Chapter 13 CAPM and APT Investments © K. Cuthbertson and D. Nitzsche

What is the risk free rate? Quiz RA = 11.2% βA=.82 RB = 17.6% βB=1.46 What is the risk free rate? What is the return on the market? What is the Market Risk Premium? © K. Cuthbertson and D. Nitzsche

Learning Objectives Link between CAPM and mean-variance portfolio theory Beta as a measure of undiversifiable risk Linear relationship between expected returns and beta of stocks- SML Use of CAPM for portfolio construction; for market risk in a portfolio; for estimation of discount factor in DFCF valuation methods, for market timing strategies © K. Cuthbertson and D. Nitzsche

Capital Market Theory: An Overview Capital market theory extends portfolio theory and develops a model for pricing all risky assets, while capital asset pricing model (CAPM) will allow you to determine the required rate of return for any risky asset based on the systematic risk in the asset

CAPM CAPM states that the expected excess return on a stock is defined by the stock’s market risk beta and by the expected excess return on the market: (ER-r)=β(ERm –r) or ER=r+β(ERm –r) © K. Cuthbertson and D. Nitzsche

Systematic Risk Risk factors that affect a large number of assets Also known as non-diversifiable risk or market risk Examples: changes in GDP, inflation, interest rates, general economic conditions

Portfolio Diversification (1)

Portfolio Diversification (2)

Measuring Systematic Risk Beta (β) is a measure of systematic risk Interpreting beta: β = 1 implies the asset has the same systematic risk as the overall market βm=Cov(Rm; Rm)/σm2 but Cov(Rm; Rm)=σm2 β < 1 implies the asset has less systematic risk than the overall market β > 1 implies the asset has more systematic risk than the overall market

High and Low Betas

Portfolio Betas Security Weight Beta A .133 3.69 B .2 0.64 C .267 1.64 Consider the previous example with the following four securities Security Weight Beta A .133 3.69 B .2 0.64 C .267 1.64 D .4 1.79 What is the portfolio beta? 1.773

CAPM and SIM SIM is statistical relationship (regression of excess returns of a stock and a benchmark) The intercept of the regression line of SIM is a performance measure Jensen’s alpha © K. Cuthbertson and D. Nitzsche

Market Index in the SIM Copyright © 2010 Nelson

Security Market Line CAPM is an asset pricing equation that explains the systematic risk and the role of diversification E(Ri) = Rf + βi(Rm-Rf) Rearrange CAPM in terms of market risk Calculate beta on historical stock returns or from financial information vendor Return averages from historical data serve as estimates of expected returns © K. Cuthbertson and D. Nitzsche

The larger is βi, the larger is the CAPM expected return ERi Figure 1 : Security market line (SML) Expected/Average Returns SML Q (buy) 14% M 13% SML/CAPM return, ERP P 9% T (sell) r = 5% Average historic return for S 4% S (sell) Beta, βi 0.5 1 1.2 The larger is βi, the larger is the CAPM expected return ERi © K. Cuthbertson and D. Nitzsche

Matrix Specific elements of a matrix are often denoted by a variable with two subscripts. For instance, a2,1 represents the element at the second row and first column © K. Cuthbertson and D. Nitzsche

Applications of CAPM Market timing Portfolio construction Value at risk Performance measure Treynor measure for excess return (uses market risk β) Sharpe measure (uses total risk σ) Jansen’s α © K. Cuthbertson and D. Nitzsche

Two Fund Separation and CML © K. Cuthbertson and D. Nitzsche

Return and Risk of Two Fund Portfolio Return is weighted average of Risk free rate and market return; portfolio weights sum to one Rp= wRf (Rf) + (1- wRf )(Rm) Risk on this portfolio is also weighted average (covariance zero; σRf =0 σRp = wRf (σRf ) + (1- wRf )(σ Rm ) © K. Cuthbertson and D. Nitzsche

Using the CML to Invest: An Example How much to invest in the riskless security? 11.5%= wRF (4%) + (1-wRF )(9%) wRF= -0.5 The investment strategy is to borrow 50% and invest 150% of equity in the market portfolio Copyright © 2010 Nelson

Background to Capital Market Theory Assumptions: All investors are Markowitz efficient investors who want to target points on the efficient frontier Investors can borrow or lend any amount of money at the risk-free rate of return (RFR) All investors have homogeneous expectations; that is, they estimate identical probability distributions for future rates of return All investors have the same one-period time horizon such as one-month, six months, or one year Continued… Copyright © 2010 Nelson

Background to Capital Market Theory Assumptions: All investments are infinitely divisible, which means that it is possible to buy or sell fractional shares of any asset or portfolio There are no taxes or transaction costs involved in buying or selling assets There is no inflation or any change in interest rates, or inflation is fully anticipated Capital markets are in equilibrium, implying that all investments are properly priced in line with their risk levels Copyright © 2010 Nelson

Background to Capital Market Theory Development of the Theory The major factor that allowed portfolio theory to develop into capital market theory is the concept of a risk-free asset An asset with zero standard deviation Zero correlation with all other risky assets Provides the risk-free rate of return (RFR) Will lie on the vertical axis of a portfolio graph Copyright © 2010 Nelson

Risk-Return Possibilities One can attain a higher expected return than is available at point M One can invest along the efficient frontier beyond point M, such as point D Copyright © 2010 Nelson

Risk-Return Possibilities With the risk-free asset, one can add leverage to the portfolio by borrowing money at the risk-free rate and investing in the risky portfolio at point M to achieve a point like E Point E dominates point D One can reduce the investment risk by lending money at the risk-free asset to reach points like C Copyright © 2010 Nelson

Risk, Diversification & the Market Portfolio: The Market Portfolio Because portfolio M lies at the point of tangency, it has the highest portfolio possibility line Everybody will want to invest in Portfolio M and borrow or lend to be somewhere on the CML It must include ALL RISKY ASSETS Copyright © 2010 Nelson

Risk, Diversification & the Market Portfolio: The Market Portfolio Since the market is in equilibrium, all assets in this portfolio are in proportion to their market values Because it contains all risky assets, it is a completely diversified portfolio, which means that all the unique risk of individual assets (unsystematic risk) is diversified away Copyright © 2010 Nelson

Risk, Diversification & the Market Portfolio Systematic Risk Only systematic risk remains in the market portfolio Variability in all risky assets caused by macroeconomic variables Variability in growth of money supply Interest rate volatility Variability in factors like (1) industrial production (2) corporate earnings (3) cash flow Can be measured by standard deviation of returns and can change over time Copyright © 2010 Nelson

Risk, Diversification & the Market Portfolio How to Measure Diversification All portfolios on the CML are perfectly positively correlated with each other and with the completely diversified market Portfolio M A completely diversified portfolio would have a correlation with the market portfolio of +1.00 Complete risk diversification means the elimination of all the unsystematic or unique risk and the systematic risk correlates perfectly with the market portfolio Copyright © 2010 Nelson

Risk, Diversification & the Market Portfolio: Eliminating Unsystematic Risk The purpose of diversification is to reduce the standard deviation of the total portfolio This assumes that imperfect correlations exist among securities Copyright © 2010 Nelson

Risk, Diversification & the Market Portfolio The CML & the Separation Theorem The CML leads all investors to invest in the M portfolio Individual investors should differ in position on the CML depending on risk preferences How an investor gets to a point on the CML is based on financing decisions Copyright © 2010 Nelson

Risk, Diversification & the Market Portfolio The CML & the Separation Theorem Risk averse investors will lend at the risk-free rate while investors preferring more risk might borrow funds at the RFR and invest in the market portfolio The investment decision of choosing the point on CML is separate from the financing decision of reaching there through either lending or borrowing Copyright © 2010 Nelson

Risk, Diversification & the Market Portfolio A Risk Measure for the CML The Markowitz portfolio model considers the average covariance with all other assets The only important consideration is the asset’s covariance with the market portfolio Copyright © 2010 Nelson