capm e 2093 - april 2005
DESCRIPTION
TRANSCRIPT
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Capital Asset Pricing Model (CAPM) Arbitrage Pricing Theory (APT)
All assets can be organized on the Security market line (SML)in the Risk - Return space.Expected return of i-th asset (security) can be calculated as:
R R R Ri f M f i ( )where: Ri … expected return on security i
Rf … risk-free return (interest rate)RM … expected return on the market portfolioRM - Rf … excess return of market portfolioi … security’s beta which measures the sensitivity of the return on asset i to
the return in the market as a wholeFile name: 1 CAPM - APT
Ready on Feb 8 - 9, 1999.
File name: 1 CAPM - APT
Ready on Feb 8 - 9, 1999.
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Assumptions of CAPM (1)
• No transaction costs
• All assets are infinitely divisible
• No taxation
• No single investor can affect the price (perfect market)
• Investors make decisions solely in terms of expected returns and standard deviations
• Unlimited short sales are allowed
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Assumptions of CAPM (2)• Unlimited lending and borrowing of funds at
the (single) risk-less rate
• Homogeneous expectations concerning the mean and variance of assets
• All investors have identical expectations with respect to the portfolio decision inputs (1.exp. returns, 2.variances, 3.correlations)
• All assets (eg, including human capital) are marketable
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Characteristic line
R R R Ri f M f i
SML can be rewritten as:
(Ri - Rf ) … excess return of the security i(RM - Rf ) … excess return of the market
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Beta estimates
R R R Ri f M f i i
Estimating beta from historical returns using regression
Beta is a slope of a characteristic line of i-th security.
The “single factor” CAPM was extended to describethe optimal intertemporal consumption decisions of investors who face multiple sources of risk, such as uncertainty over future earnings, prices of consumption goods, investment opportunities etc.The “multifactor” CAPM (also referred to as multi-beta CAPM) incorporates these extra market sources of risk
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AlphaAn investor can be convinced, that the security is wrongly pricedaccording to CAPM.His estimate will differ by I
i iinvestor
f M f iR R R R
i iinvestor
iC A P MR R
If i > 0 the investor believes that the security is undervaluedIf i < 0 the investor believes that the security is overvalued
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Impact on the characteristic line
R R R Ri
investorf i M f i i
Excess return of the security (Riinvestor - Rf ) is composed of:
1) difference between investor’s estimate and CAPM estimate (i)
2) excess return of the market times beta (RM - Rf ) *i
3) an error term (i)
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Arbitrage pricing theory (APT)• More recent and different approach to
determining the asset prices
• More general than CAPM which takes into account mean and variance of asset returns
• The basic postulate of the APT is that the market risk is itself made up of a number of separate systematic factors
• Law of one price: two assets that are the same can not sell at different prices
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Factor (index) models
• Return on any security is related to a set of systematic factors, for example:– growth of real GDP (unanticipated changes)– unanticipated changes in interest rates– unanticipated inflation– impact of the market itself– other unanticipated variables
• Not only to the market excess return
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Single factor model - return
R a b F ei i i i *Uncertain return on an i-th security is determined by:
F uncertain value of a factorai expected value of i-th security in case
the value of factor F = 0bi sensitivity of i-th security to factor Fei uncertain error term
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Single factor model - risk
i i F eib2 2 2 2 *
Risk of an i-th security is determined by:
F2 variance of factor F
ei variance of an error term
Covariance between assets i and j is:
ij i j Fb b 2
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Factor model - assumptions
• error term and factor are not correlated
• error terms of any two assets are not correlated
• returns of assets are correlated since they depend on the same factor
E 2093: Inv Valu & Port Mgmt