ASSET PRICING FACULTY F MATHEMATICS BELGRADE 2010.
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Transcript of ASSET PRICING FACULTY F MATHEMATICS BELGRADE 2010.
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ASSET PRICINGASSET PRICING
FACULTY F MATHEMATICSFACULTY F MATHEMATICS
BELGRADE BELGRADE 20102010
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IntroductionIntroduction
• Investors are concerned withInvestors are concerned with– RiskRisk– ReturnsReturns
• What determines the required What determines the required compensation for risk?compensation for risk?
• It will depend onIt will depend on– The risk faced by investorsThe risk faced by investors– The tradeoff between risk and return they The tradeoff between risk and return they
faceface
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return = R = change in asset value + income
initial value
Measuring ReturnMeasuring ReturnMeasuring ReturnMeasuring Return
• R is typically annualizedR is typically annualized• R is typically annualizedR is typically annualized
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example 1example 1example 1example 1
• Bond: 1 month holding periodBond: 1 month holding period
• buy for $9488, sell for $9528buy for $9488, sell for $9528
• 1 month R:1 month R:
• Bond: 1 month holding periodBond: 1 month holding period
• buy for $9488, sell for $9528buy for $9488, sell for $9528
• 1 month R:1 month R:
9528 - 9488
9488=0 .0042 = 0.42%
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• annualized R:annualized R:• annualized R:annualized R:
(1.0042)12 - 1 = 0.052 = 5.2%
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example 2example 2example 2example 2
• 100 shares IBM, 9 months 100 shares IBM, 9 months
• buy for $62, sell for $101.50buy for $62, sell for $101.50
• $.80 dividends$.80 dividends
• 9 month R:9 month R:
• 100 shares IBM, 9 months 100 shares IBM, 9 months
• buy for $62, sell for $101.50buy for $62, sell for $101.50
• $.80 dividends$.80 dividends
• 9 month R:9 month R:
101.50 - 62 + .80
62=0 .65 =65%
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• annualized R:annualized R:• annualized R:annualized R:
(1.65)12/9 - 1 =0 .95 = 95%
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example 3example 3example 3example 3
R Prob(R)
10% 0.2 5% 0.4-5% 0.4
E(R) = (0.2)10% + (0.4)5% + (0.4)(-5%)
= 2%
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example 4example 4example 4example 4
= (0.2)(10%-2%)2
= 0.0039
+ (0.4)(5%-2%)2
+ (0.4)(-5%-2%)2
= 6.24%
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8%9%10%11%12%13%14%15%16%17%
0% 10% 20% 30% 40%
Std. Dev.
Ex
p.
Re
t.
r=1r=0r=-1
(10%,16%)
(16%,30%)
Two risky assetsTwo risky assets
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DiversificationDiversification
# assets
systematicrisk
unsystematic risk
totalrisk
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Feasible portfoliosFeasible portfolios
Expected
return (Ei)
Std dev (i)
Efficient
frontier
Feasible Set
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Dominated and Efficient Dominated and Efficient PortfoliosPortfolios
Expected
return (Ei)
Std dev (i)
A
B
C
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Efficient frontierEfficient frontier
• 1. Find all asset expected returns 1. Find all asset expected returns and standard deviations.and standard deviations.
• 2. Pick one expected return and 2. Pick one expected return and minimize portfolio risk.minimize portfolio risk.
• 3. Pick another expected return 3. Pick another expected return and minimize portfolio risk.and minimize portfolio risk.
• 4. Use these two portfolios to map 4. Use these two portfolios to map out the efficient frontier.out the efficient frontier.
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CAPMCAPM
• CAPM Characteristics:CAPM Characteristics:– bi = sismrim/sm2bi = sismrim/sm2
• Asset Pricing Equation:Asset Pricing Equation:– E(ri) = rf + bi[E(rm)-rf]E(ri) = rf + bi[E(rm)-rf]
• CAPM is a model of what expected CAPM is a model of what expected returns returns should beshould be if if everyoneeveryone solves the solves the samesame passive portfolio passive portfolio problemproblem
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Expected
return (Ei)
Std dev (i)
D
Utility maximizing
risky-asset portfolio
Utility MaximizationUtility Maximization
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Tobin Separation Tobin Separation TheoremTheorem• When the riskfree asset is introduced,When the riskfree asset is introduced,
• All investors prefer a combination ofAll investors prefer a combination of
• 1) The riskfree asset and1) The riskfree asset and
• 2) The market portfolio2) The market portfolio
• Such combinations dominate all other Such combinations dominate all other assets and portfolios (in a sense of assets and portfolios (in a sense of risk-return)risk-return)
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All risky assets
and portfoliosExpected
return (Ei)
Std dev (i)
Riskless
asset Minimum
Variance
Portfolio
Market
Portfolio
Efficient
frontier
CMLCML
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%25.7)E(r
75.0035.0085.0035.0)E(r
r)E(rr)E(r
IBM
IBM
ifmfi
CAPMCAPM
• Suppose you have the following Suppose you have the following information:information:rf = 3.5% E(rm)=8.5% rf = 3.5% E(rm)=8.5% bIBM=0.75bIBM=0.75
• What should E(rIBM) be?What should E(rIBM) be?
• Answer:Answer: