Chapter 7 investments capital asset pricing model (CAPM)

Chapter 7 Capital Asset Pricing Model (CAPM) 7.1 The Capital Asset Pricing Model 7-2 Capital Asset Pricing Model (CAPM) • Markowitz, Sharpe, Lintner and Mossin are researchers credited with its development. • Predicts the relationship between the risk and equilibrium expected returns on risky assets. • Approach the CAPM in a simplified setting and then add complexity to the environment. 7-3 Simplifying Assumptions Individuals are alike, with the notable exceptions of initial wealth and risk aversion. • Individual investors are price takers. : There are many investors, each with an endowment of wealth that is small compared with the total endowment of all investors. • Single-period investment horizon • Investments are limited to traded financial assets. • No taxes and no transaction costs 7-4 Simplifying Assumptions (cont.) • Information is costless and available to all investors. • Investors are rational mean-variance optimizers. : All investors attempt to construct efficient frontier portfolios. • Homogeneous expectations. : All investors analyze securities in the same way and share the same economic view of the world. 7-5 Hypothetical Equilibrium • All investors will hold the same portfolio for risky assets; the “market portfolio”. Market portfolio contains all securities and the proportion of each security is its market value as a percentage of total market value. • The market portfolio will be on the efficient frontier. It will be the optimal risky portfolio, the tangency point of the capital allocation line (CAL) to the efficient frontier. • The capital market line (CML), line from the risk-free rate through the market portfolio, is the best attainable capital allocation line. 7-6 • The risk premium on the market portfolio will be proportional to the variance of the market portfolio and investors’ typical degree of risk aversion. E(rM) – rf = A* σM2 • The risk premium on individual assets will be proportional to the risk premium on the market portfolio (M) and to the beta coefficient of the security on the market portfolio. 7-7 Hypothetical Equilibrium (cont.) Why All investors Would Hold the Market Portfolio • With all assumptions, all investors should hold the same optimal risky portfolio. • They all derive identical efficient frontiers and find the same tangency portfolio for the capital allocation line from the risk-free asset to that frontier. • With everyone choosing to hold the same risky portfolio, stocks will be represented in the aggregate risky portfolio in the same proportion as they are in each investor’s risky portfolio. • The market portfolio is the aggregate of all individual portfolios. • Each investor uses the market portfolio for the optimal risky portfolio, the CAL in this case is called CML. 7-8 E(r) rf E(rM) M CML σm Capital Market Line σ M = The value weighted “Market” Portfolio of all risky assets Efficient Frontier 7-9 The Passive Strategy is Efficient • The CAPM implies that a passive strategy, using the CML as the optimal CAL, is a powerful alternative to an active strategy. • The market portfolio proportions are a result of a profit-oriented “buy” and “ sell” orders that cease only when there is no more profit to be made. • It implies that only one mutual fund of risky assets, the market portfolio, is sufficient to satisfy the investment demands of all investors.  called a mutual fund theorem • If a passive strategy is costless and efficient, why would anyone follow an active strategy? But if no one does not any security analysis, what brings about the efficiency of the market portfolio? 7-10 [...]... for all stocks 7- 25 7. 2 The CAPM and Index Models 7- 26 Security Characteristic Line (SCL) Excess Returns (i) Dispersion of the points around the line measures unsystematic risk SCL Slope = β The statistic is called σe Excess returns on market index = α Ri = α i + ßiRM + What should α equal? ei 7- 27 7-28 7- 29 7. 3 The CAPM and the Real World 7- 30 The CAPM is... portfolio • SML - Graphs individual asset risk premiums as s function of asset risk - The relevant measure of risk for an individual asset is not the asset s standard deviation - The contribution of the asset to the portfolio standard deviation is measured by the asset s beta - The SML is valid both for portfolios and individual assets 7- 18 Security Market Line (SML) Capital Market Line (CML) E(r) E(r)... Market Line (CML) E(r) E(r) CML E(rM) SML M E(rM) Efficient Frontier rf σm rf σ ß 7- 19 M = 1.0 ß 7- 19 Sample Calculations for SML Equation of the SML E(ri) = rf + βi[E(rM) - rf] E(rm) - rf = 0.08 rf = 0.03 βx = 1.25 E(rx) = 0.03 + 1.25(.08) = 13 or 13% βy = 6 E(ry) = 0.03 + 0.6(0.08) = 0. 078 or 7. 8% If β = 1? Also, If β = 0? 7- 20 Graph of Sample Calculations E(r) If the CAPM is correct, only β risk matters... gives the buyer a + abnormal return 7- 23 More on alpha and beta E(rM) = 14% βS = 1.5 rf = 5% Required return = rf + βS[E(rM) – rf] = 5 +1.5[14-5] = 18.5% If you believe the stock will actually provide a return of 17% , what is the implied alpha? α = 17% - 18.5% = -1.5% A stock with a negative alpha plots below the SML & gives the buyer a negative abnormal return 7- 24 Portfolio Betas ΣWi βi 0.50(1.5)... premium is directly proportional to both the beta and the risk premium of the market portfolio; βi[E(rM) – rf] 7- 16 Individual Stocks: Security Market Line Slope SML E(r) = (E(rM) – rf )/ βM = price of risk for market Equation of the SML (CAPM) E(ri) = rf + βi[E(rM) - rf] SML E(rM) rf ß M = 1.0 ß 7- 17 The Security Market Line • CML - Graphs the risk premiums of efficient portfolios as a function of portfolio... / 1 = [E(ri) – rf] / βi • CAPM’s expected return-beta relationship: E(ri) = rf + βi[E(rM) – rf] 7- 14 Expected Returns on Individual Securities • CAPM’s expected return-beta relationship: E(ri) = rf + βi[E(rM) – rf]  The rate of return on any asset exceeds the risk-free rate by a risk premium equal to the asset s systematic risk measure (Beta) times the risk premium of the market portfolio  Only systematic... Calculations E(r) If the CAPM is correct, only β risk matters in determining the risk premium for a given slope of the SML Rx=13% RM=11% Ry =7. 8% 3% SML 08 Whenever the CAPM holds, all securities must lie on the SML in market equilibrium .6 1.0 1.25 ßy ßM ßx ß 7- 21 13% Suppose a security with a β of is offering an expected 1.25 15% return of According to the SML, the E(r) 13% should be _ E(r)... much in the risk-free asset • In equilibrium, the risk premium on the market portfolio must be just high enough to induce investors to hold the available supply of stocks • Investors purchase stocks  their demand drives up prices  lower expected rates of return and risk premium  Given lower risk premium, relatively more risk-averse investors will move their funds to risk-free asset from the risky... returns with the market portfolio’s returns and is measured by BETA With respect to an individual security, systematic risk can be measured by βi = [COV(ri,rM)] / σ2M 7- 13 Expected Returns on Individual Securities • The risk premium of an asset is proportional to its beta • The ratio of risk premium to beta should be the same for any two securities or portfolios • If we were to compare the ratio of risk... Conclusion: As a theory, the CAPM is untestable 7- 31 However, the practicality of the CAPM is testable Betas are not as useful at predicting returns as other measurable factors may be - More advanced versions of the CAPM that do a better job at e stimating the market portfolio are useful at predicting stock re turns - Still widely used and well understood 7- 32 The principles we learn from the CAPM are . Chapter 7 Capital Asset Pricing Model (CAPM) 7. 1 The Capital Asset Pricing Model 7- 2 Capital Asset Pricing Model (CAPM) • Markowitz, Sharpe, Lintner and. the asset s beta. - The SML is valid both for portfolios and individual assets. 7- 18 Capital Market Line (CML) E(r) rf E(rM) M CML σm σ Efficient Frontier 7- 19 E(r) E(rM) rf SML M ß ß = 1.0 7- 19 Security. individual asset risk premiums as s function of asset risk. - The relevant measure of risk for an individual asset is not the asset s standard deviation. - The contribution of the asset to