Unit 5 - Portfolio Management TECHNICAL ANALYSIS Course Materials by K.Rajeswari Asst Professor SNS college of technology Unit 5 - Portfolio Management Capital Asset Pricing Model

Capital Asset Pricing Model Relates the required rate of return for any security with the market risk for the security as measured by beta Focus on the equilibrium relationship between the risk and expected return on risky assets Builds on Markowitz portfolio theory Each investor is assumed to diversify his or her portfolio according to the Markowitz model, choosing a location on the efficient frontier that matches his/her return-risk preferences 5/7/2018 V.Prabakaran, AP/MBA - IM - Unit-5 Portfolio Management 2

CAPM Assumptions All investors: Use the same information to generate an efficient frontier (i.e., identical inputs: E(R), σ, ρ) Have the same one- period time horizon Can borrow or lend money at the risk-free rate of return No transaction costs No personal income (i.e., indifferent between dividends and capital gains) taxes No inflation No single investor can affect the price of a stock (i.e., price-takers) Capital markets are in equilibrium 5/7/2018 V.Prabakaran, AP/MBA - IM - Unit-5 Portfolio Management 3

CAPM Assumptions These assumptions appear unrealistic The important issue is how well the theory predicts (describes) reality The CAPM is robust since most of its assumptions can be relaxed without significant effects on the model Not all of the CAPM assumptions are unrealistic: Some institutional investors are tax-exempt Significant reduction in transaction costs by using discount brokers and/or internet For the one-period horizon of the model, inflation may be fully (or mostly) anticipated 5/7/2018 V.Prabakaran, AP/MBA - IM - Unit-5 Portfolio Management

Market Portfolio Most important implication of the CAPM All investors hold the same optimal portfolio of risky assets As a result of the assumption that all investors have the same time horizon and homogenous expectations regarding the expected returns and risks for any given risky asset The optimal portfolio is at the highest point of tangency between RF and the efficient frontier The portfolio of all risky assets is the optimal risky portfolio called the market portfolio 5/7/2018 V.Prabakaran, AP/MBA - IM - Unit-5 Portfolio Management 4

Characteristics of the Market Portfolio (M) All risky assets must be in portfolio, so it is completely diversified Contains only systematic risk (cannot be eliminated) All securities included in proportion to their market value In theory, should contain all risky assets worldwide, both financial and real, in their proper proportions Is found by determining which efficient portfolio offers the highest risk premium, given the existence of a risk- free asset 5/7/2018 V.Prabakaran, AP/MBA - IM - Unit-5 Portfolio Management 5

The Equilibrium Risk-Return trade-off The CAPM is an equilibrium model that encompasses two important relationships: The capital market line (CML), specifies the equilibrium relationship between expected return and total risk for efficient portfolios The security market line (SML), specifies the equilibrium relationship between expected return and systematic risk 5/7/2018 V.Prabakaran, AP/MBA - IM - Unit-5 Portfolio Management

Capital Market Line Line from RF to L is capital market line (CML) x = risk premium = E(RM) - RF y = risk = M Slope = x/y = market price of risk for efficient portfolios = [E(RM) - RF]/M y-intercept = RF = price of forgone consumption L M E(RM) x RF y M Risk 6

Capital Market Line Slope of the CML is the market price of risk for efficient portfolios, or the equilibrium price of risk in the market Relationship between risk and expected return for portfolio P (Equation for CML): 5/7/2018 V.Prabakaran, AP/MBA - IM - Unit-5 Portfolio Management 7

Capital Market Line The following should be noted about the CML: Only efficient portfolios consisting of the risk-free asset and portfolio M lie on the CML It indicates the optimal expected returns associated with different portfolio risk levels It must always be upwards sloping because the price of risk must always be positive Although, it must be upward sloping ex ante (before the fact), it can be, and sometimes is, downward sloping ex post (after the fact). This merely indicates that the returns actually realized differed from those that were expected 5/7/2018 V.Prabakaran, AP/MBA - IM - Unit-5 Portfolio Management

Security Market Line CML Equation only applies to markets in equilibrium and efficient portfolios (i.e., cannot be used to assess the expected return on individual securities or inefficient portfolios) The Security Market Line depicts the tradeoff between risk and expected return for individual securities Under CAPM, all investors hold the risky portion of their portfolio in the market portfolio 5/7/2018 V.Prabakaran, AP/MBA - IM - Unit-5 Portfolio Management 8

Security Market Line The expected return on any risky asset is directly proportional to its covariance with the market portfolio Equation for expected return for an individual stock similar to CML Equation 5/7/2018 V.Prabakaran, AP/MBA - IM - Unit-5 Portfolio Management 9

Security Market Line Beta = 1.0 implies as risky as market Securities A and B are more risky than the market Beta > 1.0 Security C is less risky than the market Beta < 1.0 SML E(R) A E(RM) B C RF 0.5 1.0 1.5 2.0 BetaM 10

Security Market Line The SML represents the trade-off between systematic risk (β) and the expected return for all assets, whether individual securities, inefficient portfolios, or efficient portfolios Beta measures systematic risk Measures relative risk compared to the market portfolio of all stocks Volatility of security i is different (higher or lower) than that of the market if β_i > 1 or β_i < 1 and is equal to that of the market if β_i = 1 β_i = 1 means that for every 1% change in the market’s return, on average security i’s returns change 1% β_M = 1 and β_RF = 0 5/7/2018 V.Prabakaran, AP/MBA - IM - Unit-5 Portfolio Management 11

Security Market Line β is useful for comparing the relative systematic risk of different stocks and, in practice, is used by investors to judge a stock’s riskiness βs may vary widely across companies in different industries and within a give industry All securities should lie on the SML The expected return on the security should be only that return needed to compensate for systematic risk 5/7/2018 V.Prabakaran, AP/MBA - IM - Unit-5 Portfolio Management

SML and Asset Values Underpriced SML: Er = rf +  (Erm – rf) Overpriced rf β Underpriced  expected return > required return according to CAPM  lie “above” SML Overpriced  expected return < required return according to CAPM  lie “below” SML Correctly priced  expected return = required return according to CAPM  lie along SML 5/7/2018 V.Prabakaran, AP/MBA - IM - Unit-5 Portfolio Management

CAPM’s Expected Return-Beta Relationship Required rate of return on an asset (ki) is composed of risk-free rate (RF) risk premium (βi [ E(RM) - RF ]) Market risk premium adjusted for specific security ki = RF + βi [ E(RM) - RF ] The greater the systematic risk, the greater the required return 5/7/2018 V.Prabakaran, AP/MBA - IM - Unit-5 Portfolio Management 12

Estimating the SML To use the SML, an investor needs estimates of the return on the risk-free asset, the expected return on the market index, and the β for an individual security Treasury Bill rate used to estimate RF Expected return for the market index in not observable Estimated using past market returns and taking an expected value Estimating individual security betas is difficult β is only company-specific factor in CAPM Requires asset-specific forecast 5/7/2018 V.Prabakaran, AP/MBA - IM - Unit-5 Portfolio Management 13

Estimating Beta Market model Relates the return on each stock to the return on the market, assuming a linear relationship with an intercept and slope Rit =αi +βi RMt + eit It is identical to the single-index model except that it does not make the assumption that the error terms of the different securities are uncorrelated The Market Model produces an estimate of return for any stock 5/7/2018 V.Prabakaran, AP/MBA - IM - Unit-5 Portfolio Management 14

Estimating Beta Characteristic line A regression equation used to estimate β by regressing stock returns on market returns Line fitted to total returns for a security relative to total returns for the market index β is the slope of the characteristic line 5/7/2018 V.Prabakaran, AP/MBA - IM - Unit-5 Portfolio Management

Test of CAPM Fama and French (1992) Indicate that the CAPM’s sole risk factor, market risk β, posses no explanatory power in discriminating among the cross-sectional returns of US stocks Common market equity (ME) and the ratio of book equity to market equity (BE/ME) combine to explain the cross-section of expected returns Three-factor model (overall market factors, factors related to firm size, & BE/ME ratio) 5/7/2018 V.Prabakaran, AP/MBA - IM - Unit-5 Portfolio Management

Test of CAPM Empirical SML is “flatter” than predicted SML Fama and French (1992) Market Size Book-to-market ratio Roll’s Critique True market portfolio is unobservable Tests of CAPM are merely tests of the mean- variance efficiency of the chosen market proxy 5/7/2018 V.Prabakaran, AP/MBA - IM - Unit-5 Portfolio Management

Arbitrage Pricing Theory(APT) Based on the Law of One Price Two otherwise identical assets cannot sell at different prices Equilibrium prices adjust to eliminate all arbitrage opportunities Unlike CAPM, APT does not assume single-period investment horizon, absence of personal taxes, riskless borrowing or lending, mean-variance decisions 5/7/2018 V.Prabakaran, AP/MBA - IM - Unit-5 Portfolio Management 17

Factors APT assumes returns generated by a factor model Factor Characteristics Each risk must have a pervasive influence on stock returns Risk factors must influence expected return and have nonzero prices Risk factors must be unpredictable to the market 5/7/2018 V.Prabakaran, AP/MBA - IM - Unit-5 Portfolio Management 18

APT Model Most important are the deviations of the factors from their expected values The expected return-risk relationship for the APT can be described as: E(Rit) =a0+bi1 (risk premium for factor 1) +bi2 (risk premium for factor 2) +… +bin (risk premium for factor n) 5/7/2018 V.Prabakaran, AP/MBA - IM - Unit-5 Portfolio Management 19

APT Model Reduces to CAPM if there is only one factor and that factor is market risk Roll and Ross (1980) Factors: Changes in expected inflation Unanticipated changes in inflation Unanticipated changes in industrial production Unanticipated changes in the default risk premium Unanticipated changes in the term structure of interest rates 5/7/2018 V.Prabakaran, AP/MBA - IM - Unit-5 Portfolio Management 19

Problems with APT Factors are not well specified ex ante To implement the APT model, the factors that account for the differences among security returns are required CAPM identifies market portfolio as single factor Neither CAPM or APT has been proven superior Both rely on unobservable expectations 5/7/2018 V.Prabakaran, AP/MBA - IM - Unit-5 Portfolio Management 20

Thanks… 5/7/2018 V.Prabakaran, AP/MBA - IM - Unit-5 Portfolio Management