1. MBA & MBA – Banking and Finance (Term-IV) Course : Security Analysis and Portfolio Management Unit III: Asset Pricing Theories

2. 2 Asset Pricing Theories: Asset pricing theories describe how assets should be priced in the capital market. Following are the important theories: Capital Market Theory - CMT Capital Asset Pricing Model - CAPM Arbitrage Pricing Theory - APT

3. 3 1) Capital Market Theory It is a major extension of the portfolio theory of Markowitz. CMT tells us how assets should be priced in the capital markets if, indeed, everyone behaved in the way portfolio theory suggests. It is based on the following 8 assumptions:

4. 4 Assumptions: 1.Investors make decisions based solely upon risk and return assessments which takes the form of expected return and standard deviation measures. 2.The purchase or sale of a security can be undertaken in infinitely divisible units. 3.Investors can short sell any amount of shares without limit. 4.Purchases and sales by a single investor cannot affect prices. This means that there is perfect competition where investors in total determine prices by their actions.

5. 5 5. There are no transaction costs. 6. There is absence of personal income taxes. So one is indifferent to the form in which the return is received (dividends or capital gains) 7. The investor can borrow or lend any amount of funds desired at an identical risk less rate. 8. Investors share identical expectations with regard to the relevant decision period, the necessary decision inputs, their form and size. Otherwise there would be a family of efficient frontiers because of differences in expectations.

6. 6 Risk RFRF Expected Return σPσP RPRP B

7. 7 R p = XR M + (1-X)R F Where: R p = expected return on portfolio X = percentage of funds invested in risky portfolio (1-X) = percentage of funds invested in risk less asset R M = expected return on risky portfolio R F = expected return on risk less asset

8. 8 And: σ P = X σ M Where: σ P = expected standard deviation of the portfolio X = percentage of funds invested in risky portfolio σ M = expected standard deviation on risky portfolio

9. 9 Let point B is the optimum portfolio for an investor where R M = 0.10 and σ P =.06. If he placed one half of the available funds in the risk less asset and one half in the risky portfolio B, the combined risk-return measures for the mixed portfolio, O, can be found using above equations as :

10. 10 R P = (1/2)(.10) + (1/2)(.05) =.075 σ P = (1/2)(.06) + (1/2)(00) =.03

11. 11 Situations: There can be three cases based on the percentage of investment wealth or equity placed in the risky portfolio: Case 1: X=1, investment wealth is totally committed to the risky portfolio. Case 2: X<1, only a fraction of X is placed in the risky portfolio and remainder is lent at the rate R F. Case3: X>1, Investor is borrowing rather than lending.

12. 12 Lending Borrowing M Risk R P σPσP Expected Return

13. 13 Lending is an investment in a risk less security like T-bills or a savings account or a high grade commercial paper. Borrowing can be thought of as the use of margin. Borrowing and lending options transform the efficient frontier into a straight line.

14. 14 Point M now represents the optimal combination of risky securities. The existence of this combination simplifies the problem of portfolio selection. The investors need to only decide how much to borrow or lend. No other combination is as efficient as point M. The decision to purchase M is the investment decision and the decision to buy some risk less asset (lend) or to borrow is the financing decision. This condition gives rise to the separation theorem which implies that all investors, conservative or aggressive should hold the same mix of stocks from the efficient set. In other words all types of investors should hold identically risky portfolios. Desired risk levels are achieved through combining portfolio M with borrowing and lending.

15. 15 If all investors hold the same risky portfolio, then in equilibrium it must be the market portfolio. The market portfolio is a portfolio comprised of all risky assets. Each asset will be held in the proportion that the market value of the asset represents to the total market value of all risky assets.

16. 16 Capital Market Line: The line formed by the action of all investors mixing the market portfolio with the risk free asset is known as the capital market line. All efficient portfolios of all investors would lie along this CML.

17. 17 Where R e = expected return on efficient portfolio The subscript ‘e’ denotes an efficient portfolio The above equation can also be written as: (Expected return) = (price of time) + (Price of risk) (amount of risk)

18. 18 2) Capital Asset Pricing Model ( CAPM) Portfolio theory implied that each investor faced an efficient frontier. But differences in expectations leads to different frontiers for different investors. CAPM provides a framework for assessing whether a security is overpriced, under priced or correctly priced.

19. 19 Security Market Line : For well diversified portfolios, non systematic risk tends to go to zero, and the only relevant risk is systematic risk measured by beta. So a straight line that shows investors risk and return in terms of expected return and beta is called the SML. Thus SML provides the relationship between the expected return and beta of a security or portfolio.

20. 20 Beta Expected Return M RFRF RMRM 1.0 SML

21. 21 Equation of SML is: R i = R F + (R M –R F )β i where: R i = expected return on i th security. R F = return on risk free asset β i = beta of i th security

22. 22 CAPM: It was developed in mid 1960’s. It is referred to as Sharpe, lintner and Mossin (SLM) capital asset pricing model. The relationship between risk and return established by the SML is known as the CAPITAL ASSET PRICING MODEL. It is basically a simple linear relationship. The higher the value of beta, higher would be the risk of the security and therefore larger would be the return expected by the investors. In other words all securities are expected to yield return commensurate with the riskiness as measured by beta. This relationship is valid not only for individual securities, but is also valid for all portfolios whether efficient or inefficient.

23. 23 SML & CML It is necessary to contrast SML and CML. Both postulate a linear ( straight) line relationship between risk and return. In CML the risk is defined as total risk and is measured by standard deviation, while in SML the risk is defined as systematic risk and is measured by beta. CML is valid only for efficient portfolios while SML is valid for all portfolios and all individual securities as well. CML is the basis of the Capital market theory while SML is the basis of the Capital asset pricing model.

24. 24 Pricing of securities with CAPM: The CAPM can also be used for evaluating the pricing of securities. The expected return on security can be calculated using the CAPM formula. This return can be designated as the theoretical return. The real rate of return estimated to be realized from investing in a security can be calculated by the following formula:

25. 25 where: Ri = Estimated return P 0 = current market price P 1 = estimated market price after one year D 1 = anticipated dividend for the year

26. 26 Beta Expected return RpRp R S T U V W SML A B C

27. 27 R, S and T lie above the SML and U, V and W lie below the SML. The stocks above the SML yield higher returns for the same level of risk. They are thus under priced compared to their beta value while the stocks that lie below the SML are overpriced as the return that they provide is not commensurate to their beta value.

28. 28 Problems Q.1) Assume the assets below are correctly priced according to the SML. Derive the SML. What is the expected return on an asset with a beta of 2? R 1 = 6% B 1 = 0.5 R 2 = 12% B 2 = 1.5

29. 29 Q 2) Assume the SML is given as: R i = 0.04 + 0.08B and the estimated betas on two stocks are B x = 0.5 and B y = 2. What must the expected return on each of the two securities be in order for one to feel that they are a good purchase?

30. 30 Q.3) Calculate the expected return on the following stocks if R f =.05 and R m =.11 Stockbeta 1-.80 2.03 3.44 4.76 51.10 61.75

31. 31 3) Arbitrage Pricing Theory (APT) The theory was developed by: Stephen Ross as an alternative to CAPM in 1976. The CAPM asserts that only a single number- a security’s beta against the market- is required to measure risk. At the core of APT is the recognition that several systematic factors affect security returns.

32. 32 The APT asserts that asset prices are determined through an arbitrage relationship. It is based on the premise that two or more securities or portfolios that provide the same payoffs to their investors are same and must therefore sell at the same price. This is the ‘Law of One Price’. The fundamental logic of APT is that investors indulge in arbitrage whenever they find differences in the returns of assets with similar risk characteristics.

33. 33 In other words if there are two securities that have the same risk but different expected returns, investors will arbitrage, or eliminate, these differences by buying the security with the higher expected return (lower Price) and selling the one with lower expected return (higher price). This process of buying and selling the two securities by investor will cause the price of the security of the higher expected return to rise relatively to the one with the lower expected return. This trading activity will continue until the two securities have the same expected returns.

34. 34 Ross began with the idea that returns vary from expected levels because of : i) changes in the expected level of industrial production. ii) unanticipated inflation. iii) unanticipated movement in the shape of term structure of interest rates. iv) unanticipated shifts in risk premiums because of other economic forces.

35. 35 Assumptions of APT Investors have homogeneous expectations and are expected-utility-of-wealth maximizers. There are no imperfections or frictions in the market to impede investor buying and selling. Specifically, there are no transaction costs involved in security transactions. This assumption makes possible the arbitraging of mispriced securities thus forcing an equilibrium price.

36. 36 One important assumption of this model of equilibrium concerns the process of return generation on securities. The APT model assumes that various factors give rise to returns on securities and that the relation between security returns and that these factors is linear. Return Generating Process The APT assumes that the return on any stock is linearly related to a set of factors also referred to as systematic factors or risk factors as given in the following equation:

37. 37 Where: R i = return on stock i a i = expected return on stock i if all factors have a value of zero. I j = value of j th factor which influences the return on stock i (j = 1,…..j) b ij = sensitivity of stock i’s return to jth factor. e i = random error term which has a mean of zero and variance of σ 2 ei

38. 38 The last assumption is about the error term of above equation. The error term is expected to have a mean value of zero that is E(e) = 0.