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Risk, Dispersion of Analyst Forecasts and Stock Returns

Risk, Dispersion of Analyst Forecasts and Stock Returns. By Shisheng Qu, Laura Starks, and Hong Yan Presentation for Inquire Europe. What Do We Know (or Think We Know) about the Dispersion of Analysts Forecasts?.

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Risk, Dispersion of Analyst Forecasts and Stock Returns

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  1. Risk, Dispersion of Analyst Forecasts and Stock Returns By Shisheng Qu, Laura Starks, and Hong Yan Presentation for Inquire Europe

  2. What Do We Know (or Think We Know) about the Dispersion of Analysts Forecasts? Conflicting evidence on whether dispersion of analysts forecasts predicts future returns and the direction of the relation.

  3. What does the Dispersion of Analyst Forecasts Measure? • Dual aspects • Measure of differences of opinion among investors regarding the future earnings of the firm • Measure of uncertainty, i.e., ex ante risk, surrounding the future earnings of the firm • Dual aspects cloud the effects of dispersion on stock prices

  4. Differences of Opinion and Binding Short-sales Constraints • Argument: When short-sales constraints are binding and when investors have differences in opinions regarding equity prices, the prices tend to reflect the view of the more optimistic investors because investors with pessimistic valuations cannot easily engage in short sales. • Implication: Measures of differences of opinion (such as dispersion of analyst forecasts) should predict lower future returns.

  5. Information Risk • Argument: Information risk is a systematic risk factor that should be priced. • Implication: Measures of information risk (such as dispersion of analyst forecasts) should predict higher future returns.

  6. Principal Contributions of Paper Evidence that analyst forecast dispersion embodies information risk factors. • Stylized model to highlight effects of analyst forecast dispersion on stock prices • Introduction of new systematic risk factors based on the information risk reflected in analyst forecast dispersion and the variability of that dispersion • Empirical evidence on the pricing power of these factors

  7. Principal Empirical Results • Portfolios with higher levels of dispersion or higher levels of variability of dispersion have progressively more exposure to common risk factors: market, size and book-to-market • Factors constructed from dispersion or variability of dispersion are: • Correlated with the common risk factors, giving economic content to these factors • Have significant pricing power • Mutual fund managers’ implied expected returns are related to the levels of dispersion and variability of dispersion in stocks.

  8. Highlights of Theoretical Model • Expected return = f(Differences in forecasts only if there are differences in investors’ precisions of forecasts) • Expected price = f(investors’ forecast dispersion) • Variance of expected price = f(variability in investors’ forecast dispersion) • Dispersion and variability of dispersion capture components of information risk environment

  9. Empirical Analysis • Measures of dispersion • Relation between analyst forecast dispersion measures and commonly used systematic factors • Pricing power of analyst forecast dispersion measures using testing assets: • Size and book-to-market sorted portfolios • Industry portfolios • Relation between implied expected returns from mutual fund portfolio holdings and analyst forecast dispersion measures

  10. Data • Analysts’ current year earnings per share forecasts • Institutional Brokers Estimate System (I/B/E/S) • Monthly from 1983 through 2001 • Monthly returns (CRSP) • Firms included in the sample for a given month if: • At least five (two) analysts forecasts within month • At least 10 monthly summary statistics on I/B/E/S • Stock price greater than $5.00 • Mutual fund holdings from CDA/Spectrum

  11. Number of Firms Meeting Sample Selection Requirements

  12. Alternative Measures of Dispersion of Analyst Forecasts Base Measure: Standard deviation of monthly EPS forecasts Stock price at end of previous year Alternative Measure: Standard deviation of monthly EPS forecasts Absolute value of mean EPS forecast

  13. Variable Mean Std 5th Median 95th PRC($) 33.51 25.26 8.88 28.50 72.13 NumEst 14.3 7.6 6.0 12.0 30.0 DISP 0.68% 1. 47% 0.05% 0.33% 2. 23% DISPA 17.65% 131.15% 0.95% 4.56% 45.45% STDISP 0.27% 0.65%  0.02%  0.13%  0.88% Descriptive Statistics From Table 1

  14. RANK DISP SIZE (MM$) # of Analysts Forecasts U1 0.12% 7556 15.8 U2 0.26% 4007 14.7 U3 0.43% 3566 14.3 U4 0.77% 3049 13.9 U5 2.48% 1838 13.6 Sort Stocks into Quintile Portfolios by DISP Characteristics of Portfolios: From Table 2

  15. RANK STDISP SIZE (MM$) # of Analysts Forecasts U1 0.05% 8101 17.7 U2 0.09% 4156 15.2 U3 0.15% 3534 14.1 U4 0.26% 2617 13.0 U5 0.87% 1609 12.2 Sort Stocks into Quintile Portfolios by STDISP Characteristics of Portfolios: From Table 2

  16. DispersionQuintiles Size Small 2 3 4 Size Big All 1 1.97% 1.60% 1.49% 1.38% 1.27% 1.54% 2 1.68% 1.55% 1.34% 1.28% 1.17% 1.40% 3 1.37% 1.43% 1.36% 1.17% 1.25% 1.32% 4 1.23% 1.42% 1.22% 1.31% 1.15% 1.27% 5 0.73% 1.01% 0.99% 1.07% 1.03% 0.96% high-low -1.24% -0.59% -0.50% -0.31% -0.24% -0.58% t(high-low) -4.49 -2.01 -1.63 -1.13 -0.72 -2.15 Returns on Dispersion & Size Quintiles(At least 2 analysts and Alternative Dispersion Measure) From Table 3

  17. Dispersion Quintiles Size Small 2 3 4 Size Big All 1 1.81% 1.49% 1.35% 1.25% 1.17% 1.41% 2 1.50% 1.41% 1.39% 1.21% 1.20% 1.34% 3 1.44% 1.34% 1.29% 1.25% 1.16% 1.30% 4 1.27% 1.41% 1.24% 1.31% 1.22% 1.29% 5 0.99% 1.36% 1.15% 1.20% 1.13% 1.17% high-low -0.82% -0.13% -0.20% -0.05% -0.04% -0.25% t(high-low) -3.11 -0.68 -0.85 -0.22 -0.14 -1.48 Returns on Dispersion & Size Quintiles(At least 2 analysts and Base Dispersion Measure) From Table 3

  18. Dispersion Quintiles Size Small 2 3 4 Size Big All 1 1.74% 1.54% 1.32% 1.37% 1.36% 1.47% 2 1.60% 1.32% 1.24% 1.37% 1.14% 1.33% 3 1.67% 1.53% 1.17% 1.31% 1.13% 1.36% 4 1.48% 1.30% 1.36% 1.18% 1.18% 1.30% 5 1.32% 1.17% 1.22% 1.12% 0.98% 1.16% high-low -0.42% -0.37% -0.09% -0.25% -0.38% -0.30% t(high-low) -1.09 -1.17 -0.34 -0.71 -1.25 -1.36 Returns on Dispersion & Size Quintiles(At least 5 analysts and Alternative Dispersion Measure) From Table 3

  19. Dispersion Quintiles Small 2 3 4 Big All 1 1.54% 1.46% 1.22% 1.25% 1.22% 1.34% 2 1.63% 1.35% 1.18% 1.29% 1.35% 1.36% 3 1.56% 1.49% 1.31% 1.38% 0.97% 1.34% 4 1.67% 1.37% 1.36% 1.29% 1.09% 1.36% 5 1.40% 1.20% 1.23% 1.13% 1.16% 1.23% high-low -0.14% -0.25% 0.01% -0.11% -0.06% -0.11% t(high-low) -0.63 -0.99 0.01 -0.45 -0.18 -0.23 Returns on Dispersion & Size Quintiles(At least 5 analysts and Base Dispersion Measure) From Table 3

  20. Analyst Forecast Dispersion and Commonly Used Systematic Factors How is analyst forecast dispersion and the variability of that dispersion related to the commonly used systematic factors? • RME, Excess return on market portfolio • SMB, Size factor (Small firms minus big firms) • HML, Book-to-market factor (High minus low) • MOM, Momentum factor

  21. Intercept RME SMB HML MOM Adj. R2 U1 0.31% 0.93 -0.30 -0.34 0.05 93.7% 3.53 42.16 -10.90 -10.25 3. 03 U2 -0.11% 0.99 -0.08 0.09 -0.01 92.0% -1.18 43.51 -2.81 2.58 -0.33 U3 -0.06% 1.01 -0.10 0.21 -0.06 92.2% -0.65 45.49 -3.43 6.41 -3.79 U4 0.04% 1.06 -0.01 0.26 -0.06 90.2% 0.36 40.45 -0.35 6.59 -2.98 U5 -0.21% 1.25 0.19 0.45 -0.10 84.0% -1.27 30.83 3.84 7.36 -3.32 U5-U1 -0.51% 0.32 0.49 0.78 -0.14 34.7% -2.30 5.72 7.05 9.33 -3.59 Results for DISP-sorted portfolios Market Beta From Table 4

  22. Intercept RME SMB HML MOM Adj. R2 U1 0.31% 0.93 -0.30 -0.34 0.05 93.7% 3.53 42.16 -10.90 -10.25 3. 03 U2 -0.11% 0.99 -0.08 0.09 -0.01 92.0% -1.18 43.51 -2.81 2.58 -0.33 U3 -0.06% 1.01 -0.10 0.21 -0.06 92.2% -0.65 45.49 -3.43 6.41 -3.79 U4 0.04% 1.06 -0.01 0.26 -0.06 90.2% 0.36 40.45 -0.35 6.59 -2.98 U5 -0.21% 1.25 0.19 0.45 -0.10 84.0% -1.27 30.83 3.84 7.36 -3.32 U5-U1 -0.51% 0.32 0.49 0.78 -0.14 34.7% -2.30 5.72 7.05 9.33 -3.59 Results for DISP-sorted portfolios Size factor From Table 4

  23. Intercept RME SMB HML MOM Adj. R2 U1 0.31% 0.93 -0.30 -0.34 0.05 93.7% 3.53 42.16 -10.90 -10.25 3. 03 U2 -0.11% 0.99 -0.08 0.09 -0.01 92.0% -1.18 43.51 -2.81 2.58 -0.33 U3 -0.06% 1.01 -0.10 0.21 -0.06 92.2% -0.65 45.49 -3.43 6.41 -3.79 U4 0.04% 1.06 -0.01 0.26 -0.06 90.2% 0.36 40.45 -0.35 6.59 -2.98 U5 -0.21% 1.25 0.19 0.45 -0.10 84.0% -1.27 30.83 3.84 7.36 -3.32 U5-U1 -0.51% 0.32 0.49 0.78 -0.14 34.7% -2.30 5.72 7.05 9.33 -3.59 Results for DISP-sorted portfolios Market-to-book From Table 4

  24. Intercept RME SMB HML MOM Adj. R2 U1 0.31% 0.93 -0.30 -0.34 0.05 93.7% 3.53 42.16 -10.90 -10.25 3. 03 U2 -0.11% 0.99 -0.08 0.09 -0.01 92.0% -1.18 43.51 -2.81 2.58 -0.33 U3 -0.06% 1.01 -0.10 0.21 -0.06 92.2% -0.65 45.49 -3.43 6.41 -3.79 U4 0.04% 1.06 -0.01 0.26 -0.06 90.2% 0.36 40.45 -0.35 6.59 -2.98 U5 -0.21% 1.25 0.19 0.45 -0.10 84.0% -1.27 30.83 3.84 7.36 -3.32 U5-U1 -0.51% 0.32 0.49 0.78 -0.14 34.7% -2.30 5.72 7.05 9.33 -3.59 Results for DISP-sorted portfolios Momentum From Table 4

  25. Intercept RME SMB HML MOM Adj. R2 U1 0.31% 0.93 -0.30 -0.34 0.05 93.7% 3.53 42.16 -10.90 -10.25 3. 03 U2 -0.11% 0.99 -0.08 0.09 -0.01 92.0% -1.18 43.51 -2.81 2.58 -0.33 U3 -0.06% 1.01 -0.10 0.21 -0.06 92.2% -0.65 45.49 -3.43 6.41 -3.79 U4 0.04% 1.06 -0.01 0.26 -0.06 90.2% 0.36 40.45 -0.35 6.59 -2.98 U5 -0.21% 1.25 0.19 0.45 -0.10 84.0% -1.27 30.83 3.84 7.36 -3.32 U5-U1 -0.51% 0.32 0.49 0.78 -0.14 34.7% -2.30 5.72 7.05 9.33 -3.59 Results for DISP-sorted portfolios Differences From Table 4

  26. Factor RME SMB HML MOM DSP STDP Return 0.70% -0.12% 0.30% 1.05% -0.26% 0.08% Volatility 4.52% 3.52% 3.38% 5.31% 3.84% 3.34% t-value 2.28 -0.48 1.32 2.91 -0.99 0.36 Summary Statistics of Factors From Table 5

  27. RME SMB HML MOM DSP STDP RME 1 0.18 -0.53 -0.08 0.10 0.29 0.01 <.0001 0.25 0.13 <.0001 SMB 0.13 1 -0.49 -0.10 0.20 0.50 0.06 <.0001 0.15 0.003 <.0001 HML -0.55 -0.34 1 0.05 0.26 -0.05 <.0001 <.0001 0.50 0.00 0.44 MOM 0.00 -0.20 -0.04 1 -0.24 -0.11 0.96 0.00 0.61 0.00 0.11 DSP 0.07 0.27 0.25 -0.31 1 0.77 0.30 <.0001 0.00 <.0001 <.0001 STDP 0.26 0.48 -0.03 -0.15 0.78 1 <.0001 <.0001 0.65 0.03 <.0001 Correlations between Factors From Table 5

  28. Pricing Impact of STDP Factor on Size and Book-to-Market-Sorted Portfolios Univariate model Regress value-weighted returns of Fama-French 25 size and book-to-market ratio portfolios on STDP in a univariate model: Rit – Rft = ai + fiSTDPt + it

  29. 1.12 1.00 0.81 0.69 0.11 4.82 5.2 4.29 3.93 0.87 1.07 0.85 0.74 0.58 0.33 5.53 6.51 5.57 4.55 2.55 0.87 0.71 0.6 0.58 0.33 6.02 6.15 5.07 4.42 2.65 0.79 0.67 0.55 0.46 0.24 6.5 6.09 4.76 4.67 2.01 0.89 0.82 0.58 0.47 0.28 7.62 7.39 4.88 3.98 2.18 Coefficients On STDP t-statistics Size: Small  Big Size: Small  Big Portfolio B/M: Low  High Univariate From Table 7

  30. 19.8% 19.0% 13.8% 12.5% 0.1% 25.2% 23.6% 20.6% 14.5% 4.8% 26.5% 23.6% 18.7% 15.5% 5.6% 26.6% 22.7% 17.2% 12.8% 3.1% 33.0% 28.5% 16.5% 11.5% 3.5% R2’s from Univariate Regressions with STDP Size: Small  Big Portfolio B/M: Low  High From Table 7

  31. Pricing Impact of STDP Factor on Size and Book-to-Market-Sorted Portfolios Multivariate Model Regress value-weighted returns of Fama-French 25 size and book-to-market ratio portfolios on STDP in a multivariate model that includes the market factor: Rit – Rft = ai + biRmt + fiSTDPt + it

  32. 0.66 0.51 0.31 0.22 -0.32 3.12 3.5 2.55 1.94 -10.82 0.7 0.48 0.36 0.21 -0.05 3.85 6.62 6.05 3.43 -0.59 0.56 0.39 0.29 0.24 0 4.61 6.92 4.03 3.1 -0.02 0.5 0.38 0.27 0.17 -0.03 5.21 5.96 3.65 2.97 -0.34 0.61 0.51 0.28 0.18 0.01 6.92 7.49 3.56 1.88 0.07 Coefficients On STDP t-statistics Size: Small  Big Size: Small  Big Portfolio B/M: Low  High Multivariate From Table 7

  33. Industry coef. t-stat. R2 Aerospace 0.35 2.33 3.9% Rubber & plastic 0.32 2.15 3.7% Defense 0.37 2.62 4.1% Fabricated products 0.56 4.32 11.4% Containers 0.39 2.90 7.4% Construction 0.58 4.93 10.5% Transportation 0.49 4.75 10.1% Recreation 0.41 2.26 2.6% Coal 0.65 4.22 12.5% Electric equipment 0.25 1.77 1.3% Building materials 0.42 4.18 8.1% Nonmetallic mining 0.74 5.14 17.9% Computers 0.26 1.67 1.3% Automobiles 0.63 5.40 13.6% Measuring equipment 0.49 3.17 4.2% Chemicals 0.47 4.16 10.7% Chips 0.39 2.38 2.6% Business supplies 0.50 4.34 10.4% Precious metals 0.95 5.87 13.7% Petroleum/gas 0.56 6.41 19.0% Machinery 0.67 5.78 15.9% Steel 0.89 7.76 26.3% Pricing Impact of STDP Factor On Industry Portfolios One Factor Model From Table 8

  34. Dispersion Factors and Expected Returns • If dispersion and the variability of dispersion capture priced information factors, then they should be related to expected returns. • Test: construct implied expected returns from mutual fund managers’ portfolio holdings.

  35. Qu’s (2003) Methodology to Construct Expected Returns from Portfolio Holdings Start with the solution to basic optimization problem of an investor in a mean-variance world: s – rf s = s s s • sis the vector of expected returns on stocks • rfis the riskfree rate • s is a constant related to risk aversion • s is the covariance matrix of all stocks • s is the vector of portfolio weights

  36. Qu’s (2003) Methodology • In order to avoid the massive data problems with constructing a covariance matrix, use a five-factor principal-components model. • At the end of each year, use the past 10 years of monthly return data to find the principal components. • Estimate covariance matrices assuming five factors. • On observing a portfolio weight, use the covariance matrix calculated at the end of the previous year to calculate the implied excess returns according to the optimization equation.

  37. DISP Rank 1984 - 2001 1984 -1992 1993 - 2001 U1 20.4 22.2 18.6 U2 19.2 21.6 16.8 U3 19.4 21.8 17.1 U4 21.0 23.7 18.4 U5 23.0 26.0 20.1 U5-U1 2.6 4.3 1.5 t(U5-U1) 6.3 7.2 2.9 Average Implied Expected Excess Returns on DISP Quintile Portfolios Expected Returns From Mutual Fund Holdings From Table 9

  38. STDISP Rank 1984 - 2001 1984 -1992 1993 - 2001 U1 19.2 21.3 17.1 U2 19.0 21.2 16.8 U3 20.6 23.1 18.2 U4 21.9 24.3 19.6 U5 24.4 27.3 21.6 U5-U1 5.2 5.9 5.8 t(U5-U1) 12.1 10.9 11.5 Average Implied Expected Excess Returns on STDISP Quintile Portfolios Expected Returns From Mutual Fund Holdings From Table 9

  39. Conclusions Theoretical model • Forecast dispersion can affect stock prices only when investors have differential private information that induces differential precision in their assessment of the firm’s fundamentals. • In a dynamic setting the variability of dispersion has an unambiguous effect on price volatility, and hence, on the expected return.

  40. Conclusions Empirical Analysis • Portfolios with more dispersion or variability in dispersion have more exposure to commonly used risk factors. • Dispersion and the variability of dispersion capture components of information risk. • Factor portfolios formed on dispersion variables demonstrate significant pricing power. • Implied expected returns based on the portfolio holdings of mutual funds are related to dispersion and the variability of dispersion, consistent with the argument that these variables proxy for information risk factors.  

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