Fi8000 Capital Asset Pricing Model & Market Efficiency

1. Fi8000Capital AssetPricing Model & Market Efficiency Milind Shrikhande

2. Today • The Capital Asset Pricing Model • Market Efficiency

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 CAPM: Market Equilibrium The market portfolio (m) is on the efficient frontier and on the CML. It is the Mean-Variance optimal portfolio of risky assets. All the investors will invest in the same portfolio of risky assets: m - the market portfolio. The proportion of each asset in the market portfolio is simply the asset’s market value divided by the total wealth (market value of all assets).

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

9. The CAPM: Market Equilibrium 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 mutual fund theorem)

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

11. The 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:

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

13. 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

14. Beta Ri-rf βi Rm-rf

15. Calculating Beta

16. The CAPM Market 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. The Benefits of Diversification σp Diversifiable Risk Systematic Risk np

18. The Risk • 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).

19. The Components of Riskin the μ-σ Plane The CML μ m p i rf σ σND σD σ

20. The CAPM Market Equilibrium Find beta in the following planes Ri-Rm or (Ri-rf) – (Rm-rf) μ-σ (the CML) μ-β (the SML)

21. The CAPM: Market Equilibrium μ SML Underpriced – return is too high m Overpriced – return is too low rf β

22. 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 the CAPM equilibrium prices, which stock is underpriced and which is overpriced?

23. Project Valuation – Example 1 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)

24. Project Valuation – Example 2 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)

25. CAPM Review Under strict assumptions, the CAPM results in a prescription for a fair return (price): The fair expected return on an asset depends on the market risk premium and on beta. Stocks with high betas have higher return, but there is no compensation for any risk factor other than the systematic market risk.

26. CAPM Critique • Roll (1977) points out that the CAPM is not directly testable • It is a one period model • The market portfolio cannot be identified • To test the model, we need the market portfolio to be on the “efficient frontier” (proxies won’t work) • Indirect tests fail to support the CAPM • Other risk factors are compensated (size, book-to-market ratio), but there is no theoretical explanation for these risk factors.

27. The Efficient Market Hypothesis • The Efficient Markets Hypothesis (EMH) specifies three forms of efficiency: • Weak form market efficiency • Semi-Strong form market efficiency • Strong form market efficiency • Note that EMH is an Hypothesis • We should look for evidence that reject the hypothesis • We should look for evidence to decide which form of EMH is more likely

28. Weak Form Efficiency • Definition: A market is weak form efficient if the current asset prices reflect all historical price information • Implication: Trading strategies based on the analysis of historical prices should not yield abnormal returns (on average!)

29. Normal and Abnormal Returns • Normal returns: Fair or equilibrium returns given by a theoretical model like the CAPM • Abnormal returns: Returns that are systematically higher than the normal returns

30. Normal and Abnormal Returns • For each asset i the CAPM predicts a normal, risk-adjusted rate of return (expected return): E(Ri) = rf + βi [ E(Rm) – rf ] • We observe asset i over time, and compare the realized return Ri to the expected CAPM return: αit = Rit – E(Ri) = Rit – { rf + βi [ E(Rmt) – rf ] } • If asset i is systematically beating the CAPM expected return, we say that the return of asset i is abnormal. Abnormal return: Average[ αit ] = 1/T [αi1 + αi2 +…+ αiT] > 0

31. Semi-Strong Form Efficiency • Definition: A market is semi-strong form efficient if the current asset price reflects all publicly available information • Implication: Trading strategies based on the analysis of publicly available information (fundamental analysis such as analyst reports) should not yield abnormal returns (on average!)

32. Strong Form Efficiency • Definition: A market is strong form efficient if the current asset price reflects all information (including private / insider information) • Implication: There is no (legal) trading strategy that yields abnormal returns (on average!). One cannot make money even by following the trades of insider information.

33. Nesting • Information: Information about past prices is included in the set of publicly available information, which is included in the complete set of information. • Market efficiency: The strong form of market efficiency implies the semi-strong, which implies the weak form. Note that the strongest form of the MEH is the strongest and the most restricting assumption.

34. Evidence of Weak Form MEH • Consistent evidence: Technical trading rules, based on past price patterns, do not appear to be profitable. • Contradicting evidence: The “January” effect – almost every January, stock returns (usually for small stocks) are positive.

35. Evidence ofSemi-Strong Form MEH • Consistent evidence: New publicly available information (such as earnings release) affects prices quickly. • Contradicting evidence: Small stocks and stocks with high ratio of book-value to market-value have, on average, higher returns. Some portfolio managers consistently outperform the market (Peter Lynch, Warren Buffet, John Templeton and John Neff are in Paul Samuelson’s hall of fame, 1989).

36. Evidence of Strong Form MEH • Consistent evidence: Insiders of corporations appear able to earn abnormal returns from their trades. On average, price increases just after insiders purchase the stock and decreases just after a they sell the stock. • Contradicting evidence: Prices react to public information that had been private. For example, prices react to earning announcements even though someone must have know their contents before the official announcement day.

37. Market Efficiency and Equilibrium • An efficient market is a market in equilibrium • Inefficient markets occur when asset prices are different from their equilibrium prices • In theory, traders who exploit market inefficiencies should move the market back to equilibrium

38. The Joint Hypothesis Problem • A test of market efficiency can only be conducted by using a theoretical model to define normal (fair) returns (prices) • Finding an abnormal average return can be interpreted in more than one way: • Reject the Market Efficiency Hypothesis (MEH) • Reject the theoretical model of normal returns • Reject both

39. MEH – Are Markets Efficient? • Grossman and Stigliz (1980): the logical question must always be to what extent markets are efficient • Empirical evidence • Implications for trading strategies? • Technical analysis • Fundamental analysis • Trading on insider information (SEC regulations) • Is there a portfolio manager who systematically outperforms the market? • Is a small abnormal return detectable? • Will they tell us about their winning strategy (selection bias)? • How can we distinguish between luck and talent?

40. Practice Problems BKM Ch. 9: 1-2, 4-17, 21-28 BKM Ch. 12: 1-9, 14, 16-18, 25, 27-28