Portfolio Theory

1. Draft lecture – FIN 352 Professor Dow CSU-Northridge March 2012 Portfolio Theory

2. Modern Portfolio Theory (MPT) • If markets are generally efficient, then… • Looking for undervalued assets is not a useful investing strategy. • Does it matter what you do? • MPT looks at the investing implications of market efficiency. • Assets are evaluated in terms of risk and expected return rather than price or intrinsic value. • The hard part is how to measure risk.

3. Modern Portfolio Theory (MPT) • An individual chooses what portfolio to have. • Portfolios are judged based on expected return and risk (as measured by standard deviation). • The risk of a single asset is the risk it adds to the portfolio.

4. Three Major Parts to MPT • Market Efficiency • Previous Lecture • Portfolio Selection • We’ll learn the basic principles and calculations • Skip the more advanced calculations (see the book) • What is the bottom line for portfolio selection?

5. Three Major Parts to MPT • Market Price of Risk • Quantifying the Risk-Return Tradeoff • Theory of Expected Returns • CAPM (we’ll only cover the basics) • Issues related to measuring uncertainty • How to Evaluate Investor Performance

6. Criticisms of MPT • Markets are not necessarily efficient. • Uncertainty is not measured correctly. • Overly technical. • What is the alternative?

7. Portfolio Selection: Calculating Returns and Risk • Statistics Review • Expected Return • Standard Deviation • Covariance and Correlation • Normal Distribution • Tail Probabilities

8. Portfolio Selection: Calculating Returns and Risk • The portfolio return equals the weighted average of the individual asset returns. • RP = w1R1 + w2R2 • 60% of your wealth is in stocks, 40% in bonds. • Stocks earned 7%, bonds earned 5%. • (0.6)(7%)+(0.4)5% = 6.2%

9. Portfolio Selection: Calculating Returns and Risk • The expected return to the portfolio is the weighted average of the expected returns to the individual assets. • E(RP) = w1E(R1) + w2E(R2) • 60% of your wealth is in stocks, 40% in bonds. Stocks are expected to earned 12%, bonds are expected to earned 2%. • (0.6)(12%)+(0.4)2% = 8%

10. Portfolio Selection: Calculating Returns and Risk • Is the portfolio standard deviation the average of the individual standard deviations • NO! • Some of the changes will cancel out across securities. • This is diversification – combining different assets reduces risk.

11. Portfolio Selection: Calculating Returns and Risk • The correlation coefficient, Rho (), measures how movements in returns are related. •  > 0 • Returns tend to move in the same direction. •  < 0 • Returns tend to move in opposite directions. •  = 0 • Movements in returns are unrelated.

12. Portfolio Selection: Calculating Returns and Risk • The correlation coefficient, Rho (), determines the amount of diversification •  = 1 • Returns always move in same direction; no diversification •  = -1 • Returns always move in opposite direction; can eliminate risk completely. • 0 <  < 1 • Returns sometimes move in different directions; some diversification

13. Portfolio Selection: Calculating Returns and Risk • Negative correlations would be ideal. • Generally, security returns have positive correlations. • Why? • Correlations not equal to 1 so still opportunities for diversification.

14. Portfolio Selection: Risk and Asset Choice • <Chart: Add assets and portfolio risk falls> • How much depends on which assets. • Can’t diversify away all risk. • Non-diversifiable, systematic or market risk • Reflects changes in the economy or in the willingness of investors to bear risk.

15. Portfolio Selection: Risk and Asset Choice • <Chart: Risk and Return by Asset Class> • Higher-risk assets offered higher return on average in the past. • Mixing assets classes will provide better diversification. Lower risk for the same expected return. • Holding more of the relatively high-risk assets will increase portfolio risk (and expected return).

16. Portfolio Selection: Risk and Asset Choice • Fancy Version (discussed in book – optional, not required for class) • The Efficient Frontier • Market portfolio provides maximum diversification and is the best portfolio of risky assets. • You should hold the market portfolio and a risk-free asset; the share of each depending on your risk tolerance.

17. Portfolio Selection: Risk and Asset Choice • Our basic investment strategy up to now: • Be diversified • Choose the mix of assets to match tolerance for risk. • This basic asset allocation approach is broadly consistent with MPT. • More complicated versions for sophisticated investors.

18. Portfolio Selection: Criticisms of MPT • MPT assumptions: • Markets are efficient (talked about previously) • We know the distribution of stock returns. • Portfolio risk is adequately described by the standard deviation. • Returns are normally distributed. • Individuals only care about standard deviations. • Assumptions don’t have to hold exactly, but should be reasonably good descriptions.

19. Portfolio Selection: Criticisms of MPT • History may not predict the future • Standard deviations may change • Why? • Correlations may change • Why?

20. Portfolio Selection: Criticisms of MPT • Distributions of returns may not be normal. • Asymmetric risk • Skewness • Downside risk • Fat tails • Greater risk of extreme event • Underestimate risk • Can investors take advantage of this?

21. Portfolio Selection: Criticisms of MPT • Cannot quantify important risks. • Risk vs. Uncertainty • Risk: We know the frequency (distribution of events) • Uncertainty: We don’t know how often events will occur. • Examples? • What if we didn’t even know the event could occur?

22. Portfolio Selection: Criticisms of MPT [T]here are known knowns; there are things we know we know. We also know there are known unknowns; that is to say we know there are some things we do not know. But there are also unknown unknowns – the ones we don't know we don't know. - Donald Rumsfeld

23. Portfolio Selection: Criticisms of MPT • Black Swan Risk • What should an investor do? • Be conservative? • Be robust to shocks? • Gamble on the possibility of big changes?

24. Market Price of Risk: Portfolios • The market price of risk is the extra return you expect to get for holding an additional level of risk. • This is determined by the average of investors’ attitudes towards risk. • The market risk premium is defined as E(Rm)-Rf

25. Market Price of Risk: Risk of a Single Security • Can’t evaluate risk of a security in isolation. • How much risk does the security add to your portfolio? • Expected return to the security “should” be a function of this risk.

26. Market Price of Risk: Risk of a Single Security • Factor models. • Expected return is a function of various “factors”. • Economic factors • Business characteristics • Market returns

27. Market Price of Risk: Risk of a Single Security • Capital Asset Pricing Model (CAPM) • Risk consists of two parts • Business-specific risk • Which can be diversified away • Market risk • Which cannot be diversified away • If you hold a well-diversified portfolio, only the market risk matters. • Since only market risk matters, investors only need to be compensated for a security’s market risk.

28. Market Price of Risk: Risk of a Single Security • Beta (β) represents the amount of market risk. • How to measure β (the non-technical version). • On average, how much does the return to the asset change when the return to the market changes? • If it changes an equal percentage, it has a β of 1. • If it moves twice as much, it has a β of 2. • If it’s movements are unrelated to the market, it has a β of 0. • If it moves equally, but opposite of the market, it has a β of -1. • What determines β? • http://www.youtube.com/watch?v=zv_XSRVlFUE

29. Market Price of Risk: Risk of a Single Security • How much extra return do you get for a unit of risk? The market risk premium! • This gives us the CAPM equation • E(Ri) = Rf + βi(E(Rm) - Rf) • If the risk-free rate is 5%, the expected market return is 9% and the β of the security is 1.5, what return should it offer. • 11% • What if the β was 0.5?

30. Market Price of Risk: Risk of a Single Security • How does CAPM perform? • Beta matters • But it’s not the only thing that matters • Multi-Factor Models

31. Market Price of Risk: Evaluating Investor Performance • Why evaluate performance? • Does an investment strategy work? • Did an money manager perform better than average? • Reasons for good performance • Risk • Skill • Luck

32. Market Price of Risk: Evaluating Investor Performance • Managers exceed expectations if they have higher return than they should given the risk. • Usual caveats about repeat performance • How to measure expectations? How to measure risk?

33. Market Price of Risk: Evaluating Investor Performance • Using a benchmark: Return compared with index portfolio of similar assets. • Use standard deviation as a measure of risk. • Sharpe Ratio = E(Ri – Rf)/σ • Downside risk. • Use a model to measure of risk.

34. Market Price of Risk: Evaluating Investor Performance • CAPM provides a measure of risk. • Ri– Rf = αi+ β(Rm-Rf) + ui • α measures excess return above that implied by the CAPM • α is sometimes used as a generic term to refer to the value-added produced by the investor.