chapter 6: risk and rates of return. chapter 6: objectives inflation and rates of return how to...
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Chapter 6: Risk and Chapter 6: Risk and Rates of ReturnRates of Return
Chapter 6: ObjectivesChapter 6: Objectives
Inflation and rates of returnInflation and rates of return How to How to measuremeasure risk risk
(variance, standard deviation, beta)(variance, standard deviation, beta) How to How to reducereduce risk risk
(diversification)(diversification) How to How to priceprice riskrisk
(security market line, Capital Asset (security market line, Capital Asset Pricing Model)Pricing Model)
Risk and ReturnRisk and Return
Annual Rates of Return 1926-2002Annual Rates of Return 1926-2002
Standard Deviation Real Average ReturnStandard Deviation Real Average Return
Small- 33.2% 13.8%Small- 33.2% 13.8%
Stock Stock
Large- 20.5 9.1Large- 20.5 9.1
StockStock
Long-term 8.7 3.1Long-term 8.7 3.1
Corp-bond Corp-bond
Long-term 9.4 2.7Long-term 9.4 2.7
Gov-bond Gov-bond
U.S. Tre-bill 3.2 0.7U.S. Tre-bill 3.2 0.7
Inflation, Rates of Return, Inflation, Rates of Return, and the Fisher Effectand the Fisher Effect
InterestRates
Conceptually:
Nominalrisk-freeInterest
Rate
krf
=
Realrisk-freeInterest
Rate
k*
+
Inflation-risk
premium
IRP
Mathematically:
(1 + krf) = (1 + k*) (1 + IRP)
This is known as the “Fisher Effect”
Interest RatesInterest Rates
Suppose the real rate is 3%, and the nominal Suppose the real rate is 3%, and the nominal rate is 8%. What is the inflation rate rate is 8%. What is the inflation rate premium?premium?
(1 + k(1 + krfrf) = (1 + k*) (1 + IRP)) = (1 + k*) (1 + IRP)
(1.08) = (1.03) (1 + IRP)(1.08) = (1.03) (1 + IRP)
(1 + IRP) = (1.0485),(1 + IRP) = (1.0485), so so
IRP = 4.85%IRP = 4.85%
Interest RatesInterest Rates
Term Structure of Interest RatesTerm Structure of Interest Rates
The pattern of rates of return for debt The pattern of rates of return for debt securities that differ only in the length of securities that differ only in the length of time to maturity.time to maturity.
yieldto
maturity
time to maturity (years)
Term Structure of Interest RatesTerm Structure of Interest Rates
yieldto
maturity
time to maturity (years)
The yield curve may be downward The yield curve may be downward sloping or “inverted” if rates are sloping or “inverted” if rates are expected to fall.expected to fall.
For a Treasury security, what is For a Treasury security, what is the required rate of return?the required rate of return?
Since Treasuries are essentially Since Treasuries are essentially free of free of default riskdefault risk, the rate of return on a , the rate of return on a Treasury security is considered the Treasury security is considered the
““risk-freerisk-free”” rate of return. rate of return.
RequiredRequired
rate of rate of
returnreturn==
Risk-freeRisk-free
rate of rate of
returnreturn
For a For a corporate stock or bondcorporate stock or bond, , what is the required rate of return?what is the required rate of return?
How large of a How large of a risk premiumrisk premium should we should we require to buy a corporate security? require to buy a corporate security?
RequiredRequired
rate of rate of
returnreturn== + +
Risk-freeRisk-free
rate of rate of
returnreturn
RiskRisk
premiumpremium
ReturnsReturns
Expected ReturnExpected Return - the return that an - the return that an investor expects to earn on an asset, investor expects to earn on an asset, given its price, growth potential, etc.given its price, growth potential, etc.
Required ReturnRequired Return - the return that an - the return that an investor requires on an asset given investor requires on an asset given itsits riskrisk and market interest rates.and market interest rates.
State of Probability ReturnState of Probability Return
Economy (P) Economy (P) Orl Utility Orl TechOrl Utility Orl Tech
Recession .20 4% -10%Recession .20 4% -10%
Normal .50 10% 14%Normal .50 10% 14%
Boom .30 14% 30%Boom .30 14% 30%
For each firm, the expected return on the For each firm, the expected return on the stock is just a stock is just a weighted averageweighted average::
k = P(kk = P(k11)*k)*k11 + P(k + P(k22)*k)*k22 + ...+ P(k + ...+ P(knn)*kn)*kn
Expected ReturnExpected Return
Expected ReturnExpected Return
State of Probability ReturnState of Probability Return
Economy (P) Economy (P) Orl Utility Orl TechOrl Utility Orl Tech
Recession .20 4% -10%Recession .20 4% -10%
Normal .50 10% 14%Normal .50 10% 14%
Boom .30 14% 30%Boom .30 14% 30%
k = P(kk = P(k11)*k)*k11 + P(k + P(k22)*k)*k22 + ...+ P(k + ...+ P(knn)*kn)*kn
k k (OU) (OU) = .2 (4%) + .5 (10%) + .3 (14%) = 10%= .2 (4%) + .5 (10%) + .3 (14%) = 10%
Expected ReturnExpected Return
State of Probability ReturnState of Probability Return
Economy (P) Economy (P) Orl Utility Orl TechOrl Utility Orl Tech
Recession .20 4% -10%Recession .20 4% -10%
Normal .50 10% 14%Normal .50 10% 14%
Boom .30 14% 30%Boom .30 14% 30%
k = P(kk = P(k11)*k)*k11 + P(k + P(k22)*k)*k22 + ...+ P(k + ...+ P(knn)*kn)*kn
kk(OT) (OT) = .2 (-10%)+ .5 (14%) + .3 (30%) = 14%= .2 (-10%)+ .5 (14%) + .3 (30%) = 14%
Based only on your Based only on your expected returnexpected return
calculations, which calculations, which stock would you stock would you
prefer?prefer?
RISK?Have you considered
What is Risk?What is Risk?
The possibility that an The possibility that an actualactual return return will differ from our will differ from our expectedexpected return. return.
Uncertainty in the distribution of Uncertainty in the distribution of possible outcomes.possible outcomes.
What is Risk?What is Risk? Uncertainty in the distribution of Uncertainty in the distribution of
possible outcomes.possible outcomes.
returnreturn
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
-10 -5 0 5 10 15 20 25 30
Company B
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
4 8 12
Company A
returnreturn
How do We Measure Risk?How do We Measure Risk?
To get a general idea of a stock’s To get a general idea of a stock’s price variability, we could look at price variability, we could look at the the stock’s price rangestock’s price range over the over the past year.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
How do We Measure Risk?How do We Measure Risk?
A more scientific approach is to A more scientific approach is to examine the stock’s examine the stock’s standard standard deviationdeviation of returns. of returns.
Standard deviation is a measure of Standard deviation is a measure of the the dispersion of possible outcomesdispersion of possible outcomes. .
The greater the standard deviation, The greater the standard deviation, the greater the uncertainty, and, the greater the uncertainty, and, therefore, the greater the risk.therefore, the greater the risk.
Standard DeviationStandard Deviation
= (k= (kii - k) - k)22 P(k P(kii)) n
i=1
Utility Utility
( 4% - 10%)( 4% - 10%)22 (.2) = 7.2 (.2) = 7.2
(10% - 10%)(10% - 10%)22 (.5) = 0 (.5) = 0
(14% - 10%)(14% - 10%)22 (.3) (.3) = = 4.84.8Variance = 12Variance = 12
Stand. dev. = 12 = Stand. dev. = 12 = 3.46%3.46%
Utility Utility
( 4% - 10%)( 4% - 10%)22 (.2) = 7.2 (.2) = 7.2
(10% - 10%)(10% - 10%)22 (.5) = 0 (.5) = 0
(14% - 10%)(14% - 10%)22 (.3) (.3) = = 4.84.8Variance = 12Variance = 12
Stand. dev. = 12 = Stand. dev. = 12 = 3.46%3.46%
= (ki - k)2 P(ki) n
i=1
TechnologyTechnology
(-10% - 14%)(-10% - 14%)22 (.2) = 115.2 (.2) = 115.2
(14% - 14%)(14% - 14%)22 (.5) = 0 (.5) = 0
(30% - 14%)(30% - 14%)22 (.3) (.3) = = 76.8 76.8Variance = 192Variance = 192
Stand. dev. = 192 = Stand. dev. = 192 = 13.86%13.86%
= (ki - k)2 P(ki) n
i=1
Which stock would you prefer?Which stock would you prefer?
How would you decide?How would you decide?
Orlando OrlandoOrlando Orlando
UtilityUtilityTechnologyTechnology
Expected ReturnExpected Return 10% 14%10% 14%
Standard DeviationStandard Deviation 3.46% 13.86%3.46% 13.86%
SummarySummary
It depends on your tolerance for risk! It depends on your tolerance for risk!
Remember, there’s a tradeoff between Remember, there’s a tradeoff between risk and return.risk and return.
Return
Risk
PortfoliosPortfolios
Combining several securities Combining several securities in a in a portfolioportfolio can actually can actually reduce overall riskreduce overall risk..
How does this work?How does this work?
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
rateof
return
time
kpkA
kB
What has happened to the variability of returns for the
portfolio?
DiversificationDiversification
Investing in Investing in more than onemore than one security security to to reduce riskreduce risk..
If two stocks are If two stocks are perfectly perfectly positivelypositively correlatedcorrelated, diversification has , diversification has no no effecteffect on risk. on risk.
If two stocks are If two stocks are perfectly perfectly negativelynegatively correlatedcorrelated, the portfolio is , the portfolio is perfectlyperfectly diversified.diversified.
If you owned a share of every stock If you owned a share of every stock traded on the NYSE and NASDAQ, traded on the NYSE and NASDAQ, would you be diversified?would you be diversified?
YES!YES! Would you have eliminated all of Would you have eliminated all of
your risk?your risk?
NO!NO! Common stock portfolios still Common stock portfolios still have risk. have risk.
Some risk can be diversified Some risk can be diversified away and some cannot.away and some cannot.
Market riskMarket risk ( (systematic risk)systematic risk) is is nondiversifiable. nondiversifiable. This type of risk This type of risk cannot be diversified away.cannot be diversified away.
Company-unique riskCompany-unique risk (unsystematic (unsystematic risk)risk) is is diversifiablediversifiable. This type of risk . This type of risk can be reduced through can be reduced through diversification.diversification.
Market RiskMarket Risk
Unexpected changes in interest Unexpected changes in interest rates.rates.
Unexpected changes in cash flows Unexpected changes in cash flows due to tax rate changes, foreign due to tax rate changes, foreign competition, and the overall competition, and the overall business cycle.business cycle.
Company-unique RiskCompany-unique Risk
A company’s labor force goes on A company’s labor force goes on strike.strike.
A company’s top management dies A company’s top management dies in a plane crash.in a plane crash.
A huge oil tank bursts and floods a A huge oil tank bursts and floods a company’s production area.company’s production area.
As you add stocks to your portfolio, As you add stocks to your portfolio, company-unique risk is reduced.company-unique risk is reduced.
portfoliorisk
number of stocks
Market risk
company-unique
risk
YesYes.. For example: For example:
Interest rate changes affect all firms, but Interest rate changes affect all firms, but which would be which would be moremore affected: affected:
a) Retail food chaina) Retail food chain
b) b) Commercial bankCommercial bank
Do some firms have more Do some firms have more market risk than others?market risk than others?
NoteNoteAs we know, the market compensates As we know, the market compensates
investors for accepting risk - but investors for accepting risk - but only for only for market riskmarket risk.. Company- Company-unique risk can and should be unique risk can and should be diversified away.diversified away.
So - we need to be able to So - we need to be able to measuremeasure market risk.market risk.
This is why we have This is why we have Beta.Beta.
Beta: a measure of market risk.Beta: a measure of market risk. Specifically, beta is a measure of how Specifically, beta is a measure of how
an individual stock’s returns vary an individual stock’s returns vary with market returns.with market returns.
It’s a measure of the It’s a measure of the “sensitivity”“sensitivity” of of an individual stock’s returns to an individual stock’s returns to changes in the market.changes in the market.
A firm that has a A firm that has a beta = 1beta = 1 has has average average market riskmarket risk. The stock is no more or less . The stock is no more or less volatile than the market.volatile than the market.
A firm with a A firm with a beta > 1beta > 1 is is more volatilemore volatile than than the market. the market. (ex: technology firms)(ex: technology firms)
A firm with a A firm with a beta < 1beta < 1 is is less volatileless volatile than than the market.the market. (ex: utilities)(ex: utilities)
The market’s beta is The market’s beta is 11
Calculating BetaCalculating Beta
-5-15 5 10 15
-15
-10
-10
-5
5
10
15
XYZ Co. returns
S&P 500returns
. . . .
. . . .. . . .
. . . .
. . . .
. . . .
. . . .
. . . .
. . .
. . . .
. . . .
Beta = slope = 1.20
PPt+1t+1 60 60
PPtt 50 50
Simple Return CalculationsSimple Return Calculations
= = = 20% = 20%PPt+1t+1 - P - Pt t 60 - 50 60 - 50
PPtt 50 50
- 1- 1 = = -1-1 = 20% = 20%
t t+1
$50 $60
Portfolio BetaPortfolio Beta
Beta of Portfolio =Beta of Portfolio =
ΣΣ (percent invested in stock j) * (percent invested in stock j) *
(Bate of stock j)(Bate of stock j)
Summary:Summary:
We know how toWe know how to measuremeasure risk, using risk, using standard deviationstandard deviation for overall risk for overall risk and and betabeta for market risk. for market risk.
We know how to We know how to reducereduce overall risk overall risk to only market risk through to only market risk through diversificationdiversification..
We need to know how to We need to know how to priceprice risk so risk so we will know how much extra return we will know how much extra return we should require for accepting extra we should require for accepting extra risk.risk.
What is the Required Rate of What is the Required Rate of Return?Return?
The return on an investment The return on an investment requiredrequired by an investor given by an investor given market interest rates and the market interest rates and the investment’s investment’s riskrisk..
marketrisk
company-unique risk
can be diversifiedaway
Required
rate of
return= +
Risk-free
rate of
return
Risk
premium
RequiredRequired
rate of rate of
returnreturn
Beta
Let’s try to graph thisrelationship!
RequiredRequired
rate of rate of
returnreturn
.
Risk-freerate ofreturn(6%)
Beta
12%
1
securitymarket
line (SML)
This linear relationship between This linear relationship between risk and required return is risk and required return is known as the known as the Capital Asset Capital Asset
Pricing ModelPricing Model (CAPM). (CAPM).
RequiredRequired
rate of rate of
returnreturn
Beta
.12%
1
SML
0
Is there a riskless(zero beta) security?
Treasurysecurities are
as close to risklessas possible. Risk-free
rate ofreturn(6%)
RequiredRequired
rate of rate of
returnreturn
.
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
RequiredRequired
rate of rate of
returnreturn
.
Beta
12%
1
SML
UtilityStocks
Risk-freerate ofreturn(6%)
0
RequiredRequired
rate of rate of
returnreturn
.
Beta
12%
1
SMLHigh-techstocks
Risk-freerate ofreturn(6%)
0
kkjj = k = krfrf + + jj (k (kmm - k - krf rf ))
where:where:
kkjj = the required return on security j, = the required return on security j,
kkrfrf = the risk-free rate of interest, = the risk-free rate of interest,
jj = the beta of security j, and = the beta of security j, and
kkmm = the return on the market index. = the return on the market index.
The CAPM equation:The CAPM equation:
Example:Example:
Suppose the Treasury bond rate is Suppose the Treasury bond rate is 6%6%,, the average return on the the average return on the S&P 500 index is S&P 500 index is 12%12%,, and Walt and Walt Disney has a beta of Disney has a beta of 1.21.2..
According to the According to the CAPMCAPM, what , what should be the should be the required rate of required rate of returnreturn on Disney stock? on Disney stock?
kkjj = k = krfrf + (k + (kmm - k - krf rf ))
kkjj = .06 + 1.2 (.12 - .06) = .06 + 1.2 (.12 - .06)
kkjj = .132 = = .132 = 13.2%13.2%
According to the CAPM, Disney According to the CAPM, Disney stock should be priced to give a stock should be priced to give a 13.2%13.2% return. return.
RequiredRequired
rate of rate of
returnreturn
.
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%)
RequiredRequired
rate of rate of
returnreturn
.
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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