Fi8000 Valuation of Financial Assets

1. Fi8000Valuation ofFinancial Assets Spring Semester 2010 Dr. Isabel Tkatch Assistant Professor of Finance

2. 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

3. 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

4. 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

5. 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

6. 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

7. The Market Portfolioin the μ-σ Plane The Capital Market Line: μp= rf+[(μm-rf)/ σm]·σp μ m rf σ

8. 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)

9. Passive Investment Strategiesin the μ-σ Plane The CML: μp= rf + [(μm-rf)/ σm]·σp μ m p q rf σ

10. 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:

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

12. 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

13. Beta Ri-rf βi Rm-rf

14. Calculating Beta

15. What Affects Beta Risk?

16. 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

17. Portfolios on the SML

18. 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)

19. Benefits of Diversification σp Diversifiable Risk Systematic Risk np

20. Risk Components • The risk of any risky asset has two components • σD - The diversifiable (non-systematic, idiosyncratic, firm-specific) risk can be eliminated by adding assets to the portfolio • σND - 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 (σND).

21. Risk Componentsin the μ-σ Plane The CML μ m p μp=μi i rf σ σND σD σ

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

23. 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)

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

25. Overpricing Relative to CAPM Equilibrium Price μ SML: μi= rf+ [μm-rf]·βi m μCAPM μMarket k rf βk β

26. Underpricing Relative to CAPM Equilibrium Price μ SML: μi= rf+ [μm-rf]·βi m j μMarket μCAPM rf βj β

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

28. 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.