Aggregate Risk in Japanese Equity Markets

By
R. Anton Braun
University of Tokyo
and
Etsuro Shioji
Yokohama National University

First version: February 15, 2001
This version: July 6, 2003

We thank Tatsuyoshi Okimoto for assistance in collecting the data. We also thankToshiki Honda, Kenji Wada, and session participants at the 2002 Econometric Society
Winter Meeting and the 2002 APFA/PACAP/FMA meeting for helpful comments. The
first author received support for this project from the Foundation for International
Education and the Ministry of Education of Japan. The second author thanks the Seimei
Foundation and the Ministry of Education of Japan for financial assistance. He also
thanks Duke University for their hospitality during his half year visit.

Abstract
In the past decade Japanese households have been buffeted by some big aggregate shocks.
Economic growth has slowed, unemployment risk has risen, and asset prices have fallen
to levels not seen since the early 1980's. These shocks have hit both households' financial
and human capital. This paper develops a framework for identifying the sources of theseshocks and a way to measure how household assessments of these risks vary over time.
We consider the perspective of a forward-looking risk-averse household and derive
expected returns and time-varying risk premia for each risk factor. We then construct
times-series of historical expected risk premia using Japanese data on industry returns.
An analysis of this data provides four main findings. First, prior to 1984 expected risk
premia on identified goods market shocks, monetary policy and financial market risk are
all important determinants of industry level expected returns. Second, starting in 1984
households perceive that the risk from financial shocks is increasing and demand higher
risk premia to hold this risk. Third, between 1987 and 1990 risk premia on monetary
policy are large and positive. Monetary policy is perceived to be adding to financial risk.
Fourth, in 1990 as expected risk premia on financial risk shoot up, expected risk premia
on monetary policy shocks turn negative for all industry returns. As stock prices collapse
between 1990 and 1995, monetary policy shocks play an important role in hedging risk
emanating from the financial sector.

1

1 Introduction
In the past decade Japanese households have been buffeted by some big shocks.
Economic growth has slowed, unemployment risk has risen, and asset prices have fallen
to levels not seen since the early 1980's. These shocks have hit both households' financial
and human capital. We are interested in identifying the sources of these shocks andunderstanding how they have affected households’ asset demands in the 1980’s and1990’s. This paper describes a way to identify the structural shocks behind these eventsand measure how household assessments of the risks associated with these shocks varyover time. We consider the perspective of a forward-looking risk-averse household andderive a representation for that household’s asset demand functions. This representation
relates expected excess returns for an asset to a set of time-varying risk premia thatmeasure the contribution of each identified macroeconomic risk factor. To close themodel we follow Campbell (1996), and use a vector auto-regression (VAR) to forecast
the dynamics of the state of nature. Our work extends Campbell (1996) by identifying a
set of structural shocks to aggregate demand, aggregate supply, monetary policy,
money-demand and asset prices from the estimated coefficients of the VAR.
Our model provides a way to view the events of the 1980’s and 1990’s through the lenses
of a risk-averse household. Some surprising results emerge. Prior to 1984 all of themacroeconomic shocks are important determinants of expected excess returns for2

Japanese industry level data. From the perspective of a risk-averse household, the medianrisk premium on financial risk is about 2.9%, the risk premium on goods market demand
shocks is 0.8 %, the risk premium on technology shocks is -0.6% and the risk premium onmonetary policy is -1.8%.
However, starting in 1984 our household begins to demand a relatively large andincreasing risk premium to accept financial risks associated with holding Japanese equity.
Our household is anticipating the possibility of some big financial shocks and demandinga bigger reward to accept this risk. This risk premium spikes up in 1990 and remains highthroughout the 1990’s.
It has been argued that the Bank of Japan played an important role in the rise and fall of
the stock price boom. Bernanke and Gertler (1999) argue that easy policy in the late1980’s exacerbated the boom, Bayoumi (2000) and Cargill (2002) argue a sudden
tightening in 1989-1990 precipitated the collapse of asset prices, and McCallum (2000)
finds that monetary policy in the 1990’s was too tight, relative to the benchmarks ofeither a Taylor interest rate rule or a monetary base targeting rule. Hoshi and Kashyap(2001), in contrast, argue that it is difficult to associate the timing of the asset price boom
or collapse with the stance of monetary policy.
Our analysis sheds some light on this debate. Between 1987 and 1990 the risk premium
on monetary policy varies widely by industry but has a median value of about 3.4%.
3During this period shocks to monetary policy are adding to the overall level of expectedrisk. However, from 1990 to 1995, the expected risk premium on monetary policy turns
large and negative for all industry returns. In other words, Bank of Japan policy surprises
are perceived by our household to be hedging financial risks.
These results are not conclusive proof that the Bank of Japan caused the either the boomor the collapse. Our results though do suggest that from 1987 to 1990 market participants
were indeed anticipating the possibility that the Bank of Japan might take actions thatwould increase the risk of holding equity. However, from 1990 until about 1995 theperspective of investors was different. During this period they perceived that monetary
policy surprises would help them insure against the high risk of holding equity.

Our work is related to a large finance literature that seeks to determine the nature andnumber of distinct sources of aggregate risk that explain expected asset returns1. As in
Evans and Marshall (2001) our risk factors are identified innovations to preferences,
technology, and government policy. This provides a better way to account for the relative
contributions of alternative macroeconomic shocks in pricing assets.2

1

For some recent examples for this literature see e.g. (Fama and French (1996), Ferson
and Harvey (1996), Chan, Karceski and Lakonishok (1998) and Ang and Piazessi (1999).
See also Chan, Karceski and Lakonishok (1998), Jaganathan, Kubota and Takehara(1998), and Brown and Otsuki (1993) for analyses using Japanese data.
2
For instance, one would expect that the response of asset markets to an unexpected risein inflation would vary depending on whether it is due to an increase in oil prices or aneasing in monetary policy. By averaging across these different types of shocks one islikely to understate both the role of monetary policy and the role of oil price shocks.
4Our work is also related to the large literature on identified VAR’s.3 Following Uhlig(2001) (see also Faust (1999) and Canova and De Nicolo (2002) for related
methodologies) we identify the structural shocks by imposing sign restrictions on impulse
response functions.
The remainder of the paper is organized as follows. Section 2 describes the economic
model. Section 3 describes how the model is parameterized. Section 4 reports the results
and Section 5 contains our concluding remarks.

2 The model
Our economic model has two parts. The first part is a description of theconsumption-saving problem faced by a risk-averse household. Our goal here is to derivea representation that relates the household’s subjective demand for different assets to a setof aggregate risk factors. The second part of our economic model involves imposing
restrictions from economic theory so that we can give a structural interpretation to theserisk factors.
2.1 The household’s decision problem
Our description of the household decision problem closely follows Campbell (1993,
1996) and Campbell, Lo and MacKinlay (1997). The main distinction is that we restrict
attention to isoelastic preferences.

3

See Christiano, Eichenbaum and Evans (1999) for a recent survey of this literature.
5

Consider the problem of a household who maximizes the following life time utility
function:∞U t = ∑ β τ −t Cτ

1−γ

.

(2.1)

τ =t

subject to the budget constraint:

Wt +1 = (1 + Rm ,t +1 ) ⋅ (Wt − Ct ) .

(2.2)

In the above, Ct is consumption and Wt is wealth in period t, while Rm,t+1 is the market rateof return between period t and t+1. The parameter β is the discount factor and γ is thecoefficient of relative risk aversion. Assuming that asset returns and consumption arehomoskedastic and jointly lognormal, it can be shown that:Et [~rit +1 ] +Vii= γ ⋅ Vic2

(2.3)

where rit +1 is the excess return on asset i (that accrues to it between period t and t+1), Vii
is its variance, and Vic is the covariance with consumption growth. All the expectations,variances, and covariances are conditional on information available in period t. Using thefact that current consumption can be written as a function of current and future (expected)
wealth, we can substitute consumption out of equation (2.3) (Campbell (1993, 1996)):Et [~rit +1 ] +Vii= γ ⋅Viw + (γ − 1) ⋅Viw*
2

(2.4)

where Viw is the conditional covariance with the return on total wealth and Viw* is theconditional covariance with the following variable:
6

∞

∞

rw*,t +1 ≡ Et +1 ∑ ρ j rw,t +1+ j  − Et ∑ ρ j rw,t +1+ j 
 j =1 j =1−−−−−−−−(2.5)−−−−−−

where ρ ≡ 1 − exp( c − w ) . Here, c − w denotes the mean of the log of theconsumption- wealth ratio. Thus, this variable is the sum of revisions to expectations
about future returns on total wealth, discounted appropriately.
We assume that total wealth consists of financial, human wealth and other types of wealthsuch as land. Define the return on human capital as ry ,t , the current return on the market
portfolio as rm ,t +1 , and the present value of expectations revisions on future market
returns as:
∞

∞

rm*,t +1 ≡ Et +1 ∑ ρ j rm,t +1+ j  − Et ∑ ρ j rm,t +1+ j  .
 j =1 j =1(2.6)

Then by extending the model of Campbell (1996), to incorporate three types of wealth,
we get:Et [~rit +1 ] +Vii= γ ⋅ν ⋅Vim + γ ⋅ ω ⋅Viy + (1 −ν − ω ) ⋅Vio + [γ (1 − ω ) − 1]⋅Vim* .
2

(2.7)

The four V’s in this equation are conditional covariances between the return on asset iand:
1. current financial market returns (Vim );2. current and future labor income growth discounted in the same way as in (2.5)(Viy);
7

3. current and future returns on assets other than financial and human wealth (Vi0);
4. the present value of expectation revisions on future market returns ( Vim* ).

The share parameters ν and ω are the average shares of financial and human capital in
total wealth. In what follows, due to a lack of adequate data on returns to wealth otherthan financial and human, we assume that4

Vio = 0 .

(2.8)

Even though this covariance is assumed to be zero, other wealth matters for the
calculation of ν and ω .
2.2 Asset demand and risk

We assume that there are K distinct sources of risk, denoted ε kt +1 (where k=1, 2, .., K).
and that they are linearly related to the three return variables in the following way:*
rm ,t +1 − Et [rm,t +1 ] = ∑ ϕ mk ⋅ ε k ,t +1 , rm*,t +1 = ∑ ϕ mk
⋅ ε k ,t +1 , and ry ,t +1 = ∑ ϕ yk ⋅ ε k ,t +1 . (2.9)
K

K

K

k =1

k =1

k =1

Next combine (2.7)with (2.8) and (2.9), and denote the covariance of the excess returnon asset i with risk factor k by Vik. Then we obtain the following representation for asset
demand:4

An interesting extension of our analysis would be to model land. However, we chose toomit land from the analysis due to a lack of monthly land price data.
8

K
V
Et [~
rit +1 ] = − ii + ∑ pk ⋅Vik
2 k =1(2.10)

where pk’s are the risk prices defined as*
pk = ϕ mk ⋅ γ ⋅ν + ϕ yk ⋅ γ ⋅ ω + ϕ mk[γ (1 − ω ) − 1] .

(2.11)

Equation (2.10) equates expected returns for asset i, adjusted for the Jensen’s inequality
term, to the sum of the risk premia of the K shocks.

2.3 Dynamics of the risk factors

Following Campbell (1996) we model the dynamics of the risk factors using a VAR:

xt +1 = C0 + C ( L) xt + ut +1 , ut ~ IID(0, Σ )(2.12)

where xt is a (K × 1) vector of macroeconomic variables, L is a lag operator, and C(L) is alag polynomial and ut is a (Kx1) vector of disturbances. To identify the structural shocks,
we posit a linear relationship between the disturbances to the VAR and the structural risk
factors ε t = Put . That is we select a (K× K) matrix P such that:

Pxt +1 = PC0 + PC( L) xt + Put +1 ,E ( Put ut ' P') = I(2.13)

xt = Pxt and ε t = Put rewrite (2.12) as:
Using the transformations ~~xt +1 = PC0 + PC ( L) P −1 ~x t + ε t +1 .

(2.14)The second part of our economic model is a set of economic restrictions that serve to pin

9down P and thereby identify the particular rotation of the VAR disturbances that can beinterpreted as structural shocks to aggregate goods demand (AD), aggregate goods supply(AS), money demand (MD), monetary policy (MS) and financial markets (MARKET).
Our methodology for doing this is empirical and is easier to explain if the list of variablesin the VAR is known. For this reason the choice of variables to include in the VAR isdescribed next.
2.4 Variable Selection

Our choice of variables for the VAR is motivated by two criteria. First, the list ofvariables should collectively summarize the principal links between monetary policy andthe economy. In particular, the list should include the principal variables considered by
the Bank of Japan when conducting its monetary policy. Second, we also want the list ofvariables to capture other important sources of aggregate non-diversifiable risk in theJapanese economy. Based on these considerations we selected a VAR model with fivevariables: xt=(CPIt, Yt, Mt, Rt, MARKETt)’ . Here, CPI is the price level as measured by
the Consumer Price Index net of food expenditures, Y is the level of private economic
activities as measured by labor income, M is monetary base, R is the call rate, andMARKET is the value weighted return of stocks on the first tier of the Tokyo Stock
Exchange. 5 A notable omission from this list is an exchange rate variable. We

5

We will drop the time subscripts in our subsequent discussion.
10

experimented with runs that include the yen/$ exchange rate and found that the exchange
rate did not play an important role so we left it out due to concerns about
over-parameterization.
2.5 Identification of the Structural Shocks

Given that the VAR includes five variables identification of P (or P-1) amounts to
producing a set of economic restrictions that pin down its twenty-five elements. This isaccomplished by combining zero restrictions on the elements of P-1 with a set of
economic restrictions on the impulse response functions.
2.5.1 Zero Restrictions

Assume that the variables in the VAR are partitioned into three groups with CPI and Y in
the first group, M and R in the second group and Market in the third group.
Suppose further that P-1 is block triangular: P11−1
P −1 =  P21−1
 P −1
 31

0
P22−1
P32−1

0 

0 
P33−1 (2.15)

The four sub-blocks in the upper left corner of P-1 are dimensioned (2 × 2) and P31−1 isdimensioned (1× 2). The remaining sub-blocks are dimensioned to be conformable. This
imposes a contemporaneous block recursive structure between the three blocks. We will
identify innovations to the demand and supply for goods from the first block, innovations
to money demand and monetary policy from the second block and innovations to11

financial markets from the third block. One way to interpret these restrictions is that they
partition the monetary authority’s information set into two parts when setting policy ineach period. These restrictions imply that the monetary authority sees the current
innovations to demand and supply for goods prior to setting policy, but does not see thecurrent innovation to financial markets.
2.5.2 The macroeconomic effects of structural innovations

The zero restrictions listed above do not completely identify P-1. To complete theidentification of the structural shocks we bring in outside information about the economic
effects of each structural shock and directly impose this outside information on the set ofcandidate rotations. One way to isolate the effects of a structural shock is to calculate theimpulse response of a model economy to that shock. Dynamic competitive models of thebusiness cycle and monetary policy such as e.g. Rotemberg and Woodford (1997),
Ireland (1997), Aiyagari and Braun (1998), and Christiano, Eichenbaum and Evans(2001) have very specific implications for the dynamic response of prices, output, andnominal interest rates to impulses in to preferences, technology or monetary policy.
However, the magnitude and duration of these responses can vary substantiallydepending on the details of the model such as the form of preferences, the assumed typeof market structure and the feedback rule for monetary policy. Instead of wedding theidentification of the VAR to these types of modeling details, we prefer to look at a weaker
12set of sign restrictions on the impulse response functions that are broadly consistent witha whole class of these models. We hope by doing this we are basing our identification on
the implications of these models for which there is broadest agreement within theprofession.6
Our identifying restrictions for each of the five shocks are:(AD) Both Y and CPI go up for a majority of months 0 to 5.7(AS) Y goes up, while CPI goes down for a majority of months 0 to 5.
(MD) M goes up in month 0.
(MS) CPI goes up for the majority of months 1 to 6, and M goes up for the

majority of months 0 to 5. Y goes up for the majority of months 0 to 6, and R
goes up for a majority of months 0 to 5.
The rationale for imposing these sign restrictions on goods demand follows fromconsidering the effects of shocks to government purchases on economic activity.
Aiyagari and Braun (1998) report simulations for a costly price adjustment model that
produce these same responses when government purchases are a credit good. Similarly,
the restrictions on the responses of output and prices to a technology shock is implied by6

Our basic method though is quite general and can easily be adapted to impose otherrestrictions such as restrictions about persistence as in e.g. Blanchard and Quah (1989) oreven a particular set of restrictions implied by a fully-specified dynamic generalequilibrium model.
13

sticky price models such as Altig, Christiano, Eichenbaum and Linde (2003) as well as
flexible price models as in e.g. Aiyagari and Braun (1998).
In the literature on fully specified dynamic general equilibrium models, two types ofpredictions are obtained for the response of R to innovations in monetary policy. In somemodels, an easing in monetary policy produces a liquidity effect that lowers short-term
interest rates (see Christiano, Eichenbaum, and Evans (1999) for a recent survey).
Alternatively, sticky price models by Rotemberg (1996), Rotemberg and Woodford(1997), Ireland (2000) and Aiyagari and Braun (1998) have the property that short-term
interest rates rise. The analysis of Japanese data by Braun and Shioji (2002) gives
overwhelming support to the latter view, and thus this type of restriction is imposed in theanalysis that follows.
For money demand there is no consensus in the literature. A surprise increase in money
demand may either raise interest rates or leave them unchanged depending on the extent
to which they are accommodated by the central bank.8 For this reason we will not take an
ex ante position on money demand shocks and simply define them to be shocks to themoney market that are orthogonal to money supply shocks.
Finally, the fifth shock, namely “MARKET” shock, is identified uniquely from the blockrecursive structure we imposed in the previous section. We do not impose any other

7

The period in which the shock arrives is referred to as period 0.
14restrictions on this shock.
2.5.3 Imposing sign restrictions to identify P-1

Our method for imposing these sign restrictions is a rejection based quasi-Bayesianmonte-carlo procedure that builds on previous work by Uhlig (2001). Given a set of sign
restrictions on the impulse response functions, we randomly draw from the posterior
distributions of the matrix of reduced form VAR coefficients, the variance covariancematrix of the error term, Σ , and the free elements of P11−1 and P22−1 to find a set of
coefficients that satisfy the sign restrictions. If a particular monte-carlo draw satisfies thesign restrictions we tabulate it, otherwise it is discarded.9

3 Parameterization of the modelParameterizing the model involves:
1. assigning values to preference parameters of the household,2. parameterizing the dynamics of the conditional covariances in equation (2.10)
and choosing their parameters,
3. estimating the VAR that governs the evolution of the aggregate state,
4. and finally identifying, P-1, and thus the structural shocks.
It turns out to be convenient to describe these details in a different order. We will start by

8

See Clarida, Gertler and Gali (2000) for a nice discussion of this issue.
15

describing items 3 and 4 and then discuss item 2 and finally describe item 1.
3.1 Estimating the VAR and identifying the macroeconomic shocks

We use monthly Japanese data. The sample runs from January 1973 to December 1998.
Details on the data sources are reported in the data appendix. CPI, Y and M are all
estimated in log differences.10,11 The number of lags is chosen to be 6 based on the
Akaike information criterion. In the simulations, 200 draws are made from the posterior
distribution of the parameters of the VAR and, for each draw from the posterior, 50 draws
are made from the free parameters of the matrix P-1. Of the 200 outerloop draws from theposterior distribution 170 draws produced at least one valid innerloop draw of P-1, and theaverage number of successful innerloop draws per good outerloop draw was 4.5. This
makes for 688 valid draws out of a total of 10,000 draws. Impulse responses are reported
in Figure 1. For variables other than R, we report cumulative responses. The solid lines
are generated from the VAR model whose parameter values are set to their means acrossthe valid draws. The lower and upper dashed lines correspond to respectively the 16th and84th percentiles.

9

More details on this methodology can be found in Braun and Shioji (2002).
The augmented Dickey-Fuller test (Dickey and Fuller (1979)) indicates that these threevariables are non-stationary. And the two step test of cointegration by Engle and Granger(1987), using the critical values supplied by Engle and Yoo (1987), rejects the presence of
cointegration among the three variables.
11
It should however be kept in mind that the sign restrictions discussed in the previous
section are always imposed on their levels. For example, an AS shock is supposed toincrease levels of CPI and Y for the majority of months 0-5.
16
10

Starting with goods market shocks, both shocks to aggregate demand (AD) and shocks toaggregate supply (AS) have persistent effects on prices and labor income. One way toassess the plausibility of our identifying restrictions is to look at the response of thenominal interest rate. AD shocks have a positive effect on nominal interest rate while AS
shocks have a negative effect. This is in line with results from textbook AD-AS analysis
such as Blanchard (2003). AD shocks also have a persistent and significant negative
effect on cumulative market returns, which presumably comes from the increase in R.
Moving on to the money market shocks, money demand shocks only have a significant
effect only on monetary base. Monetary policy shocks have a large and significant effecton the price level and a small but persistent effect on labor income. Monetary policy
shocks also have a persistent effect on the cumulative market return. Finally, the responseof the market return to an innovation in MARKET is large and persistent. However, theresponse of other variables to this shock is small. Overall, the impulse responses reported
in Figure 1 are consistent with economists understanding of how these types of structural
shocks affect the macro-economy.

3.2 The specification and estimation of the conditional moments

Next we describe how we parameterize the dynamics of the conditional covariances that17

appear in the right hand side of (2.10).
There is a large econometric literature on estimating conditional covariances (see e.g.
Andersen and Bollerslev (1998) for a recent survey). We chose to use a relatively
parsimonious model of the conditional covariances and adopt a method similar to the one
employed by JP Morgan and Reuter (1996) and described in their “RiskMetrics”
handbook. The covariance between the return on the ith asset and the kth shock in period
t is estimated by:^^

COV t (~
rit +1 , ε kt +1 ) = λ ⋅ COV t −1 (~rit , ε kt ) + (1 − λ ) ⋅ ~r ⋅it ε it ,(3.1)

where λ is a constant between 0 and 1. Throughout this paper, we set the value of λ tobe equal to 0.97, following JP Morgan and Reuters (1996). The initial values are set to 0.
When computing the overall risk premium, we also estimate the Jensen’s inequality termin (2.10). We apply a similar approach we used for the covariances. First, the expected
return on the ith asset is computed by:Eˆ t (~
rit +1 ) = λ ⋅ Eˆ t −1 (~rit ) + (1 − λ ) ⋅ ~
rit .

(3.2)

Then the variance of the return on the same asset is computed as^^2
VAR t (~
rit +1 ) = λ ⋅ VAR t −1 (~rit ) + (1 − λ ) ⋅ (~rit − Et −1 (~rit )) .

(3.3)

3.3 Choice of Preference and other parameters

According to (2.11) and (2.7), four parameter values have to be chosen to compute the18risk prices. They are: ρ , which plays the role of a (monthly) discount rate; γ , thecoefficient of relative risk aversion; ν , the share of financial wealth; and ω , the share ofhuman wealth.
First, ρ is set to be equal to 0.03/12, which, corresponds to an annual discount rate of 3%.
As for the relative shares of wealth, Takayama et. al. (1990) estimate the average
financial, real and human wealth for households with two persons or more in Japan.
Using micro data (Zenkoku Shohi Jittai Chosa) from 1984, they estimate that the average
financial wealth per household was 4 million yen, the average real wealth was 24 million
yen, and the average human wealth (mainly the present value of wages) was as large as
130 million yen. For our model, this implies ν =0.0253 and ω =0.8228.12 As for γ , thecoefficient of relative risk aversion, the literature on the consumption based CAPM has
found that very high values of γ are required if the average household demand for themarket portfolio is to be consistent with the measured mean excess return on equity.
Campbell (2000) finds that for Japanese data this calls for setting γ to about 134.118.13
We will use this value of γ in our analysis. The reason for this choice is that we are using

12

Even their estimates might understate the importance of human capital. Jorgenson andFraumeni (1989) estimate not only “market” human capital (which is also defined,
basically, as the present value of wage income) but also “non-market” human capital(such as home work) for the US. Their estimates indicate that the total human capital is
five to six times larger than market human wealth. We thank Charles Yuji Horioka forbringing this work to our attention.
13
Campbell (2000) uses the sample period runs from 1970:II-1996:II.
19

financial data to back out our households attitudes towards risk and we want ourhousehold’s forecasts to capture some of the main properties of this data. Table 1 reports
risk prices using our parameterization of the model. The risk prices are computed using
the impulse responses from the VAR model whose parameter values are set to theirmeans across the valid draws. Numbers in the parentheses are the 16th and 84th
percentiles. All the risk prices are estimated to be positive. The risk price for MS is by far
the largest.

Estimate(16th and 84th
percentiles)

Table 1
Risk prices implied by the calibration
AD
AS
MD
MS
0.341
0.230
0.193
1.058
(0.017, 0.677)(-0.117, 0.564)(-0.380, 0.841)(0.609, 1.748)

Market0.227(0.035, 0.521)

3.4 Assessing the parameterization

Our objective is to use the model as a device for understanding the ex ante risks
households were facing between 1976 and 1998. However, before describing theseresults it is useful to summarize how well our household does in predicting movements inindustry excess returns. If the household does a horrible job of predicting asset returns
then there is little reason to take our results seriously. In fact it turns out that ourhousehold does reasonably well.
First, we investigate the ability of our estimates to predict the cross-section of returns forthe 28 industries in our dataset. Figure 2 displays estimates for overall expected returns
20and actual excess returns on assets, as suggested by Jagannathan and Wang (1996). The
results are averages of monthly excess returns for the period of 1976:1-1998:12. Observethat the dots are distributed symmetrically around the 45-degree line with two exceptions.
In the lower left hand side of Figure 2 there are two industries that are quite far from the
45 degree line. These two industries are mining and marine transportation. The overallcorrelation between expected and actual returns is 0.534. Out of 28 industries, actual
returns are positive for 27 and expected returns are positive for 26. Overall, ourhousehold is doing a reasonable job of predicting the cross sectional distribution of excess
industry returns.
A second way to measure the forecasting performance of our household is to look at thecontemporaneous correlation between expected excess returns in period t+1 and theactual t+1 return. Table 2 reports the median correlation, the minimum and maximum
correlations across the 28 industries and the number of industries for which thecorrelation of the predicted and actual return is positive. Results are reported for the entire
sample period of 1976:1-1998:1214, as well as for the following four sub-periods: the“pre-boom” period, 1976:1-1983:12, the “boom” period, 1984:1-1989:12, the “crash”
period, 1990:1-1994:12, the “post-crash” period, 1995:1-1998:12. Not surprisingly these14

We avoid using data from the first three years (1973-1975) because the estimatedcovariance (as well as variance) might be influenced by the choice of the initial values forthe first few years.
21

correlations are small. This reflects the well known fact that predictability of returns ismodest. Interestingly, the forecasting performance declines in the 1990’s. In Section 4
we consider this decline in forecasting performance in more detail.

Table 2
Correlation between expected period t+1 and actual t+1 excess returns
Sample period
MedianRange
Sign count
Correlation

Whole sample
Pre-boom
Boom
Crash
Post-Crash

1976:1-1998:12
1976:1-1983:12
1984:1-1989:12
1990:1-1994:12
1995:1-1998:12

3.9%
5.9%
14.0%
-17.5%-8.9%( -5.9, 15.5)( -9.0, 27.2)(-22.5, 46.7)(-31.4, 3.2)(-25.5, 1.7)

20
18
22
0
2

4 Results
Figure 3 reports time-series of expected risk premia for each type of risk and the overall
expected excess return. In each panel, the solid line presents the median across all 28
industries at each point in time. The dashed lines are the maximum and the minimum risk
premium, also computed at each point in time. These risk premia are based on the average
VAR parameterization across valid draws. Some summary statistics from Figure 3 arereported in Table 3, where we again divide the period of 1976-98 into the four
sub-periods.

22

Table 3:
Historical decomposition of median expected returns (annualized, in percentages)
Expected risk premia
ActualAD
AS
MDMS
Market − Vii / 2
Returns overall
Entire sample-0.1303.035 -0.294 -0.620 0.359 -4.565 10.458
2.223
Pre-boom
2.546-0.0260.755 -0.562 0.238 -1.770
2.851 -1.110
Boom
16.8469.907 -1.728
1.138 1.532
3.387
7.424 -2.362
Crash-15.255-3.564 -0.954 -1.864 -0.474 -18.906 22.734 -3.817
Post-crash-8.4659.583 -0.040 -1.394 0.204 -2.867 16.020 -2.560

Considering first Table 3, observe that the median expected return has the same pattern as
the median actual return. Both expected and actual returns are small in the pre-boom
period and turn positive and large in the boom period. They are both negative during thecrash period, and recover in the post-crash period. This provides further evidence that ourhousehold is doing a reasonable job of forecasting the overall risk patterns in Japanesedata. Observe next that the two most important risk factors are monetary policy andfinancial market risk. The only sub-period where we see the other risk factors playing
much role in defining overall risk is the pre-boom period.
Next we turn to consider Figure 3 in more detail.
Pre-boom period (1976-1983)

When considering the pre-boom period it is important to understand that Japanesefinancial markets during much of this period were tightly regulated. For instance as late
as 1983 only two Japanese companies (Toyota Auto and Matsushita Electric) werequalified by the government to issue unsecured bonds. By 1985 this number had risen to23

fifty-seven.15
This was also a period in which government expenditures were rapidly rising. Total
government expenditures, for instance, increased from 14% of GDP in 1976 to 18% of
GDP in 1981 and the government deficit rose from 4.2% of GDP in 1976 to a peak of 6%
in 1979 and then declined to 4.72% in 1983. It is interesting that during this same period
our household is assigning a positive and relatively large risk premium to aggregate
demand shocks.
Boom period (1984-1989)

From the perspective of our household this period is marked by two principal changes inthe sources of risk: a gradual but steady rise in the risk premium on financial market risk
and a sudden sharp increase in the risk premium on monetary policy that lasts from late1986 to the end of 1989.
The risk premium on financial market risk starts to rise in about 1984. At about this time
many regulations on financial markets were eased. For instance, the number ofcompanies qualified to issue convertible bonds rises from 25 in January of 1983 to 175 by
July of 1985. The use of warrant bonds also increased rapidly during this period both
domestically and internationally. Figure 3 indicates that by 1986 our household’s risk
premium on market risk is positive in all 28 industries.

15

See Hoshi and Kashyap (2002) for more details.
24

The second big risk event during the boom period is a sharp rise in the median risk
premium on monetary policy. The median risk premium on monetary policy is about
zero up until 1986. In 1986 it falls but then becomes positive in November and remains
positive through December 1989. Note also that the cross-sectional distribution of risk
premia on monetary policy widens in 1986 and then narrows thereafter. It is interesting toconsider what events might have produced these changes in the risk premia on monetary
policy. Between September 1985 when the Plaza accord was signed and January 1986 theBank of Japan raised interest rates and the yen appreciated from 237 yen/$ to 192 yen/$.
In January 1986 the Bank of Japan began lowering the call rate. The rationale offered forthis was that it was an effort to stabilize the yen/$ exchange rate. However, as 1986
progresses the yen continues to appreciate against the dollar. On October 31 1986 Baker
and Miyazawa meet and on the following day November 1 1986 the BOJ lowers thediscount rate. The timing of these events corresponds to the upward spike in the monetary
policy risk premia in Figure 3. Finally in May 1989 the Bank of Japan changes course andstarts raising the call rate.
Figure 3 shows how these monetary policy surprises affected our household’s perspective
about holding this type of risk. Initially he treats the easing in monetary policy as hedging
market risk. However, by 1987 its perspective has changed and it is now demanding a
positive risk premium for assets that are correlated with this risk.
25

A second way to interpret the positive risk premia on monetary policy between 1987 and1990 is by comparing the actual time path of the nominal interest rate with that prescribedby a particular interest rate rule such as the Taylor rule. McCallum (2000) provides such a
comparison. He finds that Taylor Rules fit to Japanese data imply that the call rate wastoo high between about 1988 and 1990.

Crash period (1990-1994)

The crash, which we date from 1990:1 to 1994:12 is a period where both actual andexpected returns are negative. In early 1990 the household sees a big and sudden increasein financial market risk and demands a bigger premium for holding equity in all industries.
In spite of this spike in the risk premia on financial market risk the household expects
overall returns to be negative during the first half of this period. This is because thehousehold assigns an even bigger negative risk premium to monetary policy for allindustries. Overall, the household is expecting that monetary surprises will more thanfully hedge risks emanating from financial markets between 1990 and 1992. Thereafter as
the hedging role of monetary policy shocks decline the role of market risk becomes more
important in defining overall expected returns.
A widely held view is that the reaction of the Bank of Japan to the crash was slow and too
small. McCallum (2000), for instance finds that if one adopts the benchmark of a base26

targeting rule for monetary policy that monetary policy was too tight between 1990 and
1995. Alternatively, under the benchmark of a Taylor Rule monetary policy is too tightfrom 1992 through 1997. Our analysis can’t say whether monetary policy was too loose
or too tight. What we can say though is that households perceived that the nature of risks
associated with monetary policy changed in 1990 to one of hedging financial risk.
Finally observe that Figure 3 shows a decline in the cross-sectional dispersion of risk
premia. This finding is consistent with results reported in Hamao, Mei and Xu (2003).
They use the CAPM to decompose individual stock returns into a market component andidiosyncratic component and find that the market component of individual stock returns
goes up during this period. One merit of our approach is that it provides a way tounderstand what risk factors are driving the increase in the correlations between expected
returns of different industries. In order to extract such information from our estimation
results, in Figure 4, we report estimated conditional correlations of industry returns witheach of the identified macroeconomic shocks. These conditional correlations are based on
the conditional covariances, whose derivation was explained in section 3.2. The
covariances are converted into the correlations through dividing the former by theconditional standard deviations of industry returns (square roots of the conditionalvariances whose derivation is described in (3.3)) and those of macroeconomic shocks(derived in the same way as those of industry returns). From Figure 4, we find the27following results. First, there is a sudden rise in the median correlation with financial
market shocks around 1990. We computed its subsample averages, and they were 0.559
in the boom period and 0.789 in the crash period. Second, the range of the correlations
narrows considerably around 1990: during the boom period the range of subsample
average correlations across the industries was (0.202, 0.857), and it narrows to (0.681,
0.920) during the crash period. Third, returns of all the industries become negatively
correlated with monetary policy shock in the crash period. Fourth, the range ofcorrelations with monetary policy shocks also narrows somewhat between the boom
period and the crash period. All of them contribute to increases in correlations in the
expected returns between the industries.
Post crash period (1995-1998)

In this period, the overall expected risk premium turns positive for all industries. In fact, it
returns to a level comparable to that in the boom period. Two factors are playing roles
here. On the one hand, the negative risk premium on monetary policy gradually returns tonear-zero levels for all industries (refer to the fourth panel in Figure 3). On the other hand,
the risk premium on financial market shocks remains high. We believe that this latter factreflects a lack of diversification offered by equity. Notice that the expected risk premium
on market risk is positive between 1995 and the end of the sample for all industries andthat the dispersion is low. The lack of diversification opportunities is also suggested from28

Figure 4. The figure shows that the conditional correlations of the expected returns withfinancial market shocks remained high: the subsample average of the median correlation
was 0.822. Also, the range of the correlations remained narrow: the average range was(0.698, 0.914) in this period.
Our household expected to be rewarded for taking on this risk in the form of higher
returns. These expectations, however, have not been fully born out by outcomes. Boththe results in Table 2 and Table 3 point to a break down in the forecasting ability ofhouseholds during this period. The correlation of actual with predicted returns reported inTable 2 is -8.9%. And a comparison of the expected overall median return with the actual
returns shows that households did not anticipate negative returns of this magnitude.
One possible explanation for this is our assumption that the shares of human capital,
financial capital and other capital are fixed throughout the entire sample period. During
the 1990’s the share of human capital in total wealth has likely increased. To see whether
this might offer an explanation for the poor forecasting performance in the
1995:1-1998:12 subsample, we tried increasing the share of human capital in total wealthfrom the baseline value of 82% to 90%. This change reduces the median overall risk
premium for this subsample from 9.6% to 5.1%.

29

5 Concluding Remarks
In this paper we have developed a methodology for identifying and measuring the sourceand dynamics of risk associated with holding Japanese equity. We found that the twobiggest risk factors since 1976 are monetary policy and financial market risk. Technology
shocks don’t appear to be important for understanding expected returns. Demand shocks
were of some importance in the mid to late seventies before financial markets were
deregulated but since then have been overwhelmed by monetary policy and financial
market risk. There is an important difference between the properties of these two risks.
Risk premia for financial market risk have risen and remained stuck at a high level formuch of the 1990’s. Monetary policy risk, on the other hand, has added to the risk ofholding equity for some periods but hedged market risk in other periods. Our analysis
leaves us with a puzzle. Japanese equity markets offered significantly fewer
diversification opportunities to households in the 1990’s relative to the 1980’s.
Households expected to be compensated for holding these additional risks but they were
not. Understanding why this is the case is a topic of our current research.

Data Appendix
For CPI, we took consumer price index (total) and deseasonalized using the Census X-12
ARIMA method. For Y, labor income, we take the real wage index from the Monthly
30

Labor Survey published by the Ministry of Health, Labor, and Welfare and multiply it by
the index of total number of hours published from the same source. Those are indices for
all industries, for establishments with more than 30 employees. We also tried indices forestablishments with more than 5 employees in manufacturing, and the results turned out
to be quite similar. Those indices were also deseasonalized by X-12 ARIMA. M ismonetary base, seasonally adjusted and adjusted for reserve requirement ratio changes(from the Bank of Japan). R is the call rate (collateralized, one day, monthly average).
Our data on asset returns consists primarily of 28 industrial average stock returns from theJapan Securities Research Institute. The “market” return in the VAR is the weighted
average of those 28 industrial returns.

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34

Figure 1 Impulse Responses to Structural Shocks

Each panel represents response of a variable listed at the top of the column to a one standard
deviation shock of the type listed at the end of the row.
With the exception of R, they are all cumulative responses.
The solid lines are the responses from the VAR model whose parameter values are set totheir means across the valid draws. The dashed lines are the 16th and 84th percentiles,
respectively.

CPI

Y

M

R

Market

AD

AS

MD

MS

MarketFigure 2

Actual Excess Returns and Expected Excess Returnsfor 28 industries (both in percentages)

Sample averages for the period January 1976- December 1998

Each dot represents an industry, and the solid line is the 45
degree line.

Figure 3

Expected risk premia associated with shocks to aggregate goods demand (AD), aggregate goods
supply (AS), money demand (MD), monetary policy (MS), and financial markets (Market), andoverall expected risk premia. All are in annualized rates, in percentages.

Solid lines are median risk premia across the 28 industries at each point in time, and dashed lines
are the maximum and the minimum across the 28 industries, also computed at each point in time.
Note that the first three panels use different scaling from the last three panels.

Figure 4

Estimated conditional correlations between identified structural shocks
and industry returns.

Each panel represents conditional correlations of each macroeconomic shock, listed at the top of
the panel, with the 28 industry returns. Solid lines are the median of the conditional correlations
across the 28 industries, computed at each point in time. Dashed lines are the maximum and theminimum across the 28 industries, also computed at each point in time.