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- 1. CAPM & APTTheoryMore Enquiry Call On 9307390265 AndMdgupta01@gmail.com1
- 2. 2Capital 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= + −( ) βwhere: Ri … expected return on security iRf … risk-free return (interest rate)RM … expected return on the market portfolioRM - Rf … excess return of market portfolioβi … security’s beta which measures thesensitivity of the return on asset i tothe return in the market as a wholeFile name: 1 CAPM - APTReady on Feb 8 - 9, 1999.File name: 1 CAPM - APTReady on Feb 8 - 9, 1999.
- 3. 3Assumptions 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 ofexpected returns and standard deviations• Unlimited short sales are allowed
- 4. 4Assumptions of CAPM (2)• Unlimited lending and borrowing of funds atthe (single) risk-less rate• Homogeneous expectations concerning themean and variance of assets• All investors have identical expectationswith respect to the portfolio decision inputs(1.exp. returns, 2.variances, 3.correlations)• All assets (eg, including human capital) aremarketable
- 5. 5Characteristic line( ) ( )R R R Ri f M f i− = − βSML can be rewritten as:(Ri - Rf ) … excess return of the security i(RM - Rf ) … excess return of the market
- 6. 6Beta estimates( ) ( )R R R Ri f M f i i− = − +β εEstimating beta from historical returns usingregressionBeta is a slope of a characteristic line of i-th security.The “single factor” CAPM was extended to describethe optimal intertemporal consumption decisions ofinvestors who face multiple sources of risk, such asuncertainty over future earnings, prices of consumptiongoods, investment opportunities etc.The “multifactor” CAPM (also referred to as multi-betaCAPM) incorporates these extra market sources of risk
- 7. 7AlphaAn investor can be convinced, that the security is wrongly pricedaccording to CAPM.His estimate will differ by αI( )[ ]α βi ii n v e s t o rf M f iR R R R= − − −α i ii n v e s t o riC A P MR R= −If αi > 0 the investor believes that the security is undervaluedIf αi < 0 the investor believes that the security is overvalued
- 8. 8Impact on the characteristic line( ) ( )R R R Rii n v e s t o rf i M f i i− = + − +α β εExcess return of the security (Riinvestor- Rf ) is composed of:1) difference between investor’s estimateand CAPM estimate (αi)2) excess return of the market times beta (RM - Rf ) *βi3) an error term (εi)
- 9. 9Arbitrage pricing theory (APT)• More recent and different approach todetermining the asset prices• More general than CAPM which takes intoaccount mean and variance of asset returns• The basic postulate of the APT is that themarket risk is itself made up of a number ofseparate systematic factors• Law of one price: two assets that are thesame can not sell at different prices
- 10. 10Factor (index) models• Return on any security is related to a set ofsystematic 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
- 11. 11Single factor model - returnR 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 casethe value of factor F = 0bi sensitivity of i-th security to factor Fei uncertain error term
- 12. 12Single factor model - riskσ σ σi i F e ib2 2 2 2= +*Risk of an i-th security is determined by:σF2variance of factor Fσei variance of an error termCovariance between assets i and j is:σ σi j i j Fb b= 2
- 13. 13Factor model - assumptions• error term and factor are not correlated• error terms of any two assets are notcorrelated• returns of assets are correlated since theydepend on the same factorE 2093: InvValu & PortMgmt

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