1. ASSET PRICING FACULTY F MATHEMATICS BELGRADE 2010

2. Introduction Investors are concerned with Investors are concerned with –Risk –Returns What determines the required compensation for risk? What determines the required compensation for risk? It will depend on It will depend on –The risk faced by investors –The tradeoff between risk and return they face

3. return = R = change in asset value + income initial value Measuring Return R is typically annualized R is typically annualized

4. example 1 Bond: 1 month holding period Bond: 1 month holding period buy for $9488, sell for $9528 buy for $9488, sell for $9528 1 month R: 1 month R: Bond: 1 month holding period Bond: 1 month holding period buy for $9488, sell for $9528 buy for $9488, sell for $9528 1 month R: 1 month R: 9528 - 9488 9488 =0.0042 = 0.42%

5. annualized R: annualized R: (1.0042) 12 - 1 = 0.052 = 5.2%

6. example 2 100 shares IBM, 9 months 100 shares IBM, 9 months buy for $62, sell for $101.50 buy for $62, sell for $101.50 $.80 dividends $.80 dividends 9 month R: 9 month R: 100 shares IBM, 9 months 100 shares IBM, 9 months buy for $62, sell for $101.50 buy for $62, sell for $101.50 $.80 dividends $.80 dividends 9 month R: 9 month R: 101.50 - 62 +.80 62 =0.65 =65%

7. annualized R: annualized R: (1.65) 12/9 - 1 =0.95 = 95%

8. example 3 RProb(R) 10% 0.2 5% 0.4 -5% 0.4 E(R) =(0.2)10% + (0.4)5% + (0.4)(-5%) = 2%

9. example 4   = (0.2)(10%-2%) 2 = 0.0039 + (0.4)(5%-2%) 2 + (0.4)(-5%-2%) 2  = 6.24%

10. Two risky assets

11. Diversification  # assets systematic risk unsystematic risk total risk

12. Feasible portfolios

13. Dominated and Efficient Portfolios

14. Efficient frontier 1. Find all asset expected returns and standard deviations. 1. Find all asset expected returns and standard deviations. 2. Pick one expected return and minimize portfolio risk. 2. Pick one expected return and minimize portfolio risk. 3. Pick another expected return and minimize portfolio risk. 3. Pick another expected return and minimize portfolio risk. 4. Use these two portfolios to map out the efficient frontier. 4. Use these two portfolios to map out the efficient frontier.

15. CAPM CAPM Characteristics: CAPM Characteristics: – bi = sismrim/sm2 Asset Pricing Equation: Asset Pricing Equation: –E(ri) = rf + bi[E(rm)-rf] CAPM is a model of what expected returns should be if everyone solves the same passive portfolio problem CAPM is a model of what expected returns should be if everyone solves the same passive portfolio problem

16. Utility Maximization

17. Tobin Separation Theorem When the riskfree asset is introduced, When the riskfree asset is introduced, All investors prefer a combination of All investors prefer a combination of 1) The riskfree asset and 1) The riskfree asset and 2) The market portfolio 2) The market portfolio Such combinations dominate all other assets and portfolios (in a sense of risk-return) Such combinations dominate all other assets and portfolios (in a sense of risk-return)

18. CML

19. CAPM Suppose you have the following information: rf = 3.5% E(rm)=8.5% bIBM=0.75 Suppose you have the following information: rf = 3.5% E(rm)=8.5% bIBM=0.75 What should E(rIBM) be? What should E(rIBM) be? Answer: Answer: