the rational part of momentum - columbia business school · 2019-05-14 · 6/8/2007 value investing...

6/8/2007 Value Investing Research Consortium 1

The Rational Part

of Momentum

Jim Scott

George Murillo

Heilbrunn Center for Graham and Dodd Investing

Columbia Business School

http://www.gsb.columbia.edu/

Value Investing Research Consortium 26/8/2007

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



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)



Hypothetical Momentum Deciles if the

Market were Efficient

-60%

-40%

-20%

0%

20%

40%

60%

80%

Period -2 Period -1 Period 0 Period 1 Period 2 Period 3

6 m

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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



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)



Momentum Deciles (1985 – 2006)

-60%

-40%

-20%

0%

20%

40%

60%

80%


6 m

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Momentum Deciles Returns (1985 – 2006)


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%**

`



Momentum Regressions with

Individual Stocks

Current 6 month return as a function of lagged returns

Standard errors corrected using Newey-West estimates

Ri,t = α + β1*Ri,t-1 + β2*Ri,t-2 + β3*Ri,t-3 + εi,t

Months α β1 β2 β3 R2 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%



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



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”



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



Estimating the Change in

Fundamental Value

Two period Dividend Discount Model: vit = lEit+1/(1+r) + lEit+2/(1+r)2

Eit+1 = w∙FY1 + (1 – w)∙FY2

Eit+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 Rv, where Rv

t = vit / vit-1



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



Fundamental Values and Returns

Rt = .064 + .214Rvt R2 = .107

(4.4) (16.9) n =1956

Rt = .014 + .203Rvt + .704Rind,t R2 = .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



Momentum Deciles (1985 – 2006)

-60%

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0%

20%

40%

60%

80%


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Fundamental Value Changes

Corresponding to Momentum Deciles (1985 – 2006)



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%**



Average Number of Observations per

Momentum Deciles



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



Change in Value (Rv,t-6) Deciles

(1985 – 2006)

-60%

-40%

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0%

20%

40%

60%

80%


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Low Rv 2 3 4 5 6 7 8 9 High Rv

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Stock Returns for Change in

Value (Rv) Deciles (1985 – 2006)



Low Rv,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 Rv,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%**



Fundamental Value Changes

Corresponding to Value Deciles(1985 – 2006)



Low Rv,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 Rv,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%**



An Empirical Hypothesis

Current prices partially reflect future changes in the market’s estimate of fundamental value

Pt = ltVtb0(1+Rv,t+1)

b1(1+Rv,t+2)b2

Taking logarithms and first differences yields a regression equation

Rt = a + b0rv,t + b1(rv,t+1 – rv,t) + b2(rv,t+2 – rv,t+1) + ut



Returns and

Future Value Changes

Ri,t = α + β0*Rv,t + β1*(Rv,t+1 - Rv,t)

+ β2*(Rv,t+2 - Rv,t+1) + β3*(Rv,t+3 - Rv,t+2) + ut

Months α β0 β1 β2 β3 R2 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



Observed Returns, Sorting on

Past Returns and Concurrent Rv

Low Rv 2 3 4 5 6 7 8 9 High Rv 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%



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.



Thank you



Correlations for Returns and

Change in Value

Return

Change in

Value



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**



Average Number of Observations

Low Rv 2 3 4 5 6 7 8 9 High Rv 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


the rational part of momentum - columbia business school · 2019-05-14 · 6/8/2007 value investing...

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