Speculative Betas. Harrison Hong and David Sraer Princeton University. November 16, 2012

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1 Speculative Betas Harrison Hong and David Sraer Princeton University November 16, 2012

2 Introduction Model 1 factor static Shorting Calibration OLG Exenstion Empirical analysis

3 High Risk, Low Return Puzzle Cumulative Returns jan jan jan jan jan2010 date 1st 2nd 3rd 4th 5th Beta-neutral strategy of long low beta / short high beta stocks has Sharpe of 0.75 (BBW ( 11)) Black ( 72), Pratt ( 67), Friend and Blume ( 70)

4 Our Explanation Disagreement about aggregate cash-flows + short-sales constraints Non-private information, agree to disagree Evidence of disagreement among professional forecasters and households On macroeconomic state variables such as market earnings, industrial production growth and inflation (Cukierman and Wachtel 79, Zarnowitz and Lambros 87, Kandel and Pearson 95, Mankiw, Romer and Wolfers 04) Dispersion in professional forecasts about stock market earnings varies over time and is correlated with aggregate economic uncertainty indicators (Bloom 09, Lamont 02, Yu 10) Disagreement due to heterogeneous priors or cognitive biases such as overconfidence that result in agents over-weighing private signals

5 Bloom (2012) uncertainty measure and modified Yu (2012) analyst forecast dispersion measure aggregate disagreement Sales uncertainty 01jan jan jan jan jan2010 date aggregate disagreement Sales uncertainty

6 Short-Selling Constraints Short-selling costly due to institutional constraints Large fraction of mutual funds, 20 trillion dollars under management, can t short by charter and can t use derivatives (Almazan et al. 04, Koski and Pontiff 99) Hedge fund sector with 1.8 trillion dollars can and do short

7 Key Features of Model Otherwise CAPM framework: cashflows of firms follow a one factor model Disagree about the mean of common factor and not variances Buyers such as retail mutual funds Arbitrageurs such as hedge funds who short Multi-asset model based on Chen, Hong and Stein 01 s rendition of Miller 77 single stock economy Divergence of opinion leads to over-pricing because price reflects only the views of the optimists

8 The Main Idea β scales aggregate disagreement d i = b i z + ɛ i 1. High b or β assets are more sensitive to disagreement about aggregate cashflows than low b assets. 2. Macro-disagreement: optimists z + λ, pessimists z λ 3. High b experience more divergence of opinion: optimist b i ( z + λ)and pessimists b i ( z λ) 4. Then over-pricing due to short-sales constraints 5. More shorting from arbs on high b CAPM holds when aggregate disagreement is low But high disagreement leads to inverted-u shaped: initially increasing with beta and then decreasing Kinked/concave/inverted-U shaped relationship due to disagreement having to be large enough to over-come benefits of diversification (cost of bearing idiosyncratic risk)

9 OLG Extension OLG extension to show results go through + additional implication that high beta stocks have higher share turnover Calibration exercise

10 Empirics Use modified Yu (2010) measure of dispersion of earnings forecasts and cross-sectional SD of sales growth Bloom 09 Test basic predictions/premises of the model: 1. Upward sloping SML when disagreement/uncertainty is low. 2. Inverted U-shape of SML when disagreement is high 3. More stock-level disagreement on high β stocks, especially when high aggregate disagreement. 4. More shorting on high β stocks, especially when high aggregate disagreement. 5. More turnover on high β stocks, especially when high aggregate disagreement.

11 Disagreement and CAPM: kinks Figure: Average 3-months excess returns for equal-weighted beta decile portfolios in low and high aggregate disagreement months post-ranking beta Low disagreement High disagreement

12 Stock-level disagreement, β and aggregate disagreement. Figure: Equal-weighted average of dispersion of analyst earnings forecasts by beta deciles during low and high aggregate disagreement months. stock-level disagreement post-ranking beta Low disagreement High disagreement

13 Disagreement, β and shorting activity Figure: Equal-weighted average of short interest ratio by beta deciles during low and high aggregate disagreement months. short-interest ratio post-ranking beta Low disagreement High disagreement

14 Disagreement and share turnover Figure: Equal-weighted average of share turnover for stocks by beta deciles during low and high aggregate disagreement months. turnover ratio post-ranking beta Low disagreement High disagreement

15 Outline Introduction Model 1 factor static Shorting Calibration OLG Exenstion Empirical analysis

16 Introduction Model 1 factor static Shorting Calibration OLG Exenstion Empirical analysis

17 Model Dates t = 0, 1 N risky assets and exogenous risk-free rate is r Risky asset i delivers a dividend d i at date 1: i {1,..., N}, di = b i z + ɛ i, where z N ( z, σz 2 ), ɛi N ( 0, σɛ 2 ), and cov ( z, ɛi ) = 0 Each asset is in supply 1 N : Assume N i=1 b i N = 1. 0 < b 1 < b 2 < < b N

18 Model Dates t = 0, 1 N risky assets and exogenous risk-free rate is r Risky asset i delivers a dividend d i at date 1: i {1,..., N}, di = b i z + ɛ i, where z N ( z, σz 2 ), ɛi N ( 0, σɛ 2 ), and cov ( z, ɛi ) = 0 Each asset is in supply 1 N : Assume N i=1 b i N = 1. 0 < b 1 < b 2 < < b N

19 Investors Preferences and Beliefs Two groups of investors: Short-sales constrained with heterogenous beliefs (MF - fraction α) Unconstrained with homogenous beliefs (HF or arbs - fraction 1 α) Investors have mean-variance utility functions with variance weight 1 2γ (or CARA withs risk tolerance γ) Heterogeneous beliefs about aggregate factor: E A [ z] = z + λ and E B [ z] = z λ with λ > 0 Proportion 1 2 of optimists/pessimists among SSC agents. Investors hold correct expectations about the variance of z.

20 Investors Preferences and Beliefs Two groups of investors: Short-sales constrained with heterogenous beliefs (MF - fraction α) Unconstrained with homogenous beliefs (HF or arbs - fraction 1 α) Investors have mean-variance utility functions with variance weight 1 2γ (or CARA withs risk tolerance γ) Heterogeneous beliefs about aggregate factor: E A [ z] = z + λ and E B [ z] = z λ with λ > 0 Proportion 1 2 of optimists/pessimists among SSC agents. Investors hold correct expectations about the variance of z.

21 Homoskedasticity This is just to simplify the exposition. If dividends are heteroskedastic, then need to re-rank assets b according to: 1 < < b σ1 2 N σn 2 In the data, b i is highly correlated with b σi 2 i : Figure: Sample: CRSP. Period: fraction of aggregate vol. to total vol post-ranking beta

22 Discussion of other assumptions 1. Can also have disagreement about idiosyncratic but too easy 2. No disagreement on variance/covariance matrix. Jarrow 80: more general structure but less clear implications than 1-factor model 3. Strict short-selling constraints. (realistic MF) Works with any strictly convex cost function.

23 Solving for the equilibrium Intuition: investors disagree on expected payoffs. Mechanically, disagreement is higher for high b assets (E i [ d] = b i E i [ z]). Pessimists hit binding short-sales constraints on high b assets first. 1. Posit equilibrium structure: j [1, N] such that: Assets i j (i.e. b i > b j ) such that pessimists are sidelined. All investors are long assets i < j. 2. Derive equilibrium pricing equations under j. 3. Write down conditions under which j is the marginal asset.

24 Solving for the equilibrium Intuition: investors disagree on expected payoffs. Mechanically, disagreement is higher for high b assets (E i [ d] = b i E i [ z]). Pessimists hit binding short-sales constraints on high b assets first. 1. Posit equilibrium structure: j [1, N] such that: Assets i j (i.e. b i > b j ) such that pessimists are sidelined. All investors are long assets i < j. 2. Derive equilibrium pricing equations under j. 3. Write down conditions under which j is the marginal asset.

25 Maximization program Agents are maximizing: max µ k i N i=1 µk i ( bi E k [ z] (1 + r)p i ) µ k i [ ( N ) 2 1 2γ i=1 µk i b i σ 2 z + N ( ) i=1 µ k 2 ( ) ] i σ 2 ɛ is number of shares purchased by investors in group k for asset i. For agents A and B, under the constraint: µ 0.

26 Maximization program Agents are maximizing: max µ k i N i=1 µk i ( bi E k [ z] (1 + r)p i ) µ k i [ ( N ) 2 1 2γ i=1 µk i b i σ 2 z + N ( ) i=1 µ k 2 ( ) ] i σ 2 ɛ is number of shares purchased by investors in group k for asset i. For agents A and B, under the constraint: µ 0.

27 Pricing for unconstrained assets For unconstrained assets (i < j): (( N ) ) ( z + λ)b i P i (1 + r) = 1 b k µ A k b i σz 2 + µ A i σɛ 2 γ k=1 (( N ) ) ( z λ)b i P i (1 + r) = 1 γ (( N k=1 ) b k µ B k b i σ 2 z + µ B i σ 2 ɛ ) zb i P i (1 + r) = 1 γ k=1 b k µ a k b i σ 2 z + µ a i σ 2 ɛ Market clearing condition: α ( 1 2 µa i µb i Pricing equation similar to CAPM: ) + (1 α)µ a i = 1 N zb i P i (1 + r) = 1 ( ) b }{{} i σz 2 + σ2 ɛ γ N expected excess return on asset i. }{{} risk premium ( )

28 Pricing for unconstrained assets For unconstrained assets (i < j): (( N ) ) ( z + λ)b i P i (1 + r) = 1 b k µ A k b i σz 2 + µ A i σɛ 2 γ k=1 (( N ) ) ( z λ)b i P i (1 + r) = 1 γ (( N k=1 ) b k µ B k b i σ 2 z + µ B i σ 2 ɛ ) zb i P i (1 + r) = 1 γ k=1 b k µ a k b i σ 2 z + µ a i σ 2 ɛ Market clearing condition: α ( 1 2 µa i µb i Pricing equation similar to CAPM: ) + (1 α)µ a i = 1 N zb i P i (1 + r) = 1 ( ) b }{{} i σz 2 + σ2 ɛ γ N expected excess return on asset i. }{{} risk premium ( )

29 Pricing for unconstrained assets For unconstrained assets (i < j): (( N ) ) ( z + λ)b i P i (1 + r) = 1 b k µ A k b i σz 2 + µ A i σɛ 2 γ k=1 (( N ) ) ( z λ)b i P i (1 + r) = 1 γ (( N k=1 ) b k µ B k b i σ 2 z + µ B i σ 2 ɛ ) zb i P i (1 + r) = 1 γ k=1 b k µ a k b i σ 2 z + µ a i σ 2 ɛ Market clearing condition: α ( 1 2 µa i µb i Pricing equation similar to CAPM: ) + (1 α)µ a i = 1 N zb i P i (1 + r) = 1 ( ) b }{{} i σz 2 + σ2 ɛ γ N expected excess return on asset i. }{{} risk premium ( )

30 Pricing for constrained assets For constrained assets (i j): (( N ) ) ( z + λ)b i P i (1 + r) = 1 γ (( N k=1 ) b k µ A k b i σ 2 z + µ A i σ 2 ɛ ) zb i P i (1 + r) = 1 γ µ B i = 0 With first-order condition: zb i P i (1 + r) }{{} E[ R i ] k=1 b k µ a k = 1 ( ) b i σz 2 + σ2 ɛ γ N }{{} risk premium b i σ 2 z + µ a i σ 2 ɛ π i }{{} speculative premium ( )

31 Speculative premium Speculative premium: excess-pricing over no short-sales constraint benchmark (α = 0). Derivation: sum FOC and compute j 1 k=1 b kµ B k using FOC of assets j < j. Exact form (depends on j and θ = α 2 1 α strictly with α): 2 π i σɛ = θ b 2 i ( ) λ σ2 z b k σ2 ɛ σɛ 2 + σz 2 γn γn i< j b2 i k j Speculative premium strictly increases with b i.

32 Closing the model: marginal asset Derive equilibrium holdings (conditional on j) of pessimists and derive conditions for: (µ B ) < 0 1. U B µ B j 2. µ B j 1 > 0 This is equivalent to: u j < λγ u j 1 where (u) is strictly decreasing sequence. We span entire λ space. Unique equilibrium.

33 Over-pricing 1. Low b assets are priced according to standard CAPM equation. 2. High b assets are over-priced relative to standard CAPM equation. Amount of overpricing increases with λ and α. More disagreement on high b assets thus more likely to have pessimists short thus more over-pricing through short-sale costs. (cost of shorting idiosyncratic risk is the same accross assets) High b assets are more disagreement sensitive. 2 speculative premium 3. λ α > 0. Increasing λ leads to more severe mispricing in high α environment. 4. Cutoff j increases with λ. For high λ, even low b assets can have high disagreement. 2 speculative premium 5. λ β > 0: more mispricings when sorted on shorting in high beta stocks

34 Shorting There exists ˆλ > 0 such that if λ > ˆλ: 1. HFs short at least one asset in equilibrium, i.e. µ a N < There exists ĩ such that: µ a N > µa N 1 > µã i > 0 and 3. k < ĩ, µ a k > 0. µ a N λ > µa N 1 λ > µã i λ > 0. A rise in aggregate disagreement leads to a larger increase in shorting for high b assets.

35 Security Market Line R i = b i z (1 + r)p i R M ) Var( R M ) β i = ( R i, R M = N R i i=1 N κ(λ) = σ2 λγ σ2 z ɛ N ( i ī b i) σz 2 σɛ 2+σ2 z( i<ī b2 i ) > 0. E[ R i ] = σz 2 + σ2 ɛ N β i γ for i < ī σ z 2 + σ2 ɛ N β i (1 θκ(λ)) + σ2 ɛ θ (1 + κ(λ)) γ γn for i ī Corollary: Let ˆµ be the coefficient estimate of a cross-sectional regression of realized returns R i on β i. ˆµ decreases with λ.

36 Illustration: SML Slope Conditional on Disagreement Parameters: N = 100, σ 2 z =.0022, σ 2 ɛ =.029, α =.63, γ =.6, ρ = Expected excess returns beta lambda=0 lambda=.0075 lambda=.005

37 OLG Extension t = 0, 1,... Each period t, a new generation of mass 1 is born and invest in the stock market to consume the proceeds at date t + 1. A new generation is always compose of 2 groups of agents; arbitrageurs, or Hedge Funds, in proportion 1 α, and Mutual funds in proportion α. Investors have mean-variance preferences with risk tolerance parameter 2γ. There are N assets in this economy, whose dividend process each period is given as in our static model by: d i = b i z + ɛ i

38 OLG Extension Mutual funds born at date t have heterogeneous beliefs about the expected value of z t+1 and thus about the expected dividend to be received at date t + 1 before reselling the asset. Specifically, there are two groups of mutual funds: group A of optimists MF (E A [ z t+1 ] = z + λ t ) and group B of pessimists (E B [ z t+1 ] = z λ t ). λ t {0, λ > 0} is a two-states Markov process with persistence ρ ]1/2, 1[.

39 OLG Extension 1. When ρ is large, same basic results from static setting. 2. Plus share turnover: high beta stocks have higher turnover due to more shorting and more shares which are then traded when generations changeover. 3. The differential turnover between high b assets (j î) and low b assets (j < î) is strictly greater for high disagreement states ( λ = λ > 0) than for low disagreement states ( λ = 0).

40 Resale Option and Bubble Suppose λ t = 0. Potential disagreement at t + 1 leads to potential binding constraints when λ > 0. Current generation of traders anticipate that resale price will be high when short-sales constraints are binding in the λ > 0 state. This is a version of the resale option of Harrison and Kreps 1978 and Scheinkman and Xiong 2003 (except each generation has to sell). Bubble accompanied by high turnover due to shorting by hedge funds. Like classic theories of bubbles with over-trading (too much demand met by arbs shorting)

41 Introduction Model 1 factor static Shorting Calibration OLG Exenstion Empirical analysis

42 Empirical Analysis Prediction 1: High β stocks have higher short interest, greater dispersion of opininion and higher share turnover compared to low β stocks when aggregate disagreement is high. Prediction 2: Inverted-U shape of mean returns with β in high aggregate disagreement months. Prediction 3: When aggregate disagreement increases, slope of SML decreases.

43 Empirical Analysis Prediction 1: High β stocks have higher short interest, greater dispersion of opininion and higher share turnover compared to low β stocks when aggregate disagreement is high. Prediction 2: Inverted-U shape of mean returns with β in high aggregate disagreement months. Prediction 3: When aggregate disagreement increases, slope of SML decreases.

44 Empirical Analysis Prediction 1: High β stocks have higher short interest, greater dispersion of opininion and higher share turnover compared to low β stocks when aggregate disagreement is high. Prediction 2: Inverted-U shape of mean returns with β in high aggregate disagreement months. Prediction 3: When aggregate disagreement increases, slope of SML decreases.

45 Measuring Aggregate Disagreement Tradition in the literature to proxy for stock-level disagreement using dispersion of analyst forecasts of earnings (Diether et.al. 02, Yu 09) Monthly aggregate disagreement measured as: β-weighted average of stock level disagreement Stock-level disagreement is dispersion of analyst forecast of long-run growth rate of EPS. Discussed intensively in Yu 09. Intuition for weighting scheme: low β stocks have only idiosyncratic disagreement, so should not count for aggregate disagreement. Sample: CRSP US stocks from

46 Construction of beta portfolios Each month, we use the past 12 months of daily returns to estimate market β of each stock in that cross-section. Estimation includes five lags of market returns (Dimson 79). We drop penny stocks. We construct 20 β portfolios with equal weights. Use post-ranking portfolio β defined as realized β of 20 β portfolios over whole sample results similar with trailing windows.

47 { ρt = ν + ρagg. Dis. t 1 + ω t Regression analysis Two methodologies: Pooled cross-sectional regressions: y it = α t +µβ i +νsize i +δβ i Agg. Dis. t 1 +ρsize i Agg. Dis. t 1 +ɛ it Fama MacBeth regressions: 1. First-stage: y it = α + δ t β i + ρ t Size i + ɛ it 2. Second-stage: δ t = µ + δagg. Dis. t 1 + η t

48 { ρt = ν + ρagg. Dis. t 1 + ω t Regression analysis Two methodologies: Pooled cross-sectional regressions: y it = α t +µβ i +νsize i +δβ i Agg. Dis. t 1 +ρsize i Agg. Dis. t 1 +ɛ it Fama MacBeth regressions: 1. First-stage: y it = α + δ t β i + ρ t Size i + ɛ it 2. Second-stage: δ t = µ + δagg. Dis. t 1 + η t

49 Table: β portfolios characteristics and disagreement Short Short Stock Stock Turnover Turnover Interest Interest Disagreement Disagreement (Pooled) (FM) (Pooled) (FM) (Pooled) (FM) β Agg. Dis. t 1.004***.0044*** 1.1*** 1.2***.2***.2*** (7.6) (7.7) (19) (18) (12) (12) β.0066***.0054** -2.5*** -2.6*** -.14** -.15** (2.9) (2.2) (-10) (-9.6) (-2.1) (-2) Size Agg. Dis. t ***.00083***.057** -.052**.02*** (7.8) ( 5.08 ) (2.4) (-2.39) (3.7) (-1.20) Size *** *** -.6*** * -.081***.024 (-8.3) (-4.85) (-6.2) (-1.83) (-3.7) (1.0) Observations 5, , , Adj. R

50 { φ k t = c k + ψ k Agg. Dis. t + τ k X t + ω k t Regression Analysis To capture the inverted-u shape of SML, we run Fama-MacBeth regressions. 1. First stage in repeated cross-sections: 2. Second stage in time series: r e i,t t+k = αk t + π k t β i + φ k t β 2 i + ɛ k it π k t = κ k + ι k Agg. Dis. t + ζ k X t + w k t X : SMB, HML, D/P, P/E, k months forward market return, inflation, TED spread.

51 Results Table: SML and disagreement: quadratic fit Portfolio forward excess return 1-month 3-months 6-months 12 months (1) (2) (3) (4) (5) (6) (7) (8) β 2 Agg. Dis ** -2.30** -3.39*** -4.21** -6.60*** -6.67** -8.51*** (-1.56) (-2.37) (-2.12) (-2.81) (-2.45) (-3.37) (2.57) (-3.65) β ** 8.68* 17.6*** 16.09** 36.44*** 26.47** 49.66*** (1.39) (2.53) (1.96) (2.90) (2.27) (3.70) (2.50) (3.82) β Agg. Dis. 1.00* 2.046*** 2.877* 5.26*** 4.54* 9.73** (1.68) (2.73) (1.79) (2.74) (1.76) (3.21) (1.35) (1.51) β *** *** *** ** (-1.25) (-3.31) (-1.36) (3.38) (-1.32) (-3.70) (-1.06) (-2.22) Controls NO YES NO YES NO YES NO YES Observations

52 Going from 10 th to 90 th percentile of disagreement Figure: Predicted 3 months forward excess return as a function of beta for 10 th and 90 th percentile of disagreement beta_post_average 10% disagreement 90% disagreement

53 Disagreement and the slope of the SML Slope of Security Market Line (1) (2) (3) (4) (5) (6) (7) (8) Aggregate Disagreement * ** -4.1* -3.8** -7.5* -7.4*** (-1.3) (-1.7) (-1.4) (-2) (-1.9) (-2.5) (-1.9) (-3.1) P/E.05**.16***.29***.44*** (3.1) D/P -75*** -232*** -467*** -873*** (-2.8) (-3.4) (-2.9) (-2.9) HML ** -.56*** -1** (-1.6) (-2.5) (-3.1) (-2.4) SMB -.12* -.4** -.72*** -1.1*** (-1.7) (-2.6) (-3.9) (-2.8) Inflation ** 2.1** (.99) TED Spread 1** 2.5*** 4.9*** 8.2*** (-2.2) (-2.9) (-3.3) (3.1) Forward Market Return 1.1*** 1***.96***.84*** (-23) (-13) (-10) (5.7) Constant ** 11 35** 31** (-1.3) (-0.52) (-1.6) (-0.76) (-2.1) (-1.2) (-2.2) (2) Observations

54 Robustness: Alternative measure of aggregate disagreement Bloom ( 12) cross-sectional dispersion of US Census plants sales growth. Intuition: Investors draw signals from realized distribution of growth and take signals at face value. Dispersion of investors forecast uncertainty measured in Bloom ( 12) In the data, correlates very well with our aggregate disagreement measure in overlapping sample. However, data is available since 1970

55 SML concavity using uncertainty measure Portfolio forward excess return 1-month 3-months 6-months 12 months (1) (2) (3) (4) (5) (6) (7) (8) β 2 Uncert ** ** -4.80*** *** (1.10) (-.98) (-1.64) (-1.34) (-2.17) (-2.40) (-3.23) (-3.41) β ** 24.11** 37.96*** 48.53*** (1.0) (1.42) (1.57) (1.60) (2.14) (2.57) (3.26) (3.22) β Uncert ** 3.826** *** 6.492*** (.91) (1.23) (1.37) (1.41) (2.01) (2.32) (4.35) (2.83) β ** ** * *** *** *** (-.74) (-2.19) (-1.23) (2.31) (1.93) (2.98) (4.00) (3.16) Controls No Yes No Yes No Yes No Yes Observations

56 HML by Aggregate Disagreement Figure: 3-month returns to BE/ME decile portfolios. 3-months forward return of BE/ME sorted portfolios equal weighted average BE/ME Low disagreement High disagreement

57 Concavity Controlling for HML Table: Disagreement and concavity of the Security Market Line: controlling for HML loadings of Beta Portfolios Portfolio forward excess return - expected returns from HML and SMB 3-months 6-months 12 months (1) (2) (3) (4) (5) (6) β 2 Aggregate Disagreement -1.67* -2.44** * ** (1.67) (2.39) (0.77) (1.90) (2.15) (0.78) β * 14.66*** *** 44.05** (1.88) (2.73) (1.02) (3.18) (2.20) (1.65) β Aggregate Disagreement ** * (1.24) (2.33) (0.10) (1.94) (0.42) (1.02) β *** *** *** (1.29) (3.37) (0.25) (3.86) (0.52) (3.10) Controls No Yes No Yes No Yes Observations

58 When Some Investors Head for the Exit (w/ Wenxi Jiang) Chen-Hong-Stein: Decrease in breadth of mutual fund ownership (change in fraction of MF owners = entry rate - exit rate) forecasts low stock returns Asquith-Pathak-Ritter: Top short-interest ratio (shares shorted to shares outstanding) decile under-performs rest of the stocks Show exit rate better captures short-sales constraints. Entry rate might reflects changes in limited participation and higher prices and more shorting A new measure of hedge fund breadth and exit rate which work better than mutual fund breadth. These all work better in high beta stocks, consistent with 2 speculative premium λ β > 0.

59 Short Interest Forecast of Quarterly Returns 1991 to 2008 Sort on short interest ratio Equal-Weighted Raw Return DGTW Returns Lo Beta Q2 Q3 Q4 Hi Beta Lo Beta Q2 Q3 Q4 Hi Beta Bottom 50% 2.73% 2.72% 3.43% 2.55% 1.84% 0.32% 0.32% 0.88% 0.50% 0.08% (3.22) (2.93) (3.28) (2.00) (1.05) (0.74) (0.90) (2.89) (2.09) (0.14) Top 5% 1.45% 2.01% 1.47% 0.17% -0.42% -0.65% -0.01% -0.38% -1.65% -2.95% (0.89) (1.29) (0.93) (0.10) (-0.17) (-0.49) (-0.01) (-0.37) (-2.16) (-2.47) Hi - Lo -1.28% -0.72% -1.96% -2.38% -2.26% -0.97% -0.33% -1.26% -2.15% -3.03% (-0.94) (-0.68) (-1.84) (-2.49) (-2.26) (-0.74) (-0.39) (-1.19) (-2.56) (-2.99) Among high beta stocks, in high disagreement periods (top 30%), Hi-Lo is -2.17% per quarter RAW. In low disagreement periods (bottom 30%) only -1.43% RAW.

60 Hedge Fund Exit Rate Forecast of Quarterly Returns 1991 to 2008 Sort on HF EXIT Equal-Weighted Raw Return DGTW Returns Lo Beta Q2 Q3 Q4 Hi Beta Lo Beta Q2 Q3 Q4 Hi Beta Bottom 50% 2.68% 2.76% 3.09% 2.53% 1.93% 0.29% 0.27% 0.61% 0.45% -0.25% (3.21) (2.88) (2.98) (1.95) (0.94) (0.68) (0.84) (2.64) (1.66) (-0.33) Top 5% 4.00% 2.10% 3.36% 0.78% -0.63% 2.03% -0.58% 1.26% -1.54% -3.08% (4.20) (2.19) (2.54) (0.41) (-0.31) (2.65) (-1.00) (1.06) (-1.37) (-3.02) Hi - Lo 1.35% -0.45% 0.53% -1.65% -2.44% 1.71% -0.75% 0.72% -2.01% -2.57% (2.85) (-0.86) (0.62) (-1.58) (-2.69) (2.94) (-1.45) (0.66) (-1.92) (-2.56) Among high beta stocks, in uncertain periods, Hi-Lo is -3.24% RAW. It is -2.12% RAW.

61 Mutual Fund Exit Rate Forecasts Quarterly Returns 1981 to 2008 Sort on EF EXIT Equal-Weighted Raw Return DGTW Returns Lo Beta Q2 Q3 Q4 Hi Beta Lo Beta Q2 Q3 Q4 Hi Beta Bottom 50% 3.06% 3.49% 3.54% 3.01% 2.19% 0.12% 0.43% 0.49% 0.20% -0.48% (4.66) (4.48) (4.01) (2.87) (1.49) (0.35) (1.85) (2.62) (0.94) (-0.86) Top 5% 3.04% 2.77% 2.57% 1.77% -0.08% -0.14% -0.34% 0.43% -0.56% -2.36% (3.04) (2.57) (2.38) (1.40) (-0.05) (-0.18) (-0.39) (0.81) (-0.88) (-3.19) Hi - Lo -0.02% -0.72% -0.97% -1.24% -2.26% -0.26% -0.76% -0.06% -0.76% -1.88% (-0.03) (-1.02) (-1.56) (-2.11) (-3.53) (-0.37) (-0.98) (-0.12) (-1.25) (-2.61) Among high beta stocks, in high uncertainty periods, Hi-Lo is -2.76%. It is -2.58% in low uncertainty periods.

62 Conclusion Bridge of Behavioral Finance to CAPM Behavioral Beta Finance or Behavioral Macro-Finance Speculative investors like beta high beta assets command high prices. High volatility assets associated with higher expected returns. Many potential links of existing work back to the cross-section and beta, including capital budgeting implications.