* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project

# Download E(R i ) - Cengage

Survey

Document related concepts

Algorithmic trading wikipedia , lookup

Investment banking wikipedia , lookup

Market (economics) wikipedia , lookup

Short (finance) wikipedia , lookup

Mark-to-market accounting wikipedia , lookup

Interbank lending market wikipedia , lookup

Derivative (finance) wikipedia , lookup

Financial crisis wikipedia , lookup

Private equity secondary market wikipedia , lookup

Fixed-income attribution wikipedia , lookup

Investment fund wikipedia , lookup

Stock trader wikipedia , lookup

Rate of return wikipedia , lookup

Transcript

Chapter 6 Risk and Return: The CAPM and Beyond Professor XXX Course Name / # Efficient Risky Portfolios Variance of return - a poor measure of risk Investors can only expect compensation for systematic risk Asset pricing models aim to define and quantify systematic risk Begin developing pricing model by asking: Are some portfolios better than others? 2 2 Expanding The Feasible Set On The Efficient Frontier E(RP) EF including domestic & foreign assets EF including domestic stocks, bonds, and real estate EF for portfolios of domestic stocks P 3 3 Are Some Portfolios Better Than Others? Efficient portfolios achieve the highest possible return for any level of volatility Two N –– Asset Asset Portfolios Portfolios E(RP) efficient portfolios efficient portfolios • MVP •F •E • • • • C• (50%A, • 50%B) • • • • • • D • 25%B) • • MVP (75%A, • • Stock B Stock A inefficient portfolios P 4 4 What happens when we add a risk-free asset to the picture? Expected Return (per month) and Standard Deviation for Various Portfolios 5 5 Riskless Borrowing And Lending Risky asset X Risk-free asset Y Three possible returns: -10%; 10%; 30% Return: 6% Expected return = 10% Standard deviation =16.3% Buying asset Y = Lending money at 6% interest How would a portfolio with $100 (50%) in asset X and $100 (50%) in asset Y perform? $100 Asset X $100 Asset Y 6 6 Three possible returns: -2%; 8%; 18% Expected return = 8% Standard deviation =8.16% Portfolio has lower return but also less volatility than 100% in X Portfolio has higher return and higher volatility than 100% in risk-free Riskless Borrowing And Lending (Continued) What if we sell short asset Y instead of buying it? Borrow $100 at 6% Must repay $106 Invest $300 in X Original $200 investment plus $100 in borrowed funds When X Pays –10% 7 7 Net Return on $200 Investment $270 - $106 - $200 18% $200 When X Pays 10% Net Return on $200 Investment $330 - $106 - $200 12% $200 When X Pays 30% Net Return on $200 Investment $390 - $106 - $200 42% $200 Expected return on the portfolio is 12%. Higher expected return comes at the expense of greater volatility Riskless Borrowing And Lending (Continued) The more we invest in X, the higher the expected return The expected return is higher, but so is the volatility This relationship is linear Portfolio 8 8 Expected Return Standard Deviation 50% risky, 50% risk-free 8% 8.16% 100% risky, 0% risk free 10% 16.33% 150% risky, -50% risk free 12% 24.49% Portfolios Of Risky & Risk-Free Assets E(RP) 16.5% •MF 12% 9% RF=6% • 0 9 9 •B •A 15% 30% 52% P New Efficient Frontier 10 10 The Market Portfolio Only one risky portfolio is efficient Suppose investors agree on which portfolio is efficient Equilibrium requires this to be the Market Portfolio Market Portfolio: value weighted portfolio of all available risky assets 11 11 The line connecting Rf to the market portfolio called the Capital Market Line Finding the Optimal Risky Portfolio If investors can borrow and lend at the riskfree rate, then from the entire feasible set of risky portfolios, one portfolio will emerge that maximizes the return investors can expect for a given standard deviation. To determine the composition of the optimal portfolio, you need to know the expected return and standard deviation for every risky asset, as well as the covariance between every pair of assets. 12 12 Finding the Optimal Portfolio 13 13 The Capital Market Line The line connecting Rf to the market portfolio is called the Capital Market Line (CML) CML quantifies the relationship between the expected return and standard deviation for portfolios consisting of the risk-free asset and the market portfolio, using 14 14 Capital Asset Pricing Model (CAPM) Only beta changes from one security to the next. For that reason, analysts classify the CAPM as a single-factor model, meaning that just one variable explains differences in returns across securities. 15 15 The Security Market Line Plots the relationship between expected return and betas In equilibrium, all assets lie on this line If stock lies above the line Expected return is too high Investors bid up price until expected return falls If stock lies below the line Expected return is too low Investors sell stock, driving down price until expected return rises 16 16 The Security Market Line E(RP) SML A - Undervalued • • RM RF • B • • • B - Overvalued • =1.0 17 17 A Slope = E(R ) - R = Market m F Risk Premium (MRP) i Beta im i 2 m The numerator is the covariance of the stock with the market The denominator is the market’s variance In the CAPM, a stock’s systematic risk is captured by beta The higher the beta, the higher the expected return on the stock 18 18 Beta And Expected Return Beta measures a stock’s exposure to market risk The market risk premium is the reward for bearing market risk: • Rm - Rf E(Ri) = Rf + ß [E(Rm) – Rf] 19 19 • Return for bearing no market risk • Stock’s exposure to market risk • Reward for bearing market risk Calculating Expected Returns E(Ri) = Rf + ß [E(Rm) – Rf] • Assume • Risk–free rate = 2% • Expected return on the market = 8% If Stock’s Beta Is 20 20 Then Expected Return Is 0 2% 0.5 5% 1 8% 2 14% When Beta = 0, The Return Equals The Risk-Free Return When Beta = 1, The Return Equals The Expected Market Return Scatterplot for Returns on Sharper Image and S&P500 Sharper Image Weekly Return 0.3 Slope = Beta = 1.44 0.2 0.1 0 -0.3 -0.2 -0.1 0 -0.1 0.1 R-square = 0.19 -0.2 -0.3 21 21 0.2 S&P500 Weekly Return 0.3 Scatterplot for Returns on ConAgra and S&P500 ConAgra Weekly Return 0.15 0.1 0.05 beta = 0.11 0 -0.15 -0.1 -0.05 0 0.05 -0.05 R-square = 0.003 -0.1 -0.15 22 22 0.1 S&P500 Weekly Return 0.15 Scatterplot for Returns on Citigroup and S&P500 0.2 Citigroup Weekly Return 0.15 beta = 1.20 0.1 0.05 0 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 -0.05 R-square = 0.50 -0.1 -0.15 -0.2 S&P500 Weekly Return 23 23 0.15 0.2 Using The Security Market Line The SML and where P&G and GE place on it r% SML 15 12.4% slope = E(Rm) – RF = MRP = 10% - 2% = 8% = Y ÷ X • 10 6.8% 5 Rf = 2% 24 24 P&G 1 GE 2 Shifts In The SML Due To A Shift In Required Market Return r% SML1 15 SML2 11.1% • • 10 Shift due to change in market risk premium from 8% to 7% 6.2% 5 Rf = 2% 25 25 P&G 1 GE 2 Shifts In The SML Due To A Shift In The Risk-Free Rate SML2 r% SML1 15 14.4% Shift due to change in risk-free rate from 2% to 4%, with market risk premium remaining at 8%. Note all returns increase by 2% • 10 8.8% 5 Rf = 4% 26 26 P&G 1 GE 2 Alternatives To CAPM Arbitrage Pricing Theory Fama-French Model Ri R f i1 Rm R f i 2 Rsmall Rbig i 3 Rhigh Rlow Betas represent sensitivities to each source of risk Terms in parentheses are the rewards for bearing each type of risk. 27 27 The Current State of APT 28 28 Investors demand compensation for taking risk because they are risk averse. There is widespread agreement that systematic risk drives returns. You can measure systematic risk in several different ways depending on the asset pricing model you choose. The CAPM is still widely used in practice in both corporate finance and investment-oriented professions.