CAPITAL ASSET PRICING MODEL

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1 CAPITAL ASSET PRICING MODEL RETURN. Retur i respect of a observatio is give by the followig formula R = (P P 0 ) + D P 0 Where R = Retur from the ivestmet durig this period P 0 = Curret market price P = Year ed market price D = Divided received durig the period. Expected Retur of a stock is the weighted average retur of the various observatios with probability of occurrece beig the assiged weight EV = Σ PxR EV = (MOV + 4 x RV + MPV) / 6 R = Value MOV = Most optimistic Value RV = Realistic Value MPV = Most pessimistic value RISK 3. Risk of a stock is the stadard deviatio of the stock ad is give by the followig formula Stadard Deviatio () = P d i i i= d = Deviatio = Number of observatios 4. If the probabilities are ot give it ca be assumed to be uiform 5. Alteratively the followig formula ca be used Stadard Deviatio () = P d i i i= d = Deviatio = Number of observatios DIVERSIFCATION 6. Diversificatio reduces risk. It does ot icrease retur. If you are lookig for retur, pick the best stock ad stay with it. If you are lookig to reduce risk, ivest i a portfolio of stocks Faculty: V PATTABHI RAM 9

2 PORTFOLIO 7. Risk of a two security portfolio is give by the followig formula P = ( ) ( w ) + ( ) ( w ) + ( ) ( ) ( w ) ( w ) ( Cor x x y y x y x y xy) Where ( x ) = Variace of Security X ( Y ) = Variace of Security Y (w x ) & (w y ) = Proportio of ivestmet i security X & Y (Cor xy )= Correlatio Coefficiet of security X ad Y 8. Retur of a portfolio is the weighted average retur of the securities formig the portfolio with market value of each stock beig the assiged weight Σ PxR Where P = probability R = value 9. Risk of a portfolio is NOT the weighted average risk of the security costitutig the portfolio. The oly exceptio is whe the correlatio is plus 0. Risk of a multi security portfolio is computed usig the matrix approach.. Risk reductio meas the extet to which the risk of a portfolio is less tha the weighted average risk of the securities costitutig the portfolio.. It is possible to idetify the portfolio combiatio at which risk is lowest. This is give by the followig formula - cov XY y W = x + - cov XY x y DOMINANCE 3. Security A is said to domiate Security B if a. It gives higher retur for same risk b. It carries lower risk for same retur 4. Stocks which are domiated are called iefficiet stocks. Stocks which are ot domiated are called efficiet stocks. Oly efficiet stocks are selected by a portfolio maager. 5. Although a particular stock may be domiated it could at times still form part of portfolio i such a way that the portfolio itself is ot domiated. NON DIVERSIFIABLE RISK 6. Beyod a poit diversificatio ceases to be importat. However there is o empirical evidece as to at what umber of stocks i the portfolio does diversificatio cease to be relevat 7. Risk which ca be reduced through diversificatio is called diversifiable risk or No Systematic risk Faculty: V PATTABHI RAM 30

3 8. Risk which caot be reduced through diversificatio is called NON diversifiable risk or Systematic risk 9. The umerator i the Beta formula is o-diversifiable risk. The differece betwee total risk ad o-diversifiable risk is diversifiable risk BETA 0. Beta is a measure of o-diversifiable risk. It is the ratio of o-diversifiable risk to variace of the market idex. There are three formulae for the computatio of Beta XY - X Y β = Y Y Covariace jm β = Variace m j β = x Corr jm m Where X = Retur (%) from stock X Y = Retur (%) from the stock market as a class = Number of observatios X = Arithmetic mea of rate of retur from the stock Y = Arithmetic mea of rate of retur from the market Covariace jm = Covariace betwee stock ad market Variace m = Variace of the market j = Stadard deviatio of stock m = Stadard deviatio of market returs corr = Correlatio betwee returs from stock ad stock market jm CAPM. The required retur from a stock is give by the followig CAPM formula R j = R f + β x (R m R f ) Where R j = CAPM retur R f = Risk free rate of retur β = Beta of the security R m = Retur from the market ALPHA 3. Alpha is the extet to which the actual retur of a stock i the past have bee greater tha the retur madated uder the capital asset pricig model Alpha (α) = Actual Retur CAPM retur Faculty: V PATTABHI RAM 3

4 4. The alpha of a stock is the average of the alphas of a series of observatios. CAPM AND GEARING 5. The overall beta of a compay is the weighted average beta of the assets or projects costitutig the compay 6. The overall beta of a compay is also the weighted average beta of the liabilities costitutig the compay also kow as Liability Beta 7. Hece the Asset Beta of a compay equals its liability Beta 8. The Asset Beta of all compaies operatig i the same busiess risk class is same ad hece the startig overall Asset Beta is the beta of a ulevered compay Debt β A g U + Value Where β A = Beta of asset β g = Beta geared β u = Beta ugeared Value = Debt + Equity Equity ( debt) β ( Equity) Value 9. Where taxes are ivolved D i the formula will be replaced with D*(-T). The broad formulae are as uder D (-T) Equity β + β A g U debt S+D(-T) Equity S + D( T) Where β A = Beta of asset β g = Beta geared β u = Beta ugeared ( ) ( ) LINES AND OTHER MODELS 30. The Security Market lie captures the relatioship betwee the beta of a stock ad the retur from the stock. It plots the retur of the stock for various levels of osystematic risk 3. The x-axis represets the risk (beta), ad the y-axis represets the expected retur. The market risk premium is determied from the slope of the SML. 3. The security market lie is a useful tool i determiig whether a asset beig cosidered for a portfolio offers a reasoable expected retur for risk. Idividual securities are plotted o the SML graph. If the security's risk versus expected retur is plotted above the SML, it is udervalued because the ivestor ca expect a greater retur for the iheret risk. A security plotted below the SML is overvalued because the ivestor would be acceptig less retur for the amout of risk assumed. 33. This lie graphs the systematic, or market, risk versus retur of the whole market at a certai time ad shows all risky marketable securities. It is also called the "characteristic lie" 34. The Capital Market lie captures the relatioship betwee the stadard deviatio of a stock ad the retur from the stock. Faculty: V PATTABHI RAM 3

5 It plots the retur of the stock for various levels of risk. The CML is used i the CAP model to illustrate the rates of retur for efficiet portfolios depedig o the risk-free rate of retur ad the level of risk (stadard deviatio) for a particular portfolio. The CML is derived by drawig a taget lie from the itercept poit o the efficiet frotier to the poit where the expected retur equals the risk-free rate of retur. 35. The CML is cosidered superior to the efficiet frotier sice it takes ito accout the iclusio of a risk-free asset i the portfolio. The CAPM demostrates that the market portfolio is essetially the efficiet frotier. 36. The CML replaces Beta i the CAP Model with the ratio of SD of portfolio to SD of market. 37. Risk retur ratio is the ratio of risk premium o a stock to beta of a stock. I a equilibrium market this should be same for all securities 38. Idividual securities do ot lie o CML They have some usystematic risk. 39. CML assumes o usystematic risk. All of that is take care of by diversificatio 40. The Characteristic Lie: A lie formed usig regressio aalysis that summarizes a particular security or portfolio's systematic risk ad rate of retur. The rate of retur is depedet o the stadard deviatio of the asset's returs ad the slope of the characteristic lie, which is represeted by the asset's beta. A characteristic lie of a stock is the same as the security market lie. The slope of the lie, which is a measure of systematic risk, determies the risk-retur trade-off. 4. Idividual securities as also portfolio of securities will lie i the SML because of the EMH which says that all securities will yield retur commesurate with their risk. 4. Market Model α + β x Risk premium from Idex a. There is o risk free rate b. Market risk affects the etire retur of a security ot just risk premium Expected Retur = α + (β x R m ) c. Sice there is o risk free rate, the SML formula is reduced to β x R m. To this we add the historical α to get a estimate of the rate of retur 43. Excess Retur Model a. Expected retur cosiderig risk free retur α R f x (-Port β) + CAPM retur + Error estimate 44. Multi factor model a. More tha oe factor ca drive the retur of a stock Expected retur = R f + β of GNP x (GNP R f ) + β of Iflatio x (Iflatio R f ) Faculty: V PATTABHI RAM 33

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