The Rational Part of Momentum

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

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

The Current Null Hypothesis: Market Efficiency E.g., Fama, JF,1970; JF, 1991. 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

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 2 3 4 5 6 7 8 9 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

Data Description U.S. stock returns from CRSP: 1985 2006 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 month period returns Momentum Deciles (1985 2006) 80% 60% 40% 20% 0% -20% -40% -60% Period -2 Period -1 Period 0 Period 1 Period 2 Period 3 Low Mom 2 3 4 5 6 7 8 9 High Mom Value Investing Research Consortium 6

Momentum Deciles Returns (1985 2006) 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% -37.32% 3.23% 7.24% 10.14% 2 11.11% 8.90% -18.19% 5.09% 6.76% 8.28% 3 9.54% 8.56% -9.15% 6.26% 6.97% 8.01% 4 9.29% 8.95% -2.59% 7.03% 7.41% 7.72% 5 9.33% 8.43% 3.07% 7.17% 7.32% 7.47% 6 9.39% 8.63% 8.58% 7.45% 7.35% 7.63% 7 9.68% 8.88% 14.61% 7.86% 7.55% 7.26% 8 10.10% 9.57% 22.19% 8.36% 7.69% 6.98% 9 11.38% 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%** 110.40%** 8.10%** -0.09% -4.51%** Value Investing Research Consortium 7 `

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 251 0.0653** 0.0688** 0.0140 1956 245 0.0704** 0.0053 0.0106 1764 239 0.0744** -0.0368** 0.0085 1615 245 0.0636** 0.0623** 0.0039 0.0233 1763 239 0.0738** 0.0063-0.0357** 0.0185 1605 * Significance to 95% ** Significance to 99% Value Investing Research Consortium 8

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

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

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

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

Sample Distribution by Size and Book-to-Market Avg # of Firms 1977 Low B/M 2 3 4 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

Fundamental Values and Returns R t =.064 +.214R vt R 2 =.107 (4.4) (16.9) n =1956 R t =.014 +.203R 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

6 month period returns 6 month change in Value Momentum Deciles (1985 2006) 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 2 3 4 5 6 7 8 9 High Mom Low Mom 2 3 4 5 6 7 8 9 High Mom Value Investing Research Consortium 15

Fundamental Value Changes Corresponding to Momentum Deciles (1985 2006) 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% -12.86% -5.24% 0.95% 8.42% 2 11.78% 10.91% -1.17% 0.71% 2.88% 7.54% 3 10.29% 8.30% 2.59% 3.01% 3.50% 6.06% 4 8.97% 8.33% 5.59% 4.32% 4.92% 7.02% 5 8.40% 7.58% 7.52% 6.22% 3.54% 3.99% 6 8.31% 8.38% 10.18% 6.71% 4.40% 4.27% 7 9.31% 8.76% 11.67% 7.72% 6.05% 3.81% 8 9.27% 9.66% 14.80% 9.75% 6.45% 3.77% 9 10.92% 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

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 146 170 196 196 179 145 2 159 176 196 196 188 166 3 165 179 196 196 191 172 4 166 180 196 196 192 174 5 168 181 196 196 192 177 6 169 181 196 196 193 179 7 168 180 196 196 193 179 8 165 179 196 196 193 178 9 160 176 196 196 193 178 High Mom 142 164 195 195 192 177 Value Investing Research Consortium 17

6 month period returns 6 month change in Value Change in Value (R v,t-6 ) Deciles (1985 2006) 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 2 3 4 5 6 7 8 9 High Rv Low Mom 2 3 4 5 6 7 8 9 High Mom Value Investing Research Consortium 18

Stock Returns for Change in Value (R v ) Deciles (1985 2006) 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-6 3.22% -8.16% -15.07% 5.42% 8.79% 9.49% 2 5.68% -1.10% -5.91% 5.94% 7.49% 8.05% 3 7.03% 2.93% -0.01% 6.34% 7.32% 7.32% 4 8.00% 5.82% 3.97% 6.79% 6.99% 7.35% 5 9.26% 8.23% 6.85% 7.04% 7.20% 7.28% 6 11.21% 10.71% 9.73% 7.72% 7.20% 7.35% 7 13.56% 13.59% 13.05% 7.63% 6.99% 7.21% 8 16.09% 18.21% 17.05% 7.66% 7.04% 7.28% 9 18.43% 23.70% 23.31% 8.88% 7.09% 7.14% High R v,t-6 13.96% 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%** -12.70%** Value Investing Research Consortium 19

Fundamental Value Changes Corresponding to Value Deciles (1985 2006) 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-6 10.21% 10.17% -43.65% 19.19% 13.45% 16.78% 2 6.79% 6.93% -15.30% -0.29% 4.11% 6.75% 3 5.69% 6.63% -5.29% 0.25% 1.36% 3.69% 4 6.00% 6.46% 0.32% 1.86% 1.97% 2.98% 5 7.10% 7.13% 4.15% 2.83% 2.46% 4.45% 6 8.44% 8.49% 7.48% 4.48% 3.23% 3.51% 7 10.59% 10.09% 11.20% 5.87% 4.23% 3.82% 8 13.08% 13.16% 16.48% 7.29% 4.53% 3.83% 9 18.82% 18.04% 26.64% 10.02% 5.67% 3.87% High R v,t-6 24.22% 21.35% 102.32% 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%** 145.96%** -4.46% -2.72% -12.70%** Value Investing Research Consortium 20

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

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 250 0.0704 0.3433 0.1434 0.0383 0.1234 1900 4.89 18.94 13.46 6.27 244 0.0740 0.3456 0.1291 0.0109-0.0183 0.1329 1720 5.09 16.90 9.79 1.08-2.45 Value Investing Research Consortium 22

Observed Returns, Sorting on Past Returns and Concurrent R v Low R v 2 3 4 5 6 7 8 9 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% 2-17.4% -6.2% 1.3% 5.8% 9.7% 12.9% 16.3% 18.4% 23.8% 30.7% 5.1% 3-17.8% -5.9% 0.2% 4.9% 8.3% 11.5% 14.2% 17.9% 23.1% 32.1% 6.3% 4-18.0% -6.8% -0.5% 4.6% 7.7% 10.7% 14.6% 17.7% 22.0% 30.3% 7.0% 5-18.4% -7.5% -1.5% 3.0% 7.2% 10.0% 12.7% 17.6% 21.7% 30.5% 7.2% 6-18.5% -8.4% -1.9% 2.7% 6.0% 9.3% 11.8% 16.0% 21.0% 32.0% 7.5% 7-20.5% -10.5% -2.4% 2.0% 5.0% 8.2% 11.6% 16.4% 21.8% 31.4% 7.9% 8-19.2% -11.3% -4.0% 1.3% 4.0% 7.3% 11.0% 15.4% 22.2% 30.5% 8.4% 9-23.6% -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. -18.0% -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

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

Thank you Value Investing Research Consortium 25

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 -2 0.131** 0.007** -0.008** -0.001-0.009** -0.007** Period -1 0.067** 0.133** 0.004** -0.010** 0.001-0.008** Period 0 0.026** 0.064** 0.131** 0.002-0.011** 0.001 Period 1-0.026** 0.019** 0.047** 0.135** 0.003-0.005** Period 2-0.004** -0.018** 0.012** 0.044** 0.089** 0.003 Period 3-0.010** -0.003-0.016** 0.016** 0.048** 0.090** Value Investing Research Consortium 26

Average Number of Observations Low R v 2 3 4 5 6 7 8 9 High R v Avg. Low Mom 62 32 19 12 9 9 9 10 12 21 196 2 34 31 25 19 16 14 13 14 14 16 196 3 22 26 26 24 21 18 16 15 14 15 196 4 15 22 25 25 24 21 19 16 14 13 196 5 12 18 23 26 26 24 21 18 15 12 196 6 11 16 20 25 26 26 23 20 17 13 196 7 10 14 18 22 25 26 25 23 19 14 196 8 9 13 16 19 22 25 27 25 23 18 196 9 10 12 14 14 17 21 25 29 30 25 196 High Mom 11 12 10 10 10 13 18 26 39 47 195 Avg. 196 196 196 196 196 196 196 196 196 195 1958 Value Investing Research Consortium 27