Fi8000 Valuation of Financial Assets

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

2. Risk, Return and Portfolio Theory • Risk and risk aversion • Utility theory and the intuition for risk aversion • Mean-Variance (M-V or μ-σ) criterion • The mathematics of portfolio theory • Capital allocation and the optimal portfolio • One risky asset and one risk-free asset • Two risky assets • n risky assets • n risky assets and one risk-free asset • Equilibrium in capital markets • The Capital Asset Pricing Model (CAPM) • Market Efficiency

3. Reward and Risk: Assumptions • Investors prefer more money (reward) to less: all else equal, investors prefer a higher reward to a lower one. • Investors are risk averse: all else equal, investors dislike risk. • There is a tradeoff between reward and risk: Investors will take risks only if they are compensated by a higher reward.

4. Reward and Risk ☺ Reward ☺ Risk

5. Quantifying Rewards and Risks • Reward – a measure of wealth • The expected (average) return • Risk • Measures of dispersion - variance • Other measures • Utility – a measure of welfare • Represents preferences • Accounts for both reward and risk

6. Quantifying Rewards and Risks The mathematics of portfolio theory (1-3)

7. Comparing Investments:an example Which investment will you prefer and why? • A or B? • B or C? • C or D? • C or E? • D or E? • B or E, C or F (C or E, revised)? • E or F?

8. Comparing Investments:the criteria • A vs. B – If the return is certain look for the higher return (reward) • B vs. C – A certain dollar is always better than a lottery with an expected return of one dollar • C vs. D – If the expected return (reward) is the same look for the lower variance of the return (risk) • C vs. E – If the variance of the return (risk) is the same look for the higher expected return (reward) • D vs. E – Chose the investment with the lower variance of return (risk) and higher expected return (reward) • B vs. E or C vs. F (or C vs. E) – stochastic dominance • E vs. F – maximum expected utility

9. Comparing Investments Maximum return If the return is risk-free (certain), all investors prefer the higher return Risk aversion Investors prefer a certain dollar to a lottery with an expected return of one dollar

10. Comparing Investments Maximum expected return If two risky assets have the same variance of the returns, risk-averse investors prefer the one with the higher expected return Minimum variance of the return If two risky assets have the same expected return, risk-averse investors prefer the one with the lower variance of return

11. The Mean-Variance Criterion Let A and B be two (risky) assets. All risk-averse investors prefer asset A to B if { μA ≥ μB and σA < σB } or if { μA > μB and σA ≤ σB } Note that we can apply this rule only if we assume that the distribution of returns is normal.

12. The Mean-Variance Criterion(M-V or μ-σ criterion) ☺ E(R) = μR ☺ STD(R) = σR

13. Other Criteria The basic intuition is that we care about “bad” surprises rather than all surprises. In fact dispersion (variance) may be desirable if it means that we may encounter a “good” surprise. When we assume that returns are normally distributed the expected-utility and the stochastic-dominance criteria result in the same ranking of investments as the mean-variance criterion.

14. The Normal Distribution of Returns Pr(R) 68% 95% μ- 2σ μ μ+σ μ+2σ μ- σ R

15. The Normal Distribution of Returns Pr(Return) σR: Risk μR: Reward 0 R=Return

16. The Normal DistributionHigher Reward (Expected Return) Pr(Return) μB μA < R=Return

17. The Normal DistributionLower Risk (Standard Deviation) Pr(Return) A σA < σB B μA= μB R=Return

18. Practice problems BKM Ch. 6: 7th edition: 1,13,14, 34; 8th edition : 4,13,14, CFA-8. Mathematics of Portfolio Theory: Read and practice parts 1-5.