Chapter 6 - Risk and Rates of Return
description
Transcript of Chapter 6 - Risk and Rates of Return
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Chapter 6 - Risk and Rates of Return
Return
Risk
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Tujuan Pembelajaran
Mahasiswa mampu untuk: Menjelaskan hubungan antara tingkat imbal hasil yang diharapkan dengan risikoMenjelaskan efek inflasi atas tingkat imbal hasil Menjelaskan term structure dari tingkat bungaMendefinisikan dan mengukur tingkat imbal hasil yang diharapkan dan risiko dari suatu suatu investasi Menjelaskan pengaruh diversifikasi terhadap imbal hasil yang diharapakan dan tingkat risiko dari suatu portofolio atau kombinasi asetMengukur risiko pasar dari suatu aset dan portofolio investasi Menjelaskan hubungan antara tingkat imbal hasil yang diminta investor dan tingkat risiko dari suatu investasi
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Pokok Bahasan
Tingkat imbal hasil di Pasar Keuangan Efek inflasi terhadap tingkat imbal hasil dan Efek FisherTerm Strucuture dari tingkat bungaTingkat imbal hasil yang diharapkanRisiko Risiko dan diversifikasiMengukur risiko pasarMengukur beta dari suatu portofolio Ttingkat imbal hasil yang diminta investor
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Inflation, Rates of Return, and the Fisher Effect
InterestRates
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Conceptually:Nominalrisk-freeInterest
Rate krf
=
Realrisk-freeInterest
Rate k*
+
Inflation-risk
premiumIRP
Mathematically:
(1 + krf) = (1 + k*) (1 + IRP)
This is known as the “Fisher Effect”
Interest Rates
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Interest Rates
Suppose the real rate is 3%, and the nominal rate is 8%. What is the inflation rate premium?
(1 + krf) = (1 + k*) (1 + IRP)(1.08) = (1.03) (1 + IRP)(1 + IRP) = (1.0485), so
IRP = 4.85%
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Term Structure of Interest RatesThe pattern of rates of return for debt securities that differ only in the length of time to maturity.
yieldto
maturity
time to maturity (years)
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Term Structure of Interest Rates
The yield curve may be downward sloping or “inverted” if rates are expected to fall.
yieldto
maturity
time to maturity (years)
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Term Structure of Interest Rates
The yield curve may be downward sloping or “inverted” if rates are expected to fall.
yieldto
maturity
time to maturity (years)
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For a Treasury security, what is the required rate of return?
Since Treasuries are essentially free of default risk, the rate of return on a Treasury security is considered the
“risk-free” rate of return.
Requiredrate of return
=Risk-freerate of return
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For a corporate stock or bond, what is the required rate of return?
How large of a risk premium should we require to buy a corporate security?
Requiredrate of return
= +Risk-freerate of return
Riskpremium
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Returns
Expected Return - the return that an investor expects to earn on an asset, given its price, growth potential, etc.
Required Return - the return that an investor requires on an asset given its risk and market interest rates.
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Expected Return
State of Probability ReturnEconomy (P) Orl. Utility Orl. TechRecession .20 4% -10%Normal .50 10% 14%Boom .30 14% 30%For each firm, 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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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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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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Based only on your expected return
calculations, which stock would you
prefer?
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RISK?Have you considered
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What is Risk?
The possibility that an actual return will differ from our expected return.
Uncertainty in the distribution of possible outcomes.
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What is Risk?Uncertainty in the distribution of possible outcomes.
return
00.020.040.060.080.1
0.120.140.160.180.2
-10 -5 0 5 10 15 20 25 30
Company B
00.050.1
0.150.2
0.250.3
0.350.4
0.450.5
4 8 12
Company A
return
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How do We Measure Risk?
To get a general idea of a stock’s price variability, we could look at the stock’s price range over the past year.
52 weeks Yld Vol NetHi Lo Sym Div % PE 100s Hi Lo Close Chg134 80 IBM .52 .5 21 143402 98 95 9549 -3
115 40 MSFT … 29 558918 55 52 5194 -475
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How do We Measure Risk?
A more scientific approach is to examine the stock’s standard deviation of returns.Standard deviation is a measure of the dispersion of possible outcomes. The greater the standard deviation, the greater the uncertainty, and, therefore, the greater the risk.
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Standard Deviation
= (ki - k)2 P(ki)s n
i=1S
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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)2 P(ki)s n
i=1S
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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)2 P(ki)s n
i=1S
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Which stock would you prefer?How would you decide?
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Summary Orlando Orlando
UtilityTechnology
Expected Return 10% 14%
Standard Deviation 3.46% 13.86%
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It depends on your tolerance for risk!
Remember, there’s a tradeoff between risk and return.
Return
Risk
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Portfolios
Combining several securities in a portfolio can actually reduce overall risk.How does this work?
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Suppose we have stock A and stock B. The returns on these stocks do not tend to move together over time (they are not perfectly correlated).
rateof
return
time
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Suppose we have stock A and stock B. The returns on these stocks do not tend to move together over time (they are not perfectly correlated).
rateof
return
time
kA
kB
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rateof
return
time
kpkA
kB
What has happened to the variability of returns for the
portfolio?
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Diversification
Investing in more than one security to reduce risk.If two stocks are perfectly positively correlated, diversification has no effect on risk.If two stocks are perfectly negatively correlated, the portfolio is perfectly diversified.
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If you owned a share of every stock traded on the NYSE and NASDAQ, would you be diversified?
YES!Would you have eliminated all of your risk?
NO! Common stock portfolios still have risk.
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Some risk can be diversified away and some cannot.
Market risk (systematic risk) is nondiversifiable. This type of risk cannot be diversified away.Company-unique risk (unsystematic risk) is diversifiable. This type of risk can be reduced through diversification.
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Market Risk
Unexpected changes in interest rates.Unexpected changes in cash flows due to tax rate changes, foreign competition, and the overall business cycle.
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Company-unique Risk
A company’s labor force goes on strike.A company’s top management dies in a plane crash.A huge oil tank bursts and floods a company’s production area.
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As you add stocks to your portfolio, company-unique risk is reduced.
portfoliorisk
number of stocks
Market risk
company-unique
risk
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Do some firms have more market risk than others?
Yes. For example:Interest rate changes affect all firms,
but which would be more affected:a) Retail food chainb) Commercial bank
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NoteAs we know, the market compensates
investors for accepting risk - but only for market risk. Company-unique risk can and should be diversified away.
So - we need to be able to measure market risk.
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This is why we have Beta.
Beta: a measure of market risk. Specifically, beta is a measure of how an individual stock’s returns vary with market returns.
It’s a measure of the “sensitivity” of an individual stock’s returns to changes in the market.
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The market’s beta is 1
A firm that has a beta = 1 has average market risk. The stock is no more or less volatile than the market.A firm with a beta > 1 is more volatile than the market.
(ex: technology firms)A firm with a beta < 1 is less volatile than the market.
(ex: utilities)
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Calculating Beta
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Calculating Beta
-5-15 5 10 15
-15
-10
-10
-5
5
10
15
XYZ Co. returns
S&P 500returns
. . . .
. . . .. . . .. . . .
. . . .
. . . .
. . . .. . . .
. . .
. . . .
. . . .
Beta = slope = 1.20
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Summary:
We know how to measure risk, using standard deviation for overall risk and beta for market risk.We know how to reduce overall risk to only market risk through diversification.We need to know how to price risk so we will know how much extra return we should require for accepting extra risk.
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What is the Required Rate of Return?
The return on an investment required by an investor given market interest rates and the investment’s risk.
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marketrisk
company-unique risk
can be diversifiedaway
Requiredrate of return
= +Risk-freerate of return
Riskpremium
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Requiredrate of return
Beta
Let’s try to graph thisrelationship!
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Requiredrate of return
.
Risk-freerate ofreturn(6%)
Beta
12%
1
securitymarket
line (SML)
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This linear relationship between risk and required return is known as the Capital Asset
Pricing Model (CAPM).
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Requiredrate of return
Beta
.12%
1
SML
0
Is there a riskless(zero beta) security?
Treasurysecurities are
as close to risklessas possible. Risk-free
rate ofreturn(6%)
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Requiredrate of return
.
Beta
12%
1
SMLWhere does the S&P 500fall on the SML?
The S&P 500 isa good
approximationfor the market
Risk-freerate 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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The CAPM equation:
kj = krf + j (km - krf )
where:kj = the required return on security
j,krf = the risk-free rate of interest, j = the beta of security j, and km = the return on the market index.
b
b
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Example:
Suppose the Treasury bond rate is 6%, the average return on the S&P 500 index is 12%, and Walt Disney has a beta of 1.2.According to the CAPM, what should be the required rate of return on Disney stock?
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kj = krf + (km - krf )
kj = .06 + 1.2 (.12 - .06)kj = .132 = 13.2%
According to the CAPM, Disney stock should be priced to give a 13.2% return.
b
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Requiredrate of return
.
Beta
12%
1
SML
0
Theoretically, every security should lie on the SML
If every stock is on the SML,
investors are being fully compensated for risk.Risk-free
rate ofreturn(6%)
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Requiredrate of return
.
Beta
12%
1
SML
0
If a security is abovethe SML, it isunderpriced.
If a security is below the SML, it
is overpriced.Risk-freerate ofreturn(6%)
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Pt+1 60
Pt 50
Simple Return Calculations
= = 20%Pt+1 - Pt 60 - 50
Pt 50
- 1 = -1 = 20%
t t+1
$50 $60
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(a) (b)monthly expected
month price return return (a - b)2
Dec $50.00Jan $58.00Feb $63.80Mar $59.00Apr $62.00May $64.50Jun $69.00Jul $69.00Aug $75.00Sep $82.50Oct $73.00Nov $80.00Dec $86.00
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(a) (b)monthly expected
month price return return (a - b)2
Dec $50.00Jan $58.00 0.160 0.049 0.012321Feb $63.80 0.100 0.049 0.002601Mar $59.00 -0.075 0.049 0.015376Apr $62.00 0.051 0.049 0.000004May $64.50 0.040 0.049 0.000081Jun $69.00 0.070 0.049 0.000441Jul $69.00 0.000 0.049 0.002401Aug $75.00 0.087 0.049 0.001444Sep $82.50 0.100 0.049 0.002601Oct $73.00 -0.115 0.049 0.028960Nov $80.00 0.096 0.049 0.002090Dec $86.00 0.075 0.049 0.000676
0.0781St. Dev: sum, divide by (n-1), and take sq root: