The Rational Part of Momentum

Transcription

1 The Rational Part of Momentum Jim Scott George Murillo Heilbrunn Center for Graham and Dodd Investing Columbia Business School Value Investing Research Consortium 1

2 Outline The Momentum Effect A Rationality Argument Our Measure of Fundamental Value and its Relation to Stock Returns Time Paths of Fundamental Value and Momentum An Empirical Hypothesis and Tests Value Investing Research Consortium 2

3 The Current Null Hypothesis: Market Efficiency E.g., Fama, JF,1970; JF, At any time prices fully reflect all available information. If stocks are ranked by their returns in one period, their returns before and after should equal normal returns (i.e., no Momentum Effect) Value Investing Research Consortium 3

4 6 month period returns Hypothetical Momentum Deciles if the Market were Efficient 80% 60% 40% 20% 0% -20% -40% -60% Period -2 Period -1 Period 0 Period 1 Period 2 Period 3 Low Mom High Mom Period 0 is the portfolio formation period (6 months) Period 1 is the holding period, skipping one month between formation and holding Periods -1, -2, 2 and 3 are six month periods pre and post formation of the firms Value Investing Research Consortium 4

5 Data Description U.S. stock returns from CRSP: Exclude REITs, ADRs, LPs and Closed-end Funds IBES mean EPS estimates for the current fiscal year (FY1), next year (FY2) and long term growth rate (LTG) Value Investing Research Consortium 5

6 6 month period returns Momentum Deciles ( ) 80% 60% 40% 20% 0% -20% -40% -60% Period -2 Period -1 Period 0 Period 1 Period 2 Period 3 Low Mom High Mom Value Investing Research Consortium 6

7 Momentum Deciles Returns ( ) Period -2 Period -1 Period 0 Period 1 Period 2 Period 3 t-18 to t-12 t-12 to t-6 t-6 to t t+1 to t+7 t+7 to t+13 t+13 to t+19 Low Mom 14.57% 10.08% % 3.23% 7.24% 10.14% % 8.90% % 5.09% 6.76% 8.28% % 8.56% -9.15% 6.26% 6.97% 8.01% % 8.95% -2.59% 7.03% 7.41% 7.72% % 8.43% 3.07% 7.17% 7.32% 7.47% % 8.63% 8.58% 7.45% 7.35% 7.63% % 8.88% 14.61% 7.86% 7.55% 7.26% % 9.57% 22.19% 8.36% 7.69% 6.98% % 10.85% 33.96% 8.87% 7.03% 7.02% High Mom 11.74% 14.80% 73.09% 11.33% 7.15% 5.63% Average 10.46% 9.69% 8.80% 7.26% 7.25% 7.56% High - Low -2.82% 4.73%** %** 8.10%** -0.09% -4.51%** Value Investing Research Consortium 7 `

8 Momentum Regressions with Individual Stocks Current 6 month return as a function of lagged returns Standard errors corrected using Newey-West estimates R i,t = α + β 1 *R i,t-1 + β 2 *R i,t-2 + β 3 *R i,t-3 + ε i,t Months α β 1 β 2 β 3 R 2 Avg # Obs ** ** ** ** ** ** ** ** ** * Significance to 95% ** Significance to 99% Value Investing Research Consortium 8

9 A Rational Viewpoint In a noisy rational expectations equilibrium, price changes may signal future value changes More generally, in a model of capital market equilibrium with heterogeneous expectations, informed investors expectations will only be partially revealed Value Investing Research Consortium 9

10 A Noisy Rational Equilibrium Market On the Impossibility of Informationally Efficient Markets Grossman and Stiglitz, AER, 1980 Information is costly Informed investors must have an incentive to collect it Prices only partially reflect informed investors expectations Since some investors become informed, returns today will, on average, predict future returns (As found Momentum) Efficient Capital Markets: II, Fama, JF, 1991, Since there are surely positive information and trading costs, the extreme version of the market efficiency hypothesis is surely false Value Investing Research Consortium 10

11 The role of Present Value Many models of capital market equilibrium imply that rational investors use present value formulas Many professional investors use present value formulas in their investment processes If the market is rational, then changes in present value of future cash flows should mirror returns Value Investing Research Consortium 11

12 Estimating the Change in Fundamental Value Two period Dividend Discount Model: v it = le it+1 /(1+r) + le it+2 /(1+r) 2 E it+1 = w FY1 + (1 w) FY2 E it+2 = w FY2 + (1-w) FY2 (1 + LTG), where w = number of months left in the fiscal year divided by 12 A weighted earnings estimate allows us to capture one year ahead EPS estimates each month We assume changes in near-term earnings expectations capture much of the firm-specific change in fundamental value Cross-sectionally, the change in a firm s fundamental value should be proportional to R v, where R v t = v it / v it-1 Value Investing Research Consortium 12

13 Sample Distribution by Size and Book-to-Market Avg # of Firms 1977 Low B/M High B/M Total Size Small 6.1% 6.4% 6.1% 6.0% 5.9% 30.5% 2 6.5% 5.6% 5.0% 3.9% 2.5% 23.5% 3 5.7% 4.2% 3.7% 2.6% 1.5% 17.7% 4 4.7% 3.6% 3.0% 2.2% 1.2% 14.6% Big 5.4% 3.1% 2.3% 1.8% 1.1% 13.7% Total B/M 28.5% 22.8% 20.2% 16.4% 12.0% 100.0% Firms are classified using Fama French quintile breakpoints, which are based on NYSE stocks, however our sample includes NYSE, AMEX and NASDAQ stocks Value Investing Research Consortium 13

14 Fundamental Values and Returns R t = R vt R 2 =.107 (4.4) (16.9) n =1956 R t = R vt +.704R ind,t R 2 =.173 (1.86) (16.91) (37.5) n = 1956 At individual security level, 6 month returns are significantly correlated with concurrent 6 month fundamental returns Value Investing Research Consortium 14

15 6 month period returns 6 month change in Value Momentum Deciles ( ) 80% 80% 60% 60% 40% 40% 20% 20% 0% 0% -20% -20% -40% -40% -60% Period -2 Period -1 Period 0 Period 1 Period 2 Period 3-60% Period -2 Period -1 Period 0 Period 1 Period 2 Period 3 Low Mom High Mom Low Mom High Mom Value Investing Research Consortium 15

16 Fundamental Value Changes Corresponding to Momentum Deciles ( ) Period -2 Period -1 Period 0 Period 1 Period 2 Period 3 t-18 to t-12 t-12 to t-6 t-6 to t t+1 to t+7 t+7 to t+13 t+13 to t+19 Low Mom 18.56% 14.94% % -5.24% 0.95% 8.42% % 10.91% -1.17% 0.71% 2.88% 7.54% % 8.30% 2.59% 3.01% 3.50% 6.06% % 8.33% 5.59% 4.32% 4.92% 7.02% % 7.58% 7.52% 6.22% 3.54% 3.99% % 8.38% 10.18% 6.71% 4.40% 4.27% % 8.76% 11.67% 7.72% 6.05% 3.81% % 9.66% 14.80% 9.75% 6.45% 3.77% % 12.30% 22.47% 12.90% 7.24% 3.59% High Mom 12.02% 17.52% 43.36% 20.21% 9.86% 3.93% Average 10.61% 10.54% 10.40% 6.62% 5.01% 5.15% High - Low -6.55%** 2.58% 56.22%** 25.46%** 8.91%** -4.49%** Value Investing Research Consortium 16

17 Average Number of Observations per Momentum Deciles Period -2 Period -1 Period 0 Period 1 Period 2 Period 3 t-18 to t-12 t-12 to t-6 t-6 to t t+1 to t+7 t+7 to t+13 t+13 to t+19 Low Mom High Mom Value Investing Research Consortium 17

18 6 month period returns 6 month change in Value Change in Value (R v,t-6 ) Deciles ( ) 80% 80% 60% 60% 40% 40% 20% 20% 0% 0% -20% -20% -40% -40% -60% Period -2 Period -1 Period 0 Period 1 Period 2 Period 3-60% Period -2 Period -1 Period 0 Period 1 Period 2 Period 3 Low Rv High Rv Low Mom High Mom Value Investing Research Consortium 18

19 Stock Returns for Change in Value (R v ) Deciles ( ) Period -2 Period -1 Period 0 Period 1 Period 2 Period 3 t-18 to t-12 t-12 to t-6 t-6 to t t+1 to t+7 t+7 to t+13 t+13 to t+19 Low R v,t % -8.16% % 5.42% 8.79% 9.49% % -1.10% -5.91% 5.94% 7.49% 8.05% % 2.93% -0.01% 6.34% 7.32% 7.32% % 5.82% 3.97% 6.79% 6.99% 7.35% % 8.23% 6.85% 7.04% 7.20% 7.28% % 10.71% 9.73% 7.72% 7.20% 7.35% % 13.59% 13.05% 7.63% 6.99% 7.21% % 18.21% 17.05% 7.66% 7.04% 7.28% % 23.70% 23.31% 8.88% 7.09% 7.14% High R v,t % 26.50% 35.15% 9.21% 6.35% 7.56% Average 10.46% 9.69% 8.80% 7.26% 7.25% 7.56% High Low 10.74%** 34.66%** 50.22%** 3.79%** -2.45%** %** Value Investing Research Consortium 19

20 Fundamental Value Changes Corresponding to Value Deciles ( ) Period -2 Period -1 Period 0 Period 1 Period 2 Period 3 t-18 to t-12 t-12 to t-6 t-6 to t t+1 to t+7 t+7 to t+13 t+13 to t+19 Low R v,t % 10.17% % 19.19% 13.45% 16.78% % 6.93% % -0.29% 4.11% 6.75% % 6.63% -5.29% 0.25% 1.36% 3.69% % 6.46% 0.32% 1.86% 1.97% 2.98% % 7.13% 4.15% 2.83% 2.46% 4.45% % 8.49% 7.48% 4.48% 3.23% 3.51% % 10.09% 11.20% 5.87% 4.23% 3.82% % 13.16% 16.48% 7.29% 4.53% 3.83% % 18.04% 26.64% 10.02% 5.67% 3.87% High R v,t % 21.35% % 14.73% 10.73% 4.08% Average 10.61% 10.54% 10.40% 6.62% 5.01% 5.15% High Low 14.01%** 11.18%** %** -4.46% -2.72% %** Value Investing Research Consortium 20

21 An Empirical Hypothesis Current prices partially reflect future changes in the market s estimate of fundamental value P t = l t V t b 0(1+Rv,t+1 ) b 1 (1+Rv,t+2 ) b 2 Taking logarithms and first differences yields a regression equation R t = a + b 0 r v,t + b 1 (r v,t+1 r v,t ) + b 2 (r v,t+2 r v,t+1 ) + u t Value Investing Research Consortium 21

22 Returns and Future Value Changes R i,t = α + β 0 *R v,t + β 1 *(R v,t+1 - R v,t ) + β 2 *(R v,t+2 - R v,t+1 ) + β 3 *(R v,t+3 - R v,t+2 ) + u t Months α β 0 β 1 β 2 β 3 R 2 Avg # Obs Value Investing Research Consortium 22

23 Observed Returns, Sorting on Past Returns and Concurrent R v Low R v High R v Avg. Low Mom -15.8% -3.4% 3.2% 8.4% 9.9% 14.3% 15.9% 21.0% 24.5% 31.9% 3.2% % -6.2% 1.3% 5.8% 9.7% 12.9% 16.3% 18.4% 23.8% 30.7% 5.1% % -5.9% 0.2% 4.9% 8.3% 11.5% 14.2% 17.9% 23.1% 32.1% 6.3% % -6.8% -0.5% 4.6% 7.7% 10.7% 14.6% 17.7% 22.0% 30.3% 7.0% % -7.5% -1.5% 3.0% 7.2% 10.0% 12.7% 17.6% 21.7% 30.5% 7.2% % -8.4% -1.9% 2.7% 6.0% 9.3% 11.8% 16.0% 21.0% 32.0% 7.5% % -10.5% -2.4% 2.0% 5.0% 8.2% 11.6% 16.4% 21.8% 31.4% 7.9% % -11.3% -4.0% 1.3% 4.0% 7.3% 11.0% 15.4% 22.2% 30.5% 8.4% % -12.7% -4.9% -1.0% 2.0% 5.1% 9.0% 13.6% 20.5% 32.5% 8.9% High Mom -25.2% -16.4% -7.4% -4.1% -1.9% 0.7% 6.6% 11.0% 18.7% 35.6% 11.3% Avg % -7.6% -1.2% 3.2% 6.1% 8.9% 11.9% 15.8% 21.3% 32.5% 7.3% Value Investing Research Consortium 23

24 Summary Our measure of change in fundamental value is significantly correlated with stock returns Momentum Effect is consistent with rational behavior, either: A Noisy Rational Expectations Equilibrium, or more generally, A properly specified heterogeneous expectations equilibrium On average, stock prices reflect not only current fundamental value estimates, but informed investors expectations of fundamental value as much as 12 months into the future As a result, the Momentum returns are highly correlated with concurrent fundamental return and appear to predict changes in fundamental return over the next year. Value Investing Research Consortium 24

25 Thank you Value Investing Research Consortium 25

26 Correlations for Returns and Change in Value Change in Value Return Period -2 Period -1 Period 0 Period 1 Period 2 Period 3 t-18 to t-12 t-12 to t-6 t-6 to t t+1 to t+7 t+7 to t+13 t+13 to t+19 Period ** 0.007** ** ** ** Period ** 0.133** 0.004** ** ** Period ** 0.064** 0.131** ** Period ** 0.019** 0.047** 0.135** ** Period ** ** 0.012** 0.044** 0.089** Period ** ** 0.016** 0.048** 0.090** Value Investing Research Consortium 26

27 Average Number of Observations Low R v High R v Avg. Low Mom High Mom Avg Value Investing Research Consortium 27