Fi8000 Valuation of Financial Assets Spring Semester 2010 Dr. Isabel Tkatch Assistant Professor of Finance

Today ☺ The Capital Asset Pricing Model ☺ Capital allocation – n risky assets one risk free asset ☺ CAPM equilibrium ☺ β - A new measure of risk ☺ Market Efficiency – next time

The Capital Asset Pricing Model ☺ Sharp (1968), Black (1969) and Lintner (1970) ☺ A model that tells us the fair (risk- adjusted) expected return for every individual asset ☺ A market equilibrium model

The Capital Asset Pricing Model (CAPM): Outline ☺ The assumptions of the model ☺ The market equilibrium: SML equation ☺ The two components of risk: ☺ Systematic (non-diversifiable) ☺ Non-systematic (diversifiable) ☺ Beta as a measure of systematic risk ☺ The returns and the prices of risky assets

The Capital Asset Pricing Model (CAPM): Assumptions ☺ There are many investors – each investor is a price taker ☺ All investors plan for one identical holding period ☺ All risky assets are publicly traded ☺ All investors are risk-averse and Mean-Variance optimizers ☺ Homogeneous expectations - all investors have the same information and interpret it the same way

The CAPM: Assumptions ☺ The perfect market assumption ☺ There are no taxes or transaction costs or information costs ☺ There are no frictions ☺ Stocks can be bought and sold in any quantity (even fractions) ☺ There is one risk-free asset and all investors can borrow or lend at that rate

The Market Portfolio in the μ-σ Plane σ μ The Capital Market Line: μ p = rf+[(μ m -rf) / σ m ]·σ p rf m

CAPM: Market Equilibrium All the investors will invest in the same portfolio of risky assets: m - the market portfolio. The risk preferences of the investors will result in their capital allocation between the market portfolio and the risk-free asset – i.e. the location of their portfolio on the Capital Market Line (CML). (The separation / mutual fund theorem)

Passive Investment Strategies in the μ-σ Plane σ μ The CML: μ p = rf + [(μ m -rf) / σ m ]·σ p rf m q p

CAPM: Market Equilibrium The risk premium of each risky assets will be proportional to the risk premium of the market portfolio and to the beta coefficient of the risky asset:

Capital Asset Pricing Model: The Security Market Line (SML) β μ m The SML: μ i = rf+ [μ m -rf]·β i rf q p

What is Beta? ☺ Beta is a measure of risk ☺ Beta measures how sensitive are the returns of asset i to the returns of the market portfolio ☺ Beta is the slope (coefficient) in the regression of asset i’s return (risk premium) on the market’s return (market risk premium) ☺ Beta is a relative measure of risk ·Beta < 1 : defensive asset ·Beta = 1: neutral asset ·Beta > 1: aggressive asset

Beta R m -rf R i -rf βiβi

Calculating Beta

What Affects Beta Risk?

The CAPM Equilibrium: Outline of the Proof ☺ The risk-free asset is on the SML ☺ Calculate the beta of the risk-free asset ☺ The market portfolio is on the SML ☺ Calculate the beta of the market portfolio ☺ Any M-V efficient portfolio p is on the SML ☺ Calculate the beta of an efficient portfolio ☺ Any risky asset i is on the SML

Portfolios on the SML

Project Valuation – Example Firm XYZ usually invests in projects with a risk level of β=0.8. It is considering an investment in a new project which is expected to produce a CF of $12.6M a year from now, and this CF is expected to grow at a constant rate of 2% per year forever. This CF is only an expectation and the firm’s economist estimates it’s Std to be $3M. What is the present value of the CFs of this project, if the expected annual return of the market portfolio is 12%, the annual return of money market instruments is 4% and the market is in equilibrium (CAPM)? (k = 10.4%; PV = $150M)

Benefits of Diversification npnp σpσp Diversifiable Risk Systematic Risk

Risk Components ☺ The risk of any risky asset has two components ☺ σ D - The diversifiable (non-systematic, idiosyncratic, firm-specific) risk can be eliminated by adding assets to the portfolio ☺ σ ND - The systematic (non-diversifiable, market) risk can not be eliminated through diversification ☺ According to the CAPM, investors are compensated only for the systematic component of the total asset risk (σ ND ).

Risk Components in the μ-σ Plane σ μ i The CML rf m p σDσD σ ND σ μp=μiμp=μi

CAPM Equilibrium: Risk and Return in the μ-β Plane β μ m The SML: μ i = rf+ [μ m -rf]·β i rf p,i βp=βiβp=βi μp=μiμp=μi β m =1 μmμm

Project Valuation – Example Joseph is looking for a treasure ship in the Mediterranean sea. He plans to keep looking for a year, and at the end of that year the value of his firm will be determined by the outcome of his quest. The probability of finding the $25M treasure is only 10% but he is more likely to end up with a smaller catch of only $5M. Obviously, the outcome of Joseph’s quest is independent of any macroeconomic risks, but we know that the expected annual return of the market portfolio is 14%, it’s Std is 22% and the annual return of money market instruments is 6%. What is the value of Joseph’s firm if the market is in equilibrium (CPAM)? (PV = $6.604M)

CAPM Equilibrium: Overpricing and Underpricing β μ m rf Asset k is overpriced return is too low Asset j is underpriced return is too high SML: μ i = rf+ [μ m -rf]·β i

Overpricing Relative to CAPM Equilibrium Price β μ m rf SML: μ i = rf+ [μ m -rf]·β i k βkβk μ CAPM μ Market

Underpricing Relative to CAPM Equilibrium Price β μ m rf SML: μ i = rf+ [μ m -rf]·β i βjβj μ CAPM μ Market j

The Return and the Current Price: Inversely Related A and B are two risky stocks. An analyst found that they have the following parameters: μ A =15% and β A =0.5; μ B =22% and β B =2. The risk-free rate is rf=10% and the expected return of the market portfolio is μ m =18%. Relative to CAPM equilibrium prices, which stock is underpriced and which is overpriced? (A is underpriced; B is overpriced)

Practice Problems BKM 7th Ed. Ch. 9: 1-2, 4-17, 21-28; BKM 8th Ed. Ch. 9: 1-2, 4-17, CFA: 3-10.