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Quantitative Analysis

Quantitative Analysis. Finding Alpha. Fundamental Analysis Forecast Dividends and find PV Look for stocks for which price ¹ PV Ratio Analysis Compare accounting ratios Buy neglected stocks, short glamorous stocks Quantitative Analysis

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Quantitative Analysis

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  1. Quantitative Analysis

  2. Finding Alpha • Fundamental Analysis • Forecast Dividends and find PV • Look for stocks for which price ¹PV • Ratio Analysis • Compare accounting ratios • Buy neglected stocks, short glamorous stocks • Quantitative Analysis • Estimate regressions to identify equity styles that earn alpha

  3. Quantitative Analysis • Find anomalies to the CAPM • Use regressions to forecast when the anomalies will be particularly strong. • Tilt towards styles with positive alpha • Tilt away from styles with negative alpha

  4. Misvaluation View • Misvaluation View: • Some stocks are just neglected by analysts • Over-reaction by investors • Foundation of most hedge fund equity strategies • “Once an anomaly is discovered in academics, it takes about 5 to 10 years for traders to actually make it go away” (Bob Turley, Global Alpha Fund)

  5. Value Strategies Average returns of Book-to-Market Portfolios 1927-2009 Growth Value

  6. Value Strategies Alphas of Book-to-Market Portfolios 1927-2009 Value Growth

  7. Momentum Portfolios • Portfolio Formation at the end of month t: • Calculate the return for every stock over the period from month t-12 to month t-2. • Rank all stocks by their past return • Divide stocks into 10 value-weighted portfolios • Worst 10% in one portfolio • Next 10% in next portfolio (etc.)

  8. Momentum Portfolios Average Momentum Portfolio Returns 1927-2009

  9. Momentum Portfolios Momentum Portfolio Alphas 1927-2009

  10. Quantitative Analysis • Pros: • Straight forward to implement • We know how to maximize Sharpe Ratios • We don’t have to forecast dividends • Cons • What has happened historically may not continue in the future

  11. Value and Momentum: • Why do value and momentum strategies earn positive alpha to begin with? • Misvaluation view • Neglect and Over-reaction • Broken CAPM View: • The CAPM doesn’t correctly model investor behavior. • The CAPM was not built to tell us how people should behave, but to model how they actually behave. • Perhaps the model isn’t a realistic reflection of reality.

  12. CAPM Assumptions • Everyone has same forecast of expected returns, standard deviations, and correlations. • Probably not true • When this assumption is relaxed, we still get the a CAPM-like model, but in equilibrium, the VWP is no longer MSRP. Further, it is not obvious what portfolio is MSRP. • Roll’s Critique: Non-zero alpha can be the result of 1) Prices out of equilibrium (markets inefficient) 2) You are using the wrong portfolio in your test (Value-weighted portfolio is not MSRP in equlibrium). • It’s impossible to tell which is the true cause

  13. CAPM Assumptions 2) The R-Investor only cares about maximizing Sharpe ratio • Perhaps the R-investor has other objectives.

  14. Arbitrage Pricing Theory • The CAPM should hold • APT: Ross (1976) • Makes minimal assumptions: • In equilibrium, no arbitrage opportunities • Conclusion: alphas should be zero

  15. Arbitrage Pricing Theory • Notation: • Alpha is measured as the intercept in the following regression:

  16. Arbitrage Pricing Theory • Suppose we measure the alpha of a “well diversified” portfolio. • Most of the variation is systematic • Variance of ei is small • Examples: • value portfolio top 30% (HW #17): • 82% of the total variance is systematic • For Ford Stock (HW #16) • 28% of the total variance is systematic • To an approximation, we can ignore eiin our regression for well diversified portfolios.

  17. Examples Y variables: returns on different stocks X variable: return on market Asset 1: Lot’s of variation in e 11% of variation is systematic R-squared=0.11 89% of variation is unsystematic Asset 2: Not a lot of variation in e 82% of variation is systematic R-squared=0.82 18% of variation is unsystematic

  18. Extreme Example Asset 3: All error terms are 0 100% of variation is systematic R-squared=1 0 of variation is unsystematic

  19. Examples • For the “extreme example” there is no error term: • For example 2 (well diversified portfolio): • Error terms are small • Most variation is systematic

  20. Arbitrage • APT: • Assume: In equilibrium there are no arbitrage opportunities (chance to make free money) • Claim: for well diversified portfolios, alpha must be approximately zero, or in other words, CAPM view of equilibrium is approximately correct.

  21. Arbitrage • Assume there is a well diversified portfolio (A) whose alpha is 1% • Assume beta=1.5 (arbitrary) • Assume there is some other well diversified portfolio (B) with alpha of -0.5% • Assume beta=3 (arbitrary)

  22. Arbitrage • The beta of a portfolio with weight w in A and (1-w) in B has a portfolio beta of: and a portfolio alpha of

  23. Arbitrage • Consider a portfolio (z) with a weight of 2 in asset A and a weight of -1 in asset B • But since z is well diversified:

  24. Arbitrage • But az by definition, is E[rz]-rf • But portfolio z is risk-less (approximately) • Almost all systematic risk is diversified away, because it is composed of two well-diversified portfolios. • Systematic risk has been perfectly hedged • Hence, E[rz]=rz • Because portfolio is approximately riskless, what you expect is what you get. • But since alpha=0.01 rz =rf +0.01 • Borrow at risk-free rate, invest in this portfolio. • Free money.

  25. Arbitrage • As many investors do this, what happens to the cost of portfolio z? • Goes up. • What happens to the realized return? • Goes down. • In equilibrium rz=rf

  26. Example 2 • Suppose there are two well diversified portfolios: How do you attack the arbitrage opportunity?

  27. Example 2 • Portfolio z: • Weight in A = -1 • Weight in B = 2 • Approximately riskless • Excess Return=2*.50+(-1*-.06)=1.06(%) • Borrow all you can at risk-free rate • Invest in portfolio z

  28. Long-Short Hedge Funds • Common hedge fund strategies: • Long value, short growth • Long long/short momentum strategies • AQR Capital Management • Barclay’s Global Investors Global Ascent • Goldman Sachs Global Alpha Fund

  29. Anomaly • Even though many funds are attacking these apparent arbitrage opportunities, opportunities apparently have not gone away. • Why? • Industry view: pervasive mispricing

  30. Anomaly • Academic view: • These portfolios are not really close to risk-free • Why doesn’t the risk go away? • If the “e” in portfolio A is not independent to the “e” in portfolio B, then you can actually magnify the risk of the “arbitrage” portfolio by combining A and B. • Related to stat rule number 5 - the variance of a sum of random variables depends on the covariance. • the value-weighted portfolio is not the right portfolio to measure alpha against.

  31. Arbitrage Pricing Theory • Pros of APT: • Only relies on assumption of no-arbitrage • Tells us the general form of any model of expected returns. • Expected returns must be a linear function of slope coefficients (betas). • Cons of APT • What is the right portfolio or portfolios to use in measuring alpha? • APT tells us nothing about this.

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