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ASSET PRICING

ASSET PRICING. FACULTY F MATHEMATICS BELGRADE 2010. Introduction. Investors are concerned with Risk Returns What determines the required compensation for risk? It will depend on The risk faced by investors The tradeoff between risk and return they face. Measuring Return.

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ASSET PRICING

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  1. ASSET PRICING FACULTY F MATHEMATICS BELGRADE 2010

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

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

  4. example 1 • Bond: 1 month holding period • buy for $9488, sell for $9528 • 1 month R: 9528 - 9488 =0 .0042 = 0.42% 9488

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

  6. example 2 • 100 shares IBM, 9 months • buy for $62, sell for $101.50 • $.80 dividends • 9 month R: 101.50 - 62 + .80 =0 .65 =65% 62

  7. annualized R: (1.65)12/9 - 1 =0 .95 = 95%

  8. example 3 R Prob(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 s2 = (0.2)(10%-2%)2 + (0.4)(5%-2%)2 + (0.4)(-5%-2%)2 = 0.0039 s = 6.24%

  10. Two risky assets

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

  12. Feasible portfolios

  13. Dominated and Efficient Portfolios

  14. Efficient frontier • 1. Find all asset expected returns and standard deviations. • 2. Pick one 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.

  15. CAPM • CAPM Characteristics: • bi = sismrim/sm2 • 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

  16. Utility Maximization

  17. Tobin Separation Theorem • When the riskfree asset is introduced, • All investors prefer a combination of • 1) The riskfree asset and • 2) The market portfolio • 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 • What should E(rIBM) be? • Answer:

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