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Finance 450 General Comments for Final Two Weeks

Finance 450 General Comments for Final Two Weeks. Course Goals, CAPM, APT, and Haugen’s Model, Active vs. Passive Portfolio Management, and Comments on Valuation. Welcome Back from Thanksgiving Break!. Good luck for the final two weeks of classes!. General Overview and Course Goals.

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Finance 450 General Comments for Final Two Weeks

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  1. Finance 450 General Commentsfor Final Two Weeks Course Goals, CAPM, APT, and Haugen’s Model, Active vs. Passive Portfolio Management, and Comments on Valuation

  2. Welcome Back from Thanksgiving Break! Good luck for the final two weeks of classes!

  3. General Overview and Course Goals • Give a man a fish, … • and you feed him for a day; • Teach a man to fish, … • and you feed for for a lifetime; • Teach a man to think, … • and he won’t have to eat fish every day!

  4. Goal of the Course • Not to teach you everything there is to know about analyzing securities (that would be impossible to do, given both the limited time available and the fact that the economic environment is constantly changing and evolving), • But to teach you how to think about the markets, so that you can be a more intelligent consumer of any investment advice you receive and a more critical reader of any future investment books you read (which I would anticipate and recommend that you do, since a lifetime of intelligent investing requires a lifetime of learning, and the more you read and learn, the better an investor you can be).

  5. Goal of the Course • Also, a goal is to help provide a better foundation for those of you who are considering going on for their CFA charters. • As such, the intended emphasis of this course is on aspects of investment analysis that aren’t covered in other finance classes and/or that are less readily accessible through self-study • Hopefully, the course has been successful in this regard, and you have learned a lot! • Additional comment: virtual portfolio project and English university system

  6. Now, back to the lecture!

  7. CAPM, APT, and Haugen’s Model • All three of these provide expected-return factor models that can be used to predict expected returns for individual securities • Can be used in conjunction with Markowitz optimization • Alternatively, these three models could be used to estimate the cost of equity capital for corporate financial management decisions • But, each of the three models is fundamentally different from the other models

  8. Asset Pricing Theories • Estimating expected return with the Asset Pricing Models of Modern Finance • CAPM: strong assumption -- strong prediction.

  9. Expected Return Expected Return B C x x x x x x Market Index x x x x x x x x x x x A x x x x x x x Market Beta Risk (Return Variability) Market Index on Efficient Set Corresponding Security Market Line

  10. Expected Return Expected Return Risk (Return Variability) Market Beta Market Index Inside Efficient Set Corresponding Security Market Cloud Market Index

  11. CAPM and Roll’s Critique • According to Richard Roll, the only testable implication of CAPM is that the true market portfolio is (mean-variance) efficient • i.e., CAPM implies M lies on the efficient frontier • all the other implications of CAPM, such as the SML, are a mathematical consequence of this and will follow naturally if the true market portfolio is efficient. • But, the true market portfolio is unobservable (since it contains ALL risky assets) • this leads to the problem of “benchmark error”, in which the index used as a proxy for the market portfolio does not perfectly match the true market portfolio • nor can we ever observe the true efficient frontier (it must always be estimated, and different assumptions will lead to different estimates)

  12. CAPM and Roll’s Critique • Thus, CAPM is ultimately untestable: • If a linear relationship between beta and expected return is found, just shows that proxy index is mean-variance efficient, not necessarily that the true market portfolio is mean-variance efficient, • and vice versa • Other effects of benchmark error: • Beta would be wrong • The SML would be wrong

  13. Arbitrage Pricing Theory (APT) • CAPM is criticized by Roll because of the difficulties in selecting a proxy for the market portfolio as a benchmark • An alternative pricing theory with fewer assumptions was developed by Stephen Ross: • Arbitrage Pricing Theory

  14. Arbitrage Pricing Theory - APT Three major assumptions: 1. Capital markets are perfectly competitive 2. Investors always prefer more wealth to less wealth with certainty 3. The stochastic process generating asset returns can be expressed as a linear function of a set of K factors or indexes

  15. Assumptions of CAPMThat Were Not Required by APT APT does not assume • A market portfolio that contains all risky assets, and is mean-variance efficient • Normally distributed security returns • Quadratic utility function

  16. Arbitrage Pricing Theory (APT) For i = 1 to N where: = return on asset i during a specified time period = expected return for asset i = reaction in asset i’s returns to movements in a common factor = a common factor with a zero mean that influences the returns on all assets = a unique effect on asset i’s return that, by assumption, is completely diversifiable in large portfolios and has a mean of zero = number of assets Ri Ei bik N

  17. Bik determine how each asset reacts to this common factor Each asset may be affected by growth in GNP, but the effects will differ In application of the theory, the factors are not identified Similarly to CAPM, the unique effects are independent and will be diversified away in a large portfolio Arbitrage Pricing Theory (APT)

  18. APT assumes that, in equilibrium, the return on a zero-investment, zero-systematic-risk portfolio is zero when the unique effects are diversified away The expected return on any asset i (Ei) can be expressed as: Arbitrage Pricing Theory (APT)

  19. Arbitrage Pricing Theory (APT) where: = the expected return on an asset with zero systematic risk where = the risk premium related to each of the common factors - for example the risk premium related to interest rate risk bi = the pricing relationship between the risk premium and asset i - that is how responsive asset i is to this common factor K

  20. Example of Two Stocks and a Two-Factor Model = changes in the rate of inflation. The risk premium related to this factor is 1 percent for every 1 percent change in the rate = percent growth in real GNP. The average risk premium related to this factor is 2 percent for every 1 percent change in the rate = the rate of return on a zero-systematic-risk asset (zero beta: boj=0) is 3 percent

  21. Example of Two Stocks and a Two-Factor Model = the response of asset X to changes in the rate of inflation is 0.50 = the response of asset Y to changes in the rate of inflation is 2.00 = the response of asset X to changes in the growth rate of real GNP is 1.50 = the response of asset Y to changes in the growth rate of real GNP is 1.75

  22. Example of Two Stocks and a Two-Factor Model = .03 + (.01)bi1 + (.02)bi2 Ex = .03 + (.01)(0.50) + (.02)(1.50) = .065 = 6.5% Ey = .03 + (.01)(2.00) + (.02)(1.75) = .085 = 8.5%

  23. Multiple factors expected to have an impact on all assets: Inflation Growth in GNP Major political upheavals Changes in interest rates And many more…. Contrast with CAPM insistence that only beta is relevant Arbitrage Pricing Theory (APT)

  24. APT vs. CAPM • In form, APT is similar to CAPM, but with multiple risk factors, rather than just one market risk factor, driving expected returns • In practice, APT appears to work better than CAPM • But, while CAPM has Roll’s Critique, APT has Shanken’s Critique …

  25. Shanken’s Challenge to Testability of the APT • If returns are not explained by a model, it is not considered rejection of a model; however if the factors do explain returns, it is considered support • APT has no advantage because the factors need not be observable, so equivalent sets may conform to different factor structures • Empirical formulation of the APT may yield different implications regarding the expected returns for a given set of securities • Thus, the theory cannot explain differential returns between securities because it cannot identify the relevant factor structure that explains the differential returns

  26. The Arbitrage Pricing Theory • Estimating the macro-economic betas. • Obtain a characteristic line for each risk factor • Regress return on stock against risk factor

  27. Return to G.E. 25% 20% 15% 10% 5% 0% -5% -10% -15% -20% -25% -10% -5% 0% 5% 10% Percentage Change in Yield on Long-term Govt. Bond Relationship Between Return to General Electric and Changes in Interest Rates Line of Best Fit April, 1987

  28. The Arbitrage Pricing Theory • Estimating the macro-economic betas. • No-arbitrage condition for asset pricing. • If risk-return relationship is non-linear, you can arbitrage.

  29. Asset Pricing Theories • Estimating expected return with the Asset Pricing Models of Modern Finance • CAPM: strong assumption -- strong prediction. • APT: weak assumption -- weak prediction.

  30. Expected Return 35% F E D 25% C 15% B A 5% -3 -1 -5% 1 3 Interest Rate Beta -15% Curved Relationship Between Expected Return and Interest Rate Beta

  31. The Arbitrage Pricing Theory • Two stocks: • A: E(r) = 4%; Interest-rate beta = -2.20 • B: E(r) = 26%; Interest-rate beta = 1.83 • Invest 54.54% in E and 45.46% in A. • Portfolio E(r) = .5454 * 26% + .4546 * 4% = 16% • Portfolio beta = .5454 * 1.83 + .4546 * -2.20 = 0 • With many combinations like this, you can create a risk-free portfolio with a 16% expected return.

  32. The Arbitrage Pricing Theory • Two different stocks: • C: E(r) = 15%; Interest-rate beta = -1.00 • D: E(r) = 25%; Interest-rate beta = 1.00 • Invest 50.00% in E and 50.00% in A. • Portfolio E(r) = .5000 * 25% + .4546 * 15% = 20% • Portfolio beta = .5000 * 1.00 + .5000 * -1.00 = 0 • With many combinations like this, you can create a risk-free portfolio with a 20% expected return. Then sell-short the 16% and invest the proceeds in the 20% to arbitrage.

  33. The Arbitrage Pricing Theory • No-arbitrage condition for asset pricing. • If risk-return relationship is non-linear, you can arbitrage. • Attempts to arbitrage will force linearity in relationship between risk and return.

  34. Expected Return 35% F E 25% D 15% C 5% B A -3 -1 1 3 -5% Interest Rate Beta -15% APT Relationship Between Expected Return and Interest Rate Beta

  35. The Arbitrage Pricing Theory • But, finite samples and fat-tailed distributions preclude the formation of the riskless hedges that are necessary to ensure that the theory holds • E.g., LTCM • More significantly, true risk factors never known for sure • Moreover, if markets are inefficient, then factors other than risk factors may also be important • This is the key contribution of Haugen

  36. Haugen’s Approach • Two components: • Risk factor model • for modeling stocks’ risks and covariances • Ad hoc expected return factor model • for predicting stocks’ expected returns • allow both risk factors and non-risk factors • Combine together using Markowitz portfolio optimization

  37. Probability Distribution For Returns to a Portfolio Probability Variance of Return Possible Rates of Returns Expected Return

  38. Risk Factor Models • The variance of stock returns can be split into two components: • Variance = systematic risk + diversifiable risk • Systematic risk is modeled using an APT-type risk-factor model • Measures extent to which stocks’ returns [jointly] move up and down over time • Estimated using time-series data • Diversifiable risk is reduced through optimal diversification

  39. Expected Return Factor Models • Expected return factor models measure / predict the extent to which the stocks’ returns are different from each other within a given period of time.

  40. Expected Return Factor Models • The factors in an expected return model represent the character of the companies. • They might include the history of their stock prices, its size, financial condition, cheapness or dearness of prices in the market, etc. • Unlike CAPM and APT, not only risk factors such as market beta or APT betas are included • Factor payoffs are estimated by relating individual stock returns to individual stock characteristics over the cross-section of a stock population (here the largest 3000 U.S. stocks).

  41. Five Factor Families • Risk • Market and APT betas, TIE, debt ratio, etc., values and trends thereof • Liquidity • Market cap., price, trading volume, etc. • Price level • E/P, B/P, Sales/P, CF/P, Div/P • Profitability • Profit margin, ROE, ROA, earnings surprise, etc. • Price history (technical factors) • Excess return over past 1, 2, 3, 6, 12, 24, & 60 months

  42. The Most Important Factors • The monthly slopes (payoffs) are averages over the period 1979 through mid 1986. • “T” statistics on the averages are computed, and the stocks are ranked by the absolute values of the “Ts”.

  43. 1979/01 through 1986/07 through 1993/12 1986/06 Factor Mean Confidence Mean Confidence One-month excess return -0.97% 99% -0.72% 99% Twelve-month excess 0.52% 99% 0.52% 99% return Trading volume/market -0.35% 99% -0.20% 98% cap Two-month excess return -0.20% 99% -0.11% 99% Earnings to price 0.27% 99% 0.26% 99% Return on equity 0.24% 99% 0.13% 97% Book to price 0.35% 99% 0.39% 99% Trading volume trend -0.10% 99% -0.09% 99% Six-month excess return 0.24% 99% 0.19% 99% Cash flow to price 0.13% 99% 0.26% 99% Most Important Factors

  44. The Most Important Factors • Among the factors that are significant (i.e., that can be used to distinguish between which companies will have higher returns and which will have lower returns) are: • A number of liquidity factors • Various fundamental factors, indicating value with growth • Technical factors, indicating short-term reversals and intermediate term momentum • Suggest that technical factors provide marginal value when used in conjunction with fundamental analysis • Notably, no CAPM or APT risk factors are included!

  45. The Great Race(From Ch. 13)

  46. A Test of Relative Predictive Power1980 -1997 Model employing factors exploiting the market’s tendencies to over- and under-react vs. Models employing risk factors only (“deductive” models of modern finance).

  47. The Ad Hoc Expected Return Factor Model • Risk • Liquidity • Profitability • Price level • Price history • Earnings revision and surprise

  48. Average Annualized Return 45% 40% 35% 30% 25% 20% 15% 10% 5% 0% Decile 1 2 3 4 5 6 7 8 9 10 Decile Returns for the Ad Hoc Factor Model (1980 through mid 1997)

  49. The Capital Asset Pricing Model • Market beta measured over the trailing 3 to 5-year periods). • Stocks ranked by beta and formed into deciles monthly.

  50. Average Annualized Return 45% 40% 35% 30% 25% 20% 15% 10% 5% 0% Decile 1 2 3 4 5 6 7 8 9 10 Decile Returns for CAPM Model

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