godina?
$1.00 + ($9.50 - $10.00 )$10.00R = = 5%
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Prinosi (Returns)
• O~ekuvan prinos (Expected Return) – prinos koj investitorot o~ekuva da go zaraboti od sredstvoto, od negovata cena, potencijalen rast i sl.
• Baran prinos (Required Return) – prinos koj investitorot go bara za odredeno sredstvo zaradi negoviot rizik (return that an investor requires on an asset given its risk).
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O~ekuvan prinos (Expected Return)
State of Probability ReturnEconomy (P) Orl. Utility Orl. TechRecession .20 4% ‐10%Normal .50 10% 14%Boom .30 14% 30%P (probability)- verojatnostR (return)- mo`en prinosZa sekoja firma, o~ekuvan prinos na akcija e ponderiran prosek (the expected return on the stock is just a weighted average):
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O~ekuvan prinos (Expected Return)
State of Probability ReturnEconomy (P) Orl. Utility Orl. TechRecession .20 4% ‐10%Normal .50 10% 14%Boom .30 14% 30%
Za sekoja firma, o~ekuvan prinos na akcija e ponderiran prosek (the expected return on the stock is just a weighted average):
k = P(k1)*k1 + P(k2)*k2 + ...+ P(kn)*kn
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O~ekuvan prinos (Expected Return)
State of Probability ReturnEconomy (P) Orl. Utility Orl. TechRecession .20 4% ‐10%Normal .50 10% 14%Boom .30 14% 30%
k = P(k1)*k1 + P(k2)*k2 + ...+ P(kn)*kn
k (OU) = .2 (4%) + .5 (10%) + .3 (14%) = 10%
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O~ekuvan prinos (Expected Return)
State of Probability ReturnEconomy (P) Orl. Utility Orl. TechRecession .20 4% ‐10%Normal .50 10% 14%Boom .30 14% 30%
k = P(k1)*k1 + P(k2)*k2 + ...+ P(kn)*kn
k (OI) = .2 (‐10%)+ .5 (14%) + .3 (30%) = 14%
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Presmetuvawe na o~ekuvaniot prinos (Expected Return)
R = ( Ri )( Pi )R – o~ekuvan prinos za sredstvoto,Ri – prinos za i‐ verojatnost,Pi – verojatnost deka }e se slu~i prinosot,n – vkupen broj na mo`nostite.
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Ako treba da se odlu~ite samo vrz osnova na
o~ekuvaniot prinos, za koja akcija vie bi se
odlu~ile?
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Dali razmislivteza rizikot?
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[to e rizik (Risk)?
• Verojatnost deka ostvareniot prinos(actual return) }e bide razli~en od na{iot o~ekuvan prinos (expected return).
• Nesigurnosta na mo`nite ishodi(Uncertainty in the distribution of possible outcomes).
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[to e rizik?• Nesigurnosta na mo`nite
ishodi.
00.05
0.10.15
0.20.25
0.30.35
0.40.45
0.5
4 8 12
Company A
return
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[to e rizik?• Nesigurnosta na mo`nite
ishodi.
00.020.040.060.080.1
0.120.140.160.180.2
-10 -5 0 5 10 15 20 25 30
Company B
return
00.05
0.10.15
0.20.25
0.30.35
0.40.45
0.5
4 8 12
Company A
return
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Kako go merime rizikot(How do we Measure Risk)?• Za da dobiete osnovna idea za
varijabilnosta na cenite na akciite, bi trebale da gi poglednete cenite na akciite vo izminatite godini.
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Kako go merime rizikot?• Mnogu podobar i sekako nau~en priod e
ispituvawe na standardnata devijacija na prinosite na akciite (stock’s STANDARD DEVIATION of returns).
• Standardnata devijacija e merka na disperzija na mo`nite ishodi (measure of the dispersion of possible outcomes).
• Kolku e pogolema standardnata devijacija, tolku e pogolema nesigurnosta i ottuka povisok e rizikot(The greater the standard deviation, the greater the uncertainty, and therefore , the greater the RISK).
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Standardna Devijacija
n
i=1= (ki ‐ k) P(ki)
2
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• Standardnata devijacija se presmetuva preku slednite ~ekori:
• se presmetuva o~ekuvaniot prinos (R ‐ return)• se odzema o~ekuvanata stapka na prinos (R) od mo`nite
stapki na prinos (Ri), i se dobiva serija - niza na devijacii od R:
• Devijacija = Ri ‐ R• Se kvadrira sekoja devijacija (zatoa {to ima i negativni
broevi), se mno`i rezultatot so verojatnosta (P) na takviot ishod i se sobira za da se dobie varijansa na distribucijata na verojatnosta:
• Varijansa = 2 = Ri ‐ R2Pi• Se vadi kvadraten koren od varijansata za da se dobie
standardnata devijacija
ii PRR 2
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Orlando Utility, Inc.
= (ki - k) P(ki)2 n
i=1
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Orlando Utility, Inc. ( 4% ‐ 10%)2 (.2) = 7.2
n
i=1= (ki - k) P(ki)2
n
i=1
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Orlando Utility, Inc. ( 4% ‐ 10%)2 (.2) = 7.2(10% ‐ 10%)2 (.5) = 0
= (ki - k) P(ki)2 n
i=1
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Orlando Utility, Inc. ( 4% ‐ 10%)2 (.2) = 7.2(10% ‐ 10%)2 (.5) = 0(14% ‐ 10%)2 (.3) = 4.8
= (ki - k) P(ki)2 n
i=1
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Orlando Utility, Inc. ( 4% ‐ 10%)2 (.2) = 7.2(10% ‐ 10%)2 (.5) = 0(14% ‐ 10%)2 (.3) = 4.8Variance = 12
= (ki - k) P(ki)2 n
i=1
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Orlando Utility, Inc. ( 4% ‐ 10%)2 (.2) = 7.2(10% ‐ 10%)2 (.5) = 0(14% ‐ 10%)2 (.3) = 4.8Variance = 12Stand. dev. = 12 = 3.46%
= (ki - k) P(ki)2 n
i=1
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Orlando Technology, Inc.
= (ki - k) P(ki)2 n
i=1
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Orlando Technology, Inc. (‐10% ‐ 14%)2 (.2) = 115.2
= (ki - k) P(ki)2 n
i=1
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Orlando Technology, Inc. (‐10% ‐ 14%)2 (.2) = 115.2(14% ‐ 14%)2 (.5) = 0
= (ki - k) P(ki)2 n
i=1
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Orlando Technology, Inc. (‐10% ‐ 14%)2 (.2) = 115.2(14% ‐ 14%)2 (.5) = 0(30% ‐ 14%)2 (.3) = 76.8
= (ki - k) P(ki)2 n
i=1
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Orlando Technology, Inc. (‐10% ‐ 14%)2 (.2) = 115.2(14% ‐ 14%)2 (.5) = 0(30% ‐ 14%)2 (.3) = 76.8Variance = 192
= (ki - k) P(ki)2 n
i=1
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Orlando Technology, Inc. (‐10% ‐ 14%)2 (.2) = 115.2(14% ‐ 14%)2 (.5) = 0(30% ‐ 14%)2 (.3) = 76.8Variance = 192Stand. dev. = 192 = 13.86%
= (ki - k) P(ki)2 n
i=1
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Koeficient na varijacijaCoefficient of Variation
Mera za relativnata disperzija, koja se koristi za sporedba na rizkot na oddelni sredstva vo odnos na razli~nite o~ekuvani prinosi od istite.Toa e merka za RELATIVNOSTA na rizikot.
CV = / RCV of OT = .1386 / .14 = 0.99
CV of OU = 0.0346 / .14 = 0.02
CV na OU e pomal, {to zna~i deka e pomalku rizi~no vlo`uvaweto.
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Koja akcija vie bi izbrale?
Kako }e odlu~ite?
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Koja akcija vie bi izbrale?Kako }e odlu~ite?
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Rezime
Orlando OrlandoUtilityTechnology
Expected Return 10% 14%
Standard Deviation 3.46% 13.86%
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• Toa zavisi od va{ata tolerancija na rizikot (tolerance for risk)!
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Toa zavisi od va{ata tolerancija na rizikot!
Zapamtete postoi soodnos pome|u rizikot i prinosot (tradeoff between risk and return).
Return
Risk
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Stav kon rizikot (Risk Attitudes)
Ekvivalent na sigurnosta (Certainty Equivalent (CE) e iznos na pari koj investitorot bi go baral so sigurnost za da bide indiferenten pome|u odredeniot iznos i iznosot koj se o~ekuva deka }e se dobie so rizik vo isto vreme.
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Risk Attitudes
Certainty equivalent > Expected valuePriem~ivi (Risk Preference)
Certainty equivalent = Expected valueRisk Indifference
Certainty equivalent < Expected valueRisk Aversion
Most individuals are Risk Averse.
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Primer
Imate izbor (1) $25,000 garantirani ili (2) nesiguren prihod od $100,000 (50% {ansi) ili $0 (50% {ansi). O~ekuvana vrednost od kockata e $50,000.
Vi ste Risk Averse ako izberete $25,000.Vie ste Risk Indifferent ako ne mo`ete da se odlu~ite.
Vie ste Risk Preference ako izbravte da se kockate za $0 ili $100,000.
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Portfolio (Portfolios)
• Kombinacija na nekolku hartii od vrednost vo portfolio mo`at definitivno da go reduciraat vkupniot rizik (Combining several securities in a portfolio can actually reduce overall risk).
• Kako toa se pravi?
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Pretpostavuvame deka imame akcija A i akcija B. Prinosite na ovie akcii nemaat isto dvi`ewe niz vreme (ne se perfektno korelirani).
rateof return
time
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Pretpostavuvame deka imame akcija A i akcija B. Prinosite na ovie akcii nemaat isto dvi`ewe niz vreme (ne se perfektno korelirani).
rateof return
time
kA
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Pretpostavuvame deka imame akcija A i akcija B. Prinosite na ovie akcii nemaat isto dvi`ewe niz vreme (ne se perfektno korelirani).
rateof return
time
kA
kB
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Pretpostavuvame deka imame akcija A i akcija B. Prinosite na ovie akcii nemaat isto dvi`ewe niz vreme (ne se perfektno korelirani).
rateof return
time
kp
kA
kB
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[to se slu~uva so varijabilnosta na prinosite vo portfolioto?
rateof return
time
kp
kA
kB
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Diverzifikacija (Diversification)• Investirawe vo pove}e od edna hartija od
vrednost za da se reducira rizikot.• Dokolku dve akcii se perfektno pozitivno
korelirani diverzfikacijata nema efekt na rizikot (If two stocks are perfectly positivelycorrelated, diversification has no effect on risk).
• Dokolku dve akcii se perfektno negativno korelirani portfolioto e perfektno diverzifizirano (If two stocks are perfectly negatively correlated, the portfolio is perfectlydiversified).
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Koeficient na korelacija (Correlation Coefficient)
Koeficientot na korelacija go meri iznosot vo koj prinosot od hartiite od vrednost se vo odnos eden so drug.– Pozitivna korelacija zna~i deka prinosite na
hartiite od vrednost se dvi`at zaedno (ako edna raste, raste i drugata).
– Negativna korelacija zna~i deka prinosite se dvi`at vo sprotivna nasoka.
– Nula korelacija (Zero correlation) zna~i deka prinosite ne se povrzani eden so drug.
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Presmetka na o~ekuvan prinos na portfolioto(Portfolio Expected Return)
RP = ( Wj )( Rj )RP – o~ekuvan prinos na portfolioto,Wj – u~estvo (investiciona proporcija) na j
sredstvoto vo portfolioto,Rj – o~ekuvan prinos na sredstvoto j,m – vkupen broj na sredstva vo portfolioto.
Prinosot na portfolio e ednostavno ponderirana sredina na prinosot od oddelnite hartii od vrednost.
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Presmetka na Standardna Devijacija na portfolioto
• Rizikot na portfolio ne e ponderirana prose~na sredina na standardnite devijacii na oddelnite hartii od vrednost. Rizikot na portfolioto ne zavisi samo od rizi~nosta na hartiite od vrednost, koi go so~inuvaat portfolioto, tuku i od vrskite koi postojat pome|u tie hartii od vrednost.
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Presmetka na Standardna Devijacija na portfolioto
• Ne e mo`no da se presmeta standardna devijacija na prinosot na portfolioto so ednostavno presmetuvawe ponderirana sredina na standardnite devijacii na oddelnite hartii od vrednost. Namesto toa, standardnata devijacija na distribucijata na verojatnosta na mo`noto portfolio iznesuva:
m ‐ vkupniot broj na hartii od vrednost vo portfolio, Aj ‐ del od vkupnite pari koj e investiran vo hartija od
vrednost j; Ak ‐ del investiran vo hartija od vrednost kσ‐ kovarijansa pome|u prinosite za j i k sredstvo
m
j
m
kjkkjp AA
1 1
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[to e kovarijansa (Covariance)?
jk = j k r jk
j ‐ standardna devijacija na j sredstvoto vo portfolioto,
k ‐ standardna devijacija na ksredstvoto vo portfolioto,
rjk – koeficient na korelacija pome|u j i k sredstvo vo portfolioto.
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Primer za rizik na portfolioto i o~ekuvan prinos
Portfolio Risk and Expected Return
Imate portfolio od Akcija D i Akcija BW. Investirate $2,000 vo Akcija BW i $3,000 vo Akcija D. O~ekuvan prinos i standardna devijacija na Akcijata D se 8%i 10.65%, a na akcijata BW e 0.9 i 0.1315. Koeficient na korelacija pome|u BW i D e 0.75.
Koj e o~ekuvaniot prinos i standardna devijacija na portfolioto?
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Presmetka na o~ekuvan prinos na portfolioto
Determining Portfolio Expected ReturnWBW = $2,000 / $5,000 = .4WD = $3,000 / $5,000 = .6
RP = (WBW)(RBW) + (WD)(RD)RP = (.4)(9%) + (.6)(8%)
RP = (3.6%) + (4.8%) = 8.4%
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Presmetka na standardna devijacija na portfolioto
Determining Portfolio Standard DeviationPortfolio od 2 sredstva:Col 1 Col 2
Row 1WBW WBW BW,BW WBW WD BW,D
Row 2 WD WBW D,BW WD WD D,D
Ova e matrica varijansa-kovarijansa za dva sredstva vo portfolioto.
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Presmetka na standardna devijacija na portfolioto
Two‐asset portfolio:Col 1 Col 2
Row 1 (.4)(.4)(.0173) (.4)(.6)(.0105)Row 2 (.6)(.4)(.0105) (.6)(.6)(.0113)
Vneseni se vrednostite vo matricata na variance ‐ covariance.
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Presmetka na standardna devijacija na portfolioto
Two‐asset portfolio:Col 1 Col 2
Row 1 (.0028) (.0025)Row 2 (.0025) (.0041)
Presmetani se vrednosti vo matricata variance ‐covariance.
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Presmetka na standardna devijacija na portfolioto
P = .0028 + (2)(.0025) + .0041P = SQRT(.0119)
P = .1091 or 10.91%Standardna devijacija na prinosot na portfolioto ne e ponderirana sredina
na standardnite devijacii na oddelnite hartii od vrednost.
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Summary of the Portfolio Return and Risk Calculation
Stock C Stock D PortfolioReturn 9.00% 8.00% 8.64%Stand.Dev. 13.15% 10.65% 10.91%CV 1.46 1.33 1.26
Portfolioto ima najnizok koeficient na varijacija kako rezultat na diverzifikacijata.
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Diversification and the Correlation Coefficient
Combining securities that are not perfectly positively correlated reduces risk.
Combining securities that are not perfectly positively correlated reduces risk.
INVE
STM
ENT
RET
UR
N
TIME
SECURITY E SECURITY FCombination
E and F
TIME TIMETIME
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Premija za rizik vo kontekst na portfolioRisk Premiums in a Portfolio Context
• Za rizik koj mo`e da se diverzificira ne trebapremija za rizik (risk premium).
• Pazarot bara prinos za premijata koja se odnesuvana u~estvoto na sredstvoto vo rizikot nadiverzificiranoto portfolio.
• Diverzifikacijata funkcionira poradi toa {tocenite na akcite ne se dvi`at ednakvo.
• Rizikot na portfolioto zavisi prvo od rizikot naindividualnoto sredstvo i vtoro soodnosot naprinosite na sredstvata vo portfolioto.
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• Dokolku poseduvate udeli na sekoja akcija so koja se trguva na NYSE i NASDAQ, dali }e bidete diverzificirani?DA!
• Dali ste gi eliminirale site va{i rizici?
NE! Portfolijata na obi~ni akcii seu{te sodr`at rizik (Pr. Oktomvri1987 stock market “crash?”)
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Nekoi rizici mo`at da bidat diverzificirani, a nekoi nemo`at.
• Pazaren rizik (Market Risk) - u{te nare~en - nediverzificiran rizik (Nondiversifiable risk). Takviot rizik ne mo`e da se diverzificira. (Sistemski rizik)
• Specifi~en rizik (Firm‐Specific risk) u{te nare~en diverzificiran rizik (diversifiable risk). Takviot vid na rizik mo`e da se reducira preku diverzifikacija. (Nesistemski rizik)
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Rizici• Vkupen rizik = sistemski rizik +
nesistemski rizik
Systematic versus Unsystematic Risk
Total Risk = Market Risk + Unique RiskMarket Risk = Systematic RiskUnique Risk = Unsystematic, or Diversifiable Risk
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• Sistemskiot rizik e neizbe`en, odnosno toa e onoj rizik koj ne mo`e da se diverzificira, dodeka nesistemskiot mo`e da se izbegne ili da se diverzificira.
• Sistemskiot rizik gi opfa}a vkupnite pazarni rizici (promeni koi ja opfa}aat celata nacionalna ekonomija, dano~ni reformi, promeni vo svetskata ekonomija i sl.), odnosno rizici koi va`at za site hartii od vrednost i koi ne mo`at da se eliminiraat so diverzifikacija. Duri i investitor koj poseduva mnogu diverzificirano portfolio e izlo`en na ovoj vid na rizik.
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• Vtoriod vid rizik (nesistemskiot) e specifi~en za sekoja pooddelna kompanija i ne zavisi od ekonomskite, politi~kite i drugi faktori, koi vlijaat na hartiite od vrednost na sistemski na~in. Taka na primer, {trajk vo kompanijata mo`e da ima vlijane vrz edna kompanija ili pojavata na nov konkurent i nova tehnologija. So diverzifikacija ovoj vid rizik mo`e da se reducira, pa duri i potpolno da se eliminira, dokolku diverzifikacijata e efikasna.
• Poradi toa, ne e relevanten celokupniot rizik na dr`ewe na portfolioto, zatoa {to del od nego mo`e zasekoga{ da se otkloni so diverzifikacija.
• Nesistemskiot rizik s# pobavno se pribli`uva kon nulata, so dodavawe novi, slu~ajno izbrani hartii od vrednost vo portfolioto. Razli~ni istra`uvawa poka`uvaat deka e dovolno da se zemat 15-20 slu~ajno izbrani akcii, za da se eliminira najgolemiot del od nesistemskiot rizik na edno portfolio. Toa zna~i deka mo`e da se postigne zna~itelno reducirawe na nesistemskiot rizik ve}e so umerena diverzifikacija.
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Pazaren rizik - Market Risk
• Neo~ekuvani promeni vo kamatnite stapki.
• Neo~ekuvani promeni vo pari~nite tekovi kako rezultat na promeni na dano~nite stapki, vlijanieto na stranska konkurencija i celokupniot biznis ciklus.
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Specifi~ni rizici
Firm-Specific Risk• [trajk na rabotnicite vo firmata od koja sme gi kupile akciite.
• Menaxerite na kompanijata zaginale vo avionskla nesre}a.
• Poplava, po`ar, zagaduvawe na okolinata na kompanijata, zemjotres i sl.
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So dodavawe (kupuvawe) na novi akcii vo va{eto portfolio, specifi~niot rizik za firmata se reducira.
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portfoliorisk
number of stocks
Kako dodavate novi akcii vo va{eto portfolio, specifi~niot rizik za firmata se reducira.
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portfoliorisk
number of stocksMarket risk
Kako dodavate novi akcii vo va{eto portfolio, specifi~niot rizik za firmata se reducira.
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Kako dodavate novi akcii vo va{eto portfolio, specifi~niot rizik za firmata se reducira.
portfoliorisk
number of stocksMarket risk
Firm-specificrisk
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Dali nekoi kompanii imaat pogolem pazaren rizik od drugite?
DA. Na primer:Promenite na kamatnite stapki vlijaat na site firmi, no na nekoi pove}e :
a) Trgovija so prehrambeni stoki na malo b) Delovna banka
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DA. Na primer:Promenite na kamatnite stapki vlijaat na site firmi, no na koi pove}e :
a)Trgovija so prehrambeni stoki na malo b) Delovna banka
Dali nekoi kompanii imaat pogolem pazaren rizik od drugite?
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• ZapamtetePazarot gi kompenzira investitorite za prifateniot rizik- no samo za pazarniot rizik(market risk). Specifi~niot rizik(Firm‐specific risk) mo`e i treba da se diverzificira.
Zatoa – treba da znaeme da go izmerime pazarniot rizik.
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Zatoa nie ja imame BETA.
Beta: merka za pazaren rizik (a measure of market risk).
Poto~no, toa e merka za varijabilnosta na prinosot na odredena individualna akcija vo odnos na pazarnite prinosi. ( Specifically, it is a measure of how an individual stock’s returns vary with market returns).
Toa e merka za ostelivosta na prinosot na individualna akcija vo odnos na promenite na pazarot. (It’s a measure of the “sensitivity” of an individual stock’s returns to changes in the market).
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• Firma koja ima beta = 1 ima prose~en pazaren rizik. Akcijata ne e ni pove}e ni pomalku promenliva (nepostojana-volatile) od pazarot.
• Firma so beta > 1 e popromenliva (more volatile) od pazarot (pr. Kompjuterska firma).
• Firma so beta < 1 e pomalku promenliva(less volatile) od pazarot (pr. ESM‐utilities).
Pazarnata beta =1The market’s beta is 1
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BETA
• Betata e, zna~i, indikator za rizikot na imotot vo odnos na pazarot vo celina ili nekoj drug sporedben indikator (Standard & Pur 500) ili nekoj drug alternativen parametar. Beta e merilo na sistemskiot rizik na investicii vo razni sredstva.
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Betas for Stocks in Different Industries
• Textile Companies Retailers• Burlington Industries 0.70 Dayton Hudson 1.05• Cone Mills 0.70 Federated Stores 1.15• Guilford Mills 0.60 JC Penney 0.95• Unifi 0.65 Sears, Roebuck 1.10• Westpoint Stevens 0.60 Wal‐Mart 0.95• Foreign Electronics Firms Gold/Silver Mining Companies• Hitachi 0.75 Barrick Gold 0.70• NEC Corporation 0.70 Coeur D’Alene Mines 0.75• Pioneer Electronics 0.80 Homestake 0.65• Sony Corporation 0.95 Newmont Mining 0.70• Philips Electronics 1.25 Placer Dome, Inc. 0.90
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Presmetka na Beta
-5-15 5 10 15
-15
-10
-10
-5
5
10
15
XYZ Co. returns
S&P 500returns
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Presmetka na Beta
-5-15 5 10 15
-15
-10
-10
-5
5
10
15
XYZ Co. returns
S&P 500returns
. . . .
. . . .. . . .. . . .
. . . .
. . . .
. . . .. . . .
. . .
. . . .
. . . .
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Presmetka na Beta
-5-15 5 10 15
-15
-10
-10
-5
5
10
15
XYZ Co. returns
S&P 500returns
. . . .
. . . .. . . .. . . .
. . . .
. . . .
. . . .. . . .
. . .
. . . .
. . . .
Beta = nagib= 1.20
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Pravecot koj e prilagoden na to~kite ja opi{uva funkcionalnatavrska pome|u natprose~nite prinosi na oddelna hartija odvrednost i o~ekuvanite prinosi na pazarnoto portfolio. Ovojpravec e poznat kako karakteristi~en pravec i se koristi kakomerka na o~ekuvanata funkcionalna vrska koja postoi pome|u oviedva vida natprose~ni prinosi.
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The Characteristic LineKarakteristi~en pravec e odnos pome|u istoriskiteprinosi za individualna hartija od vrednost napazarot. Taa se dobiva so sobirawe na podatocite zaindividualna hartija od vrednost i presmetka navkupniot prinos za odredena godina. Podatoci zapo{iroki portfolia, kako S&P 500, mo`at, istotaka, da se sobiraat za da go poka`at mo`niot setna prinosi na pazarot. Prika`uvawe na takvitepodatoci na grafikon i stavawe na linija niz nivkoja najdobro odgovara na regresionata analiza nija dava karakterist~i~~nata linija ili pravec.
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Rezime:
• Nau~ivme kako se meri rizikot, so koristewe na standardna devijacija za vkupniot rizik i beta za pazarniot rizik.
• Nau~ivme kako se reducira vkupniot rizik -samo na pazaren (sistemski rizik) preku diverzifikacija.
• Potrebno e da znaeme kako da go vrednuvame rizikot (how to price risk) za da znaeme kolku dopolnitelen prinos }e barame za prifa}awe na dopolnitelen rizik (accepting extra risk).
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[to e barana stapka na prinos?What is the Required Rate of Return?
• Prinos na investicija baran od investitorot zaradi investicioniot rizik.
• The return on an investment required by an investor given the investment’s risk.
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Requiredrate of return
=
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Requiredrate of return
=Risk-free
rate ofreturn
+
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Requiredrate of return
=Risk-free
rate ofreturn
+Risk
Premium
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Requiredrate of return
=Risk-free
rate ofreturn
+Risk
Premium
MarketRisk
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Requiredrate of return
=Risk-free
rate ofreturn
+Risk
Premium
MarketRisk
Firm-specificRisk
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= +Required
rate of return
Risk-freerate ofreturn
RiskPremium
MarketRisk
Firm-specificRisk
can be diversifiedaway
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Requiredrate of return
Beta
Da se obideme da go prika`eme odnosot grafi~ki!
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Requiredrate of return
Risk-freerate ofreturn(6%)
Beta
12% .
1
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Requiredrate of return
Risk-freerate ofreturn(6%)
Beta
12% .
1
securitymarket
line (SML)
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Linija na kapitalnite pazari
Capital Market Line (CML) ili SML pretstavuva pazarensoodnos pome|u rizikot i prinosot za efikasniportfolija i se kombinacija pome|u bezrizi~nitesredstva i pazarni portfolia.
Kombinacijata pome|u bezrizi~nite sredstva irizi~nite portfolia investitorite gi pravat vozavisnost na svoite preferencii na rizikot.
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Linija na kapitalnite pazari
M = 1.0Systematic Risk (Beta)
Rf
RM
Req
uire
d R
etur
n
RiskPremium
Risk-freeReturn
Rj = Rf + j(RM - Rf)
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B
Standard deviation
Expe
cted
retu
rn
A
A is the minimum-risk-minimum-expected return portfolio
B is the maximum-risk-maximum-expected return portfolio
The Efficient Frontier
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Efikasni horizontiEfficient Frontier
• Mo`na kombinacija (Opportunity Set)– Site mo`ni kombinacii na rizik i prinos koi mo`at da se
napravat so odreden hartii od vrednost.
• Efikasni horizonti ili efikasni kombinacii (Efficient Frontier orEfficient Set)– Portfolia koi imaat najvisok prinos za odredeno nivo na
rizik ili
– Portfolia koi imaat najnizok rizik za odredeno nivo naprinos.
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G
Standard deviation
Expe
cted
retu
rn M
CD
Rf
FE
Capital market line
F
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Takviot linearen odnos pome|u rizikot i baranata stapka na prinos e poznata
kako Model za ocenka na kapitalni sredstva.
This linear relationship between risk and required return is known as the Capital
Asset Pricing Model (CAPM).
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Requiredrate of return
Risk-freerate ofreturn(6%)
Beta
12% .
1
SML
0
Dali postoi bezrizi~na (zero beta) hartija od
vrednost?
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Requiredrate of return
Beta
12% .
1
SML
0
Dali postoi bezrizi~na(zero beta) hartija od vrednost?
Treasurysecurities se
najblisku dobezrizi~nosta
Risk-freerate ofreturn(6%)
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Requiredrate of return
Beta
12% .
1
SMLKade se nao|a S&P 500na SML?
Risk-freerate ofreturn(6%)
0
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Requiredrate of return
Beta
12% .
1
SMLKade se nao|a S&P 500na SML?
S&P 500 e dobra aproksimacija
na pazarotRisk-free
rate ofreturn(6%)
0
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Requiredrate of return
Beta
12% .
1
SML
UtilityStocks
Risk-freerate ofreturn(6%)
0
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Requiredrate of return
Beta
12% .
1
SMLHigh-techstocks
Risk-freerate ofreturn(6%)
0
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Capital Asset Pricing Model (CAPM)
CAPM e model koj go objasnuva odnosot pome|u rizikot i o~ekuvaniot (baraniot) prinos; vo ovoj model, o~ekuvaniot (baraniot) prinos na hartijata od vrednost e risk‐free rate(bezrizi~nata stapka) plus premium (premija za rizik) bazirana na systematic risk(sistemskiot rizik) na hartijata od vrednost.
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CAPM ravenka:
kj = krf + β(km ‐ krf)
kade:kj = barana stapka na prinos na sredstvo j (Required
Return on security j),krf = bezrizi~na kamatna stapka (the risk‐free rate of
interest),β = beta na hartija od vrednost j (the beta of security j),
km = prinos na pazarniot indeks (the return on the market index).
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Primer:
• Pretpostavete deka stapka naTreasury bond e 6%, prose~niot prinos na S&P 500 index e 12%, a firmata Walt Disney ima beta = 1.2.
• Spored CAPM, kolku treba da iznesuva baranata stapka na prinos(required rate of return) na Disney stock?
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kj = krf + (km - krf)
kj = .06 + 1.2 (.12 ‐ .06)kj = .132 = 13.2%
Soglasno CAPM, Disney stock treba da bidat vrednuvani so 13.2% prinos.
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Osnovni poraki na CAPM
• Ako sakate da zarabotite povisoki prinosi, morate da bidete podgotveni da prevzemete povisoki rizici.
• Ako ne ste celosno diverzificirani, ste prevzemale rizik bez nadomest.
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Requiredrate of return
Beta
12% .
1
SML
0
Teoretski, sekoja hartija od vrednosttreba da le`i na SML
Risk-freerate ofreturn(6%)
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Requiredrate of return
Beta
12% .
1
SML
0
Teoretski, sekoja hartija od vrednosttreba da le`i na SML
Ako sekoja akcija e na SML, investitorite se celosno kompenzirani
za rizikot.Risk-free
rate ofreturn(6%)
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Requiredrate of return
Beta
12% .
1
SML
0
Ako HV e nad SML, taa ePodceneta (underpriced).
Risk-freerate ofreturn(6%)
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Requiredrate of return
Beta
12% .
1
SML
0
Ako HV e nad SML, taa e Podceneta (underpriced).
Ako HV e pod SML, taa e preceneta (overpriced).
Risk-freerate ofreturn(6%)
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Determination of the Required Rate of Return
Lisa Miller at Basket Wonders is attempting to determine the rate of return required by their stock investors. Lisa is using a 6% Rf and a long‐term market expected rate of return of 10%. A stock analyst following the firm has calculated that the firm beta is 1.2. What is the required rate of return on the stock of Basket Wonders?
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BWs Required Rate of Return
RBW = Rf + j(RM ‐ Rf)RBW = 6% + 1.2(10% ‐ 6%)
RBW = 10.8%The required rate of return exceeds the market
rate of return as BW’s beta exceeds the market beta (1.0).
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Determination of the Intrinsic Value of BW
Lisa Miller at BW is also attempting to determine the intrinsic value of the stock. She is using the constant growth model. Lisa estimates that the dividend next
period will be $0.50 and that BW will grow at a constant rate of 5.8%. The stock is currently selling
for $15.
What is the intrinsic value of the stock? Is the stock over or underpriced?
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Determination of the Intrinsic Value of BW
The stock is OVERVALUED as the market price ($15) exceeds the intrinsic value ($10).The stock is OVERVALUED as the market
price ($15) exceeds the intrinsic value ($10).
$0.5010.8% - 5.8%
IntrinsicValue
=
= $10
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Practice Problem:• Find the intrinsic value of a common stock with the following information:
• ROE = 20%• 50% retention of earnings• Beta = 1.4• recent dividend = $4.30• Treasury bond yield = 7.5%• Return on the S&P 500 = 12%• Market price for common stock = $100• Should you buy the stock?