Presentation by Michael-Paul James on The Dog That Did Not Bark: A Defense of Return Predictability by John H. Cochrane

1. The Dog That Did Not Bark: A
Defense of Return Predictability
Paper by John H. Cochrane
Presentation by Michael-Paul James
1

2. Table of contents
Introduction
Economic significance, Statistical
significance, Powerful long-horizon
regressions?, Out-of-sample R2,
Common misunderstandings
01
2
Michael-Paul James
Null Hypothesis
02
Distribution
Distribution of Regression
Coefficients and t-statistics, Return
and dividend-growth forecasts,
Long-run coefficients, Long-run
estimates and tests
03
Correlation
Power, Correlation, and the φ View,
The source of negative correlation,
Which is the right region?—statistics
04
Autocorrelation
Autocorrelation φ, Unit Roots,
Bubbles, and Priors, How large can φ
be?, Results for different φ values, An
overall number
05
Long-run
Power in Long-run Regression
Coefficients?, Long-horizon
regressions compared, Implications
and nonimplications
06
Out-of-Sample
Out of sample R2 as a test
Reconciliation
07
What about. . .
Repurchases, specification, and
additional variables, Direct
long-horizon estimates and hidden
dividend growth, Bias in forecast
estimates
08

3. Introduction
01
Economic significance
Statistical significance
Powerful long-horizon regressions?
Out-of-sample R2
Common misunderstandings
3
Michael-Paul James

4. Empirical Observations
4
Michael-Paul James
● The Center for Research in Security Prices (CRSP) data set from
1926-2004
○ Value weighted portfolio (S&P500?)
○ Risk free rate from 3-month treasury bill

5. TABLE
1:
Forecasting
Regressions
5
Rt+1
is the real return, deflated by the CPI, Dt+1
/Dt
is real dividend growth, and Dt
/Pt
is the dividend-price ratio of the CRSP value-weighted
portfolio. Rf
t+1
is the real return on 3-month Treasury-Bills. Small letters are logs of corresponding capital letters. Annual data, 1926–2004. σ(bx)
gives the standard deviation of the fitted value of the regression.
Table 1: Forecasting regressions
Regression b t R2
(%) σ(bx)(%)
Expected Return Rt+1
= a + b(Dt
/Pt
) + εt+1
3.39 2.28** 5.8 4.9
Risk Premium Rt+1
− Rf
t
= a + b(Dt
/Pt
) + εt+1
3.83 2.61** 7.4 5.6
Dividend Growth Dt+1
/Dt
= a + b(Dt
/Pt
) + εt+1
0.07 0.06 0.0001 0.001
Log of Return rt+1
= ar
+ br
(dt
− pt
) + εr
t+1
0.097 1.92* 4.0 4.0
Log of Dividend Growth Δdt+1
= ad
+ bd
(dt
− pt
) + εdp
t+1
0.008 0.18 0.0 0.003
R2
rises with horizon
reaching 30-60%
Positive slope Coefficient
imply prices rise with
dividend yields with no offset
Dividend Growth
is not forecastable

6. Empirical Observations and Argument
6
Michael-Paul James
● If we cannot predict returns, dividend growth must be predictable to
explain the observed variation in dividend yields.
○ Dividend growth is not insignificant and has the wrong sign
■ Higher dividend yields should be the result of a lower price.
■ Lower price signals: market expects lower future dividend yield.
○ If returns nor dividend growth is forecastable, dividend yield should
be constant. It is not.
■ Present value assumption
■ Post dividend yield shock, dividend growth or return must be
forecastable due to stationarity of dividend yield

7. Statistical Significance
7
Michael-Paul James
● Expected returns and risk premium are marginally significant at the 5%
level
● Corrected p-values were 17% (1927-1996) and 15% (1952-1996)
○ Derived from the finite-sample distribution of the return-
forecasting
○ Stambaugh (1986, 1999)
● Null hypothesis: if returns are not forecastable then dividend growth
must be forecastable.
○ Evaluate the join distribution of returns and dividend growth
○ Weak evidence against the null from returns evaluation
○ Absence of dividend growth forecastability provides stronger
evidence against the null.

8. Long Horizon
8
Michael-Paul James
● Long horizon return forecast implied by one year regressions
○ br
lr
= br
/ (1 - ρϕ)
■ ϕ: dividend yield autocorrelation
■ ρ: constant related to dividend yield.
○ br
lr
is larger than the sample value only <2% of the time.
● ϵr
, return shocks, and ϵdp
, dividend yield shocks, are negatively and
strongly correlated.
○ Price rise raises returns and lowers dividend yields.
● If ρϕ = 1, the equation explodes.
○ ρ ≈ 0.96

9. Long Horizon
9
Michael-Paul James
● Dividend yield variation in part is due to changing dividend growth
forecasts (Dogs that bark)
● blr
r
-bd
lr
=1
○ Long run return forecasts less long run dividend growth forecasts
equals 1
○ The test is the same whether one examines returns on dividend
growth which removes ambiguity of short horizon coefficients.

10. Long Horizon
10
Michael-Paul James
● Conflicting messages
○ T-statistics rise with long run return regressions
■ Fama & French, 1988
○ Others found that 1 to 5 year return forecasts lower t-stats
■ Boudoukh, Richardson, and Whitelaw 2006
○ Longer horizons (>10) have power advantages
■ Campbell, 2001; Valkanov, 2003

11. Out of Sample & Point Estimates
11
Michael-Paul James
● Dividend yield and other relevant variables do not work out of sample
○ Goyal and Welch 2003, 2005
● Point estimates are very forecastable
○ 15% chance of seeing Table 1 by chance (Stambaugh 1999)
● The point of the paper is the statistics of return forecastability not
forecasting returns best practices.

12. Null Hypothesis
02
12
Michael-Paul James

13. TABLE
2:
Forecasting
regressions
and
null
hypothesis
13
Each row represents an OLS forecasting regression on the log dividend yield in annual CRSP data 1927–2004. For example, the first row presents
the regression rt+1
= ar
+ br
(dt
− pt
) + εr
t+1
. Standard errors σ(b) include a GMM correction for heteroskedasticity. The ‘‘implied’’ column calculates
each coefficient based on the other two coefficients and the identity br
= 1 − ρφ + bd
, using ρ = 0.9638. The diagonals of the ‘‘ε s. d.’’ matrix give
the standard deviation of the regression errors in percent; the off-diagonals give the correlation between errors in percent. The ‘‘Null’’ columns
describes coefficients used to simulate data under the null hypothesis that returns are not predictable.
Table 2: Forecasting regressions and null hypothesis
Estimates ε s. d. (diagonal) and correlation. Null 1 Null 2
b,φ σ(b) implied r Δd dp b,φ b,φ
r 0.097 0.050 0.101 19.6 66 −70 0 0
Δd 0.008 0.044 0.004 66 14.0 7.5 −0.0931 −0.046
dp 0.941 0.047 0.945 −70 7.5 15.3 0.941 0.99
Strong negative correlation of
return and dividend yield shocks
Low correlation between dividend
growth and yield shocks
Aggregate dividends are volatile
20% standard deviation of returns
14% standard deviation of
dividend-growth
Sample estimate

14. 14
Regression
● First-order Vector Autoregressive (VAR) model to model log returns, log
dividend growth, and log dividend yields

15. 15
Campbell-Shiller (1988) linearization

16. 16
Projections
Present dividend yield of
the log return
Log dividend yield Log dividend growth

17. Table
5:
The
effects
of
dividend-yield
autocorrelation
φ
17
The first column gives the assumed value of φ. ‘‘Draw φ’’ draws φ from the concentrated unconditional likelihood function displayed in Figure 4.
‘‘Percent probability values’’ give the percent chance of seeing each statistic larger than the sample value. br is the return forecasting
coefficient, bd is the dividend-growth forecasting coefficient. blr
is the long-run regression coefficient, blr
r
= br
/(1 − ρφ). blr
min
and blr
max
are the
smallest and largest values across the three ways of calculating the sample value of br
/(1 − ρφ), depending on which coefficient is implied by the
identity br
= 1 − ρφ + bd
. σ(dp) gives the implied standard deviation of the dividend yield σ(dp) = σ(εdp
)/sqrt[1 − φ2]. Half life is the value of τ such
that φτ
= 1/2.
Table 5: The effects of dividend-yield autocorrelation φ
Percent probability values Other
Null Real returns Excess returns Statistics
φ br
bd
blr
min
blr
max
br
bd
blr
min
blr
max
σ(dp) 1/2life
0.90 24 0.6 0.3 0.6 19 0.4 0.1 0.2 0.35 6.6
0.941 22 1.6 1.2 1.7 17 1.1 0.5 0.7 0.45 11.4
0.96 22 2.6 2.0 2.8 17 1.6 0.8 1.2 0.55 17.0
0.98 21 4.9 4.3 5.5 17 2.7 1.8 2.5 0.77 34.3
0.99 21 6.3 5.9 7.4 17 3.6 2.7 3.6 1.09 69.0
1.00 22 8.7 8.1 10 16 4.4 3.7 4.8 ∞ ∞
1.01 19 11 11 13 14 5.1 5.1 6.3 ∞ ∞
Draw φ 23 1.6 1.4 1.7 18 1.1 0.6 0.8

18. 18
Linking errors
We can remove the intercepts because the variables are demeaned.

19. 19
Null Hypothesis of the Simulation
● 50,000 artificial datasets from each null
● Sample estimate of the covariance matrix for the error terms
● For φ < 1, Draw first d0
- p0
from
● For φ > 1, start with d0
- p0
= 0
● Draw ϵt
d
and ϵt
dp
as random normals to simulate the system forward

20. Distribution
03
Distribution of Regression Coefficients and t-statistics
Return and dividend-growth forecasts
Long-run coefficients
Long-run estimates and tests
20
Michael-Paul James

21. Table 3: Percent probability values under the φ = 0.941 null
br
tr
bd
td
Real 22.3 10.3 1.77 1.67
Excess 17.4 6.32 1.11 0.87
TABLE
3:
Percent
probability
values
under
the
φ
=
0.941
null
21
Each column gives the probability that the indicated coefficients are greater than their sample values, under the
null. Monte Carlo simulation of the null described in Table 2 with 50,000 draws.
Monte Carlo produces
larger coefficient than
sample 22% of the time
Monte Carlo produces
larger t-stat than sample
10% of the time
We cannot reject the null
at the 5% level
Monte Carlo produces
larger coefficient than
sample 1.8% of the time
Monte Carlo produces
larger t-stat than sample
1.7% of the time
The lack of dividend forecastability in the data gives
far stronger statistical evidence against the null than
does the presence of return forecastability, lowering
probability values from the 10–20% range to the 1–2%
range.

22. FIGURE
1
22
Figure 1
Joint distribution of return and
dividend-growth forecasting
coefficients (left) and t-statistics
(right). The lines and large dots
give the sample estimates. The
triangle gives the null. One
thousand simulations are plotted
for clarity; each point represents
1/10% probability. Percentages are
the fraction of 50,000 simulations
that fall in the indicated
quadrants.

23. TABLE
2:
Forecasting
regressions
and
null
hypothesis
23
The long-run return forecast coefficient blr
r
is computed as blr
r
= br
/(1 − ρφ), where br is the regression coefficient of one-year returns rt+1
on dt
−
pt
, φ is the autocorrelation of dt
− pt
, ρ = 0.961, and similarly for the long-run dividend-growth forecast coefficient blrd. The standard error is
calculated from standard errors for br and φ by the delta method. The t-statistic for Δd is the statistic for the hypothesis blrd = −1. Percent
probability values (%p value) are generated by Monte Carlo under the φ = 0.941 null. The range of probability values is given over the three
choices of which coefficient (br
, φ, bd
) is implied from the other two.
Table 4: Long-run regression coefficients
Variable blr
s.e. t %p-value
r 1.09 0.44 2.48 1.39–1.83
Δd 0.09 0.44 2.48 1.39–1.83
Excess r 1.23 0.47 2.62 0.47–0.69
>100% of dividend yield volatility
coming from returns, since dividend
growth goes the wrong way

24. Correlation
04
Power, Correlation, and the φ View
The source of negative correlation
Which is the right region?—statistics
24
Michael-Paul James

25. FIGURE
2
&
3
25
Figure 2
Distribution of blr
r
= br
/(1 − ρφ). The vertical bar gives
the corresponding value in the data.
Figure 3
Joint distribution of return and dividend yield
forecasting coefficients br
, φ. In each graph the
triangle marks the null hypothesis used to generate
the data and the circle marks the estimated
coefficients br, φ.The diagonal dashed line marked
‘‘bd
’’ marks the line br
= 1 − ρφ + bd
; points above and
to the right are draws in which bd exceeds its
sample value. The solid diagonal line marked ‘‘blr
r
’’
marks the line defined by br
/(1 − ρφ) = br
/(1 − ρφ);
points above and to the right are draws in which
blrr exceeds its sample value. Numbers are the
percentage of the draws that fall in the indicated
quadrants.
larger coefficient than
sample 22% of the time

26. Autocorrelation
05
Autocorrelation φ, Unit Roots, Bubbles, and Priors
How large can φ be?
Results for different φ values
An overall number
26
Michael-Paul James

27. FIGURE
4
27
Figure 4
Likelihood function for φ, the
autoregressive parameter for
dividend yields. The likelihood is
based on an autoregressive model,
dt+1
− pt+1
= adp
+ φ(dt
− pt
) + εdp
t+1
.
The intercept adp
and innovation
variance σ2
(εdp
) are maximized out.

28. Long-run
06
Power in Long-run Regression Coefficients?
Long-horizon regressions compared
Implications and nonimplications
28
Michael-Paul James

29. Table
6:
Long-horizon
forecasting
regressions
29
In each case b(k)r gives the point estimate in the data. The column labeled ‘‘p-value’’ gives the percent probability value—the percentage of
simulations in which the long-horizon regression coefficient b(k)
r
exceeded the sample value b(k)
r
. φ = 0.94, 0.99 indicates the assumed
dividend-yield autocorrelation φ in the null hypothesis. ‘‘Direct’’ constructs long horizon returns and explicitly runs them on dividend yields.
‘‘Implied’’ calculates the indicated long-horizon regression coefficient from one-period regression coefficients. For example, the 5-year weighted
implied coefficient is calculated as b(5)
r
= Σ5
j=1
ρj−1
φj−1
br
= (1 − ρ5
φ5
)/(1 − ρφ)br
.
Table 6: Long-horizon forecasting regressions
Weighted Unweighted
Direct Implied Direct Implied
coeff. p-value φ= coeff. p-value φ= coeff. p-value φ= coeff. p-value φ=
k b(k)r 0.94 0.99 b(k)r 0.94 0.99 b(k)r 0.94 0.99 b(k)r 0.94 0.99
1 0.10 22 22 0.10 22 22 0.10 22 22 0.10 22 22
5 0.35 28 29 0.40 17 19 0.37 29 29 0.43 16 18
10 0.80 16 16 0.65 10 15 0.92 16 16 1.02 9.0 14
15 1.38 4.4 4.7 0.80 6.2 12 1.68 4.8 5.0 1.26 4.3 10
20 1.49 4.7 5.2 0.89 4.1 9.8 1.78 7.8 8.3 1.41 2.2 7.6
∞ 1.04 1.8 7.3 1.64 0.5 8.9
Br
lr
as an infinite horizon
coefficient
Br
lr
= br
/(1-ρϕ) as an implication
of first order VAR coefficients
Br
lr
is weighted by ρ
Conventional 5-year and even 10-year horizons do not go far enough
out to see the power advantages of long horizon regressions

30. FIGURE
5
30
Figure 5
Joint distribution of br
and φ
estimates, together with regions
implied by long-run regressions. The
lines give the rejection regions
implied by long-horizon return
regressions at the indicated horizon.
For example, the points above and to
the right of the line marked ‘‘5’’ are
simulations in which coefficient b(5)
r
= (1 + ρφ +· · ·+ρ4
φ4
)br
are larger than
its value in the data. The dashed line
marked ‘‘∞, unweighted’’ plots the
line where br
/(1 − φ) equals its value
in the data, corresponding to the
infinite-horizon unweighted
regression.

31. Out-of-Sample
07
Out of sample R2 as a test
Reconciliation
31
Michael-Paul James

32. FIGURE
6
32
Figure 6
Distribution of the Goyal–Welch statistic under the null that returns are forecastable and dividend growth is not forecastable. The statistic is the
root mean squared error from using the sample mean return from time 1 to time t to forecast returns at t + 1, less the root mean squared error
from using a dividend yield regression from time 1 to time t to forecast returns at time t + 1.
The sample mean is a
better out-of-sample
forecaster than the
dividend yield
Poor out-of sample R2
does not reject the
null that returns are
predictable

33. What about. . .
08
Repurchases, specification, and additional variables
Direct long-horizon estimates and hidden dividend growth
Bias in forecast estimates
33
Michael-Paul James

34. FIGURE
6
34
Figure 7
Regression forecasts of discounted
dividend growth Σk
j=1
ρj−1
Δdt+j
(top) and
returns Σk
j=1
ρj−1
rt+j
(bottom) on the log
dividend yield dt
− pt
, as a function of
the horizon k. Triangles are direct
estimates: I form the weighted
long-horizon returns and run them on
dividend yields—for example, β(Σk
j=1
ρj−1
Δdt+j
, dt
− pt
). Circles sum individual
estimates: I run dividend growth and
return at year t + j on the dividend
yield at t and then sum up the
coefficients—for example, Σk
j=1
ρj−1
β
(Δdt+j
, dt
− pt
). The dashed lines are the
long-run coefficients implied by the
VAR—for example, Σk
j=1
ρj−1
φj−1
bd
.
Variance decomposition for div-yields
*
**
Δ are direct direct regressions*
○ sum individual regression coefficients**
Little explained by dividend growth
Return forecasts
account for volatility

35. Table
7:
Means
of
estimated
parameters
35
Means are taken over 50,000 simulations of the Monte Carlo described in Table 2
Table 7: Means of estimated parameters
br
bd
φ blr
r
blr
d
φ = 0.941 Null 0 −0.093 0.941 0 −1
Mean 0.049 −0.097 0.886 0.24 −0.77
φ = 0.99 Null 0 −0.046 0.990 0 −1
Mean 0.057 −0.050 0.926 0.43 −0.57
φ: Biased downward
br
: Biased upward (half of sample estimate br
≈ 0.10)

36. Long Horizon
36
Michael-Paul James
● If returns really are not forecastable, then dividend growth must be
forecastable in order to generate the observed variation in
dividend-price ratios
● Do not see forecastability even looking 25 years out, there is no
evidence that high market price-dividend ratios are associated with
higher subsequent dividend growth
● Absence of dividend-growth forecastability in our data provides much
stronger evidence against this null than does the presence of one-year
return forecastability

37. You are Amazing
Ask me all the questions you desire. I will do my best to answer honestly
and strive to grasp your intent and creativity.
37
Michael-Paul James

38. Variable definitions and relationships
38
Michael-Paul James
● Rt+1
real return
● Rxt+1
real return with dividends
● rt+1
log real return
● dt
dividend at time t
● Dt+1
/Dt
real dividend growth
● Dt
/Pt
dividend price ratio of CRSP value weighted portfolio
● Rt+1
f
real return on 3 month treasury bill
● ϕ dividend yield autocorrelation
● bd
dividend growth forecast
● br
return forecast coefficient
● br
lr
= br
/(1-ρϕ) weighted long horizon return forecast coefficient
● ϵr
return shocks
● ϵdp
dividend yield shocks
● ρ volatility[?]
● blr
r
long run returns forecast coefficient
● bd
lr
dividend growth forecast coefficient
● blr
r
-bd
lr
=1 given in text (1536)
● VAR Vector autoregression