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The dynamics of U.S. equity risk premia :
lessons from professionals’view
Université Université de Paris Ouest Nanterre La Défense
(bâtiments K et G)
200, Avenue de la République
92001 NANTERRE CEDEX
Tél et Fax : 33.(0)1.40.97.59.07
Email : secretariateconomix@uparis10.fr
Document de Travail
Working Paper
200925
Alain Abou et Georges Prat
EconomiX
http://economix.uparis10.fr/
Université Paris X NanterreUMR 7166 CNRS
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THE DYNAMICS OF U.S. EQUITY RISK PREMIA:
LESSONS FROM PROFESSIONALS’ VIEW
Abou Alain* and Prat Georges**
December 2008
* Research Associate Professor, CNRS (Centre National de la Recherche Scientifique),
alain.abou@uparis10.fr, EconomiX, University of Paris Ouest Nanterre La Défense,
Bât G, 200 avenue de la République, 92001, Nanterre Cedex, France
** Research Professor, CNRS, corresponding author, georges.prat@uparis10.fr,
EconomiX, University of Paris Ouest Nanterre La Défense, Bât G, 200 avenue de la
République, 92001, Nanterre Cedex, France, Tel : 33 (0) 1 40 97 59 68, Fax : 33 (0) 1 40 97
59 07.
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THE DYNAMICS OF U.S. EQUITY RISK PREMIA:
LESSONS FROM PROFESSIONALS’ VIEW
Abstract  Semiannual surveys carried out by J. Livingston on a panel of experts have enabled us to
compute the expected returns over the time span 1semester and 2semesters ahead on a portfolio made
up of US industrial stocks. We calculated about 3000 individual exante equity risk premia over the
period 1952 to 1993 (82 semesters) defined as the difference between these expected stock returns and
the riskfree forward rate given by zero coupon bonds. Unlike any other study, our contribution is to
analyse premia deduced from surveys data, at the micro level, per date and over a long period. Three
main conclusions may be drawn from our analysis of these exante premia. First, the mean values of
these premia are closer to the predictions derived from the consumptionbased asset pricing theory than
the ones obtained for the expost premia. Second, the experts' professional affiliation appears to be a
significant criterion in discriminating premia. Third, in accordance with the Arbitrage Pricing Theory,
individual exante premia depend both on macroeconomic and idiosyncratic common factors:
the former are represented by a set of macroeconomic variables observable by all agents, and
the latter by experts‟ personal forecasts about the future state of the economy, as defined by
expected inflation and industrial production growth rate.
JEL classification : D81 ; D84 ; E44 ; G12 ; G14
Key words: stock price expectations, equity risk premium, survey micro data
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THE DYNAMICS OF U.S. EQUITY RISK PREMIA:
LESSONS FROM PROFESSIONALS’ VIEW
1  Introduction
The equity risk premium is a critical input planning decision, in particular for pension
funds and retirees. From a practical point of view, due to the fact that the key input in asset
allocation models (e.g. the CAPM) is the value for the equity risk premium, the mainstream
theories are rather inoperative without a good estimate of the equity premium. As portfolio
decisions are based on the expected (or exante) risk premium, and because the investment
implication of the premium may depend on why it gets its expected value, a thorough
understanding of this magnitude and of its factors are key points for financial economists.
Moreover, as underlined by Graham and Harvey (2003), the equity premium has a large
quantitative impact on the equities level: a one percent shift in the equity risk premium could add
or subtract $ 1 trillion (i.e. $ 1012 millions) to the US stock market value.
In the literature, the stock market risk premium is traditionally estimated using long
term historical average of excess stock returns (i.e. the mean of the expost equity premia) with
respect to the riskfree rate. However, as illustrated with the famous “equity premium puzzle”
debate initiated by Mehra and Prescott (1985), these historical averages (about 67% per year in
the US market) are much too large compared to the predictions from Lucas‟ consumptionbased
asset pricing model (about 12% per year). Interestingly, Fama and French (2002) suggest an
explanation: because actual returns include “large unexpected gains”, the observed equity
returns over the past halfcentury are higher on average than expected returns. If it is true, this
implies that using historical averages of excess stock returns is misleading to estimate the exante
premium. This is a key point: contrary to the expost premium, the exante premium is conditional on
the information available at time t when agents choose the structure of their portfolios. It may be viewed
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as the premium that necessarily arises out from the actual decisionmaking process. Fama and French
provide empirical evidences using fundamentals based on the GordonShapiro stock valuation
formula. This last one defines the exante risk premium as the sum of the dividends yield (S&P
500) and the historical rate of growth in dividends (as a proxy of the expected long term growth
rate) minus the riskfree bonds yield. For the 19512000 period, they found that the annual ex
ante equity premia range between 2.5% and 4.3%. These values are significantly lower than the
historical average of excess stock returns: as estimated in particular by Ibbotson and Chen
(2001), averages range between 4 and 6% over the second half of the 20th century. Other debates
in the literature concern the time varying character and term structure equity risk premia. As we
will show later, authors strongly suggest that risk premia are both time varying and horizon dependant.
Overall, for a given value of the equity risk premium, four main questions arise: is it an expost or
an exante magnitude? If it is an exante one, how to measure it? At what date it is observed? What is the
timehorizon of the underlying investment decision? Moreover, a last but not least point relates to the fact
that, since the market premium is based on the forecasts made by market participants, it is worth
considering the characteristics and the factors of exante premia at the individual level. This paper analyses
individual and time varying exante risk premia worked out for an industrial portfolio in the US stock
market over the time span horizon 1semester to 2semesters ahead. These premia are defined by the
difference between the expected returns of this portfolio issued from surveys and the riskfree rate over the
same horizon. As shown later, using expected stock returns revealed from surveys is not new in the
literature. However, no other study analyses per date over a long period and at the microeconomic level the
premia deduced from the Livingston surveys. By generating about 3000 individual exante risk premia over
the 41year period between 1952 and 1993, this paper analyses straightforwardly the factors that drive their
dynamics.
The structure of the paper is as follows. Part 2 provides a review of the literature that
investigates the concept of exante risk premium and its empirical analysis. Part 3 deals with measuring
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and describing the statistical properties of exante premia as inferred from stock price forecasts provided
by the Livingston surveys. Based on the conditional APT framework, Part 4 aims to identify which
factors determine the dynamics of these exante premia. Concluding remarks follow in the final section
(Part 5).
2 – Exante equity risk premia in the literature: concepts and empirical results
The first heading deals with the link between the basic concept considered in this paper,
namely the individual equity risk premium, and the relevant concept in stock valuation models, namely
the market risk premium. The second heading relates to whether risk premia should be viewed as ex
ante or expost magnitudes. The third heading shows that equity risk premia may be viewed as either
longterm or shortterm phenomena. The fourth heading describes the main empirical approaches and
results found in the literature related to exante equity risk premia.
2.1 – From individual risk premia to the market risk premium
To clarify the link between individual risk premia and the market risk premium, let us
consider the market of a given equity. At time t, an agent whose required exante premium1 is greater
than the market excess return will sell stocks in order to buy the riskfree asset, whereas another agent
whose required premium is lower than the market excess return will sell the riskfree asset and buy
stocks. If stocks sellers and riskfree asset purchasers are more numerous than agents having opposite
positions, then the price of the stock will drop whereas the price of the riskfree asset will rise. This
implies both an increasing stock return and a decreasing riskfree rate, resulting in a higher market
excess return. Consequently, the number of stocks sellers goes down whereas the number of riskfree
asset purchasers increases. Market equilibrium will be reached when supply matches demand for both
kinds of assets. This occurs when the weight of agents having required premium greater than the market
excess return offsets the weight of the agents whose required premium is lower than the market excess
return. At this point, there is no arbitrage opportunity between stocks and the riskfree asset, and prices
are such that the average of the individual required exante risk premia equals the market excess return,
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which then represents the exante market risk premium.2 If the market is efficient, the adjustment
described above is instantaneous. This shows that, if at any time a survey asked all market participants
to disclose their expected stock return, we would be able to measure the exante market premium using
the average of the exante individual premia, and this suggests that our approach makes sense, although
our sample does not obviously represent all market participants.
2.2 – Exante versus expost risk premia
Exante market risk premia differ from expost risk premia mainly analysed in the literature.
Unlike exante premia, expost premia are deduced from the return observed between t and t+1 and not
from the return expected between t and t+1. The expost representation implies both theoretical and
empirical limitations. On the theoretical ground, investors being unable to use expost premia to make
their financial choices at time t, this magnitude cannot be regarded as a decisionmaking concept, unless
the perfect foresight hypothesis holds, in which case the returns expected at time t for t+1 do exactly
match the returns observed expost between time t and t+1. However, it is clear that there is no risk
premia in such a setup, so that the expost excess return cannot be viewed as a risk premium.
Considering now the rational expectation hypothesis (REH), the expost premium appears to be the
rational exante premium plus a white noise representing the expost forecasting error. In this instance,
because the rational return expectation is unknown, trying to measure exante premia is subject to ad
hoc assumptions about how rational expectations are formed. Empirical evidences shows that because
of excessively large error terms, the values of expost premia are almost often as negative as positive
and this is somewhat disconcerting and likely to generate severe econometric biases, in particular
when errors are not white noises (among others, see MpackoPriso (2001)). Moreover, experts‟
expected returns derived from Livingston‟s surveys convey systematic forecast errors (Abou and Prat
(1997)), suggesting to model exante premia without assuming the REH.
2.3 – Equity risk premium: longterm view versus shortterm view
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Should equity risk premium be viewed as a longterm or a shortterm phenomenon? Two points
must be distinguished. The first one relates to the relevant timehorizon for the expected premium.
Interestingly, Barberis (2000) builds optimal portfolios made up of stocks and bonds quoted on the US
market. He shows that, taking into account predictable features of stock returns, the optimum is reached
by 40% of stocks for a onemonth time horizon and by 100% of stocks for a 10year time horizon. This
result helps to understand why risk premia may be viewed both within a longterm time horizon and
within a shortterm horizon. In fact, when returns are partially predictable on the basis of their past
values and/or macroeconomic variables, agents do not require a unique risk premium but a set of
premia scaled by the time horizon.3 So, as shown below, it is likely to find a term structure for ex
ante equity premia based on survey data about stock price expectations (see Welch (2000), Prat (2001)).
Bounded although distinct from the former, the second point concerns the frequency to
which it is relevant to observe the equity premium. The longterm view refers to the wellknown debate
about the “equity premium puzzle”: with reasonable preference parameters values, that are the risk
aversion coefficient and the subjective discount factor, theoretical risk premia inferred from the
consumption assetbased general equilibrium model are far too low (about 12% a year) as against
observed market premia, which stand about 6% a year on average (Mehra and Prescott (1985)).
According to this calibration approach, the risk premium is viewed as a longterm phenomenon since
historical averages over many years are considered. It is worth noting that, after many unsuccessful
attempts published in the literature4, Benartzi and Thaler (1995) suggest solving the premium puzzle by
assuming that longterm investors typically adopt myopic behaviour when measuring the returns of their
portfolios. They found that longterm investors measure returns over a period of less than one year: this
“mental accounting hypothesis” is shown to be a valuable explanation in solving the puzzle. It suggests
that analysing shortterm dynamics of premia makes sense even when longterm investors are involved,
which further clarifies the numerous studies found in the literature that analyse risk premia' shortterm
movements. For instance, French et al. (1987) showed that monthly risk premia fluctuations on the US
stock market are partly driven by ARCH effects. Again, De Santis and Gerard (1997) analysed the
factors explaining the shortterm dynamics of premia by using a conditional multivariate Capital Asset
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Pricing Model. Moreover, as regards passive and active mutual funds portfolios, Kryzanowski et al.
(1997) pointed out how relevant the Conditional Arbitrage Pricing Theory is to account for monthly
premia fluctuations on the Canadian stock market.
As a matter of fact, the literature strongly suggests that it is relevant studying premia
dynamics both as a longterm and a shortterm phenomenon. In this paper, these two aspects are taken
into account. Using the Livingston survey's semiannual data to compute individual forward exante
premia over the time span 1semester and 2semesters ahead, we examine over 41 years altogether the
longterm historical averages and variances, the discrepancy between agents and the factors of the
dynamics of the premia.
2.4 – Exante market risk premium as measured in the literature: backward versus forward
approaches
Generally speaking, an exante premium is defined by a given representation of the expected
return at time t for a future time horizon. Two ways of measuring exante premia follow from the
literature. Whether assuming a simple or a complex expectational process, the first approach is
backward looking since the expected return depends on the historical values of returns and/or other
observable variables.5 The second approach is forward looking since it relies on stock prices forecast
survey data and does not require any hypothesis on the underlying expectational process.
Many studies in the literature use lagged predictors to forecast the excess equity returns:
dividend yield, earnings price ratio, shortterm interest rate, payout ratio, term and default
spread, inflation rate, booktomarket ratio, consumption and wealth, etc. As a result, no robust
predictors are found. In particular, Goyal and Welch (2003, 2006) used most of afore mentioned
predictors and could not identify one that would have been robust enough for forecasting the
equity premium. This is probably the main reason explaining why the usual method to estimate
the exante equity risk premium is to extrapolate historical averages of the difference between
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returns of the stock market portfolio and a riskfree debt rate. For example, Ibbotson Associates
(2006) consider that the relevant historical premium is 7.1% during the period 19262005. Siegel
(2005) shows that the premium was substantially lower during the periods 18021870 (3.17%)
and 18711925 (3.99%). Dimson, Marsh and Staunton (2003) put into evidence that premia were
generally higher during the second half of the 20th century. These estimations seem to be
particularly widespread according to the averaged period, underlying the weak power of
historical averages to inform about future values. Booth (1999) shows that the magnitude of the
error implied by using the historical equity premium as an estimate of the expected equity
premium is rather substantial, while Shiller (2000) points out that “the future will not necessarily
be like the past”. These empirical evidences lead Fernandez (2006, p.12) to conclude that “the
historical equity premium change over time and it is not clear why capital market data from the
19th century or from the first half of the 20th century may be useful in estimating expected returns
in the 21st century …the historical equity premium is not a good indicator of the expected equity
premium”.
These difficulties led Fama and French (2002) to suggest another approach to measure the ex
ante equity premium. These authors inferred exante premia on the US stock market (S&P index) from
the present value model. They assume that at any time t, both the riskfree rate and the expected growth
rate of dividends (or earnings) per share would remain unchanged no matter the future time span; these
restrictive hypotheses led them to use the wellknown dividends discount model (DDM) formula
proposed by Gordon where the expected rates of growth in dividends (earnings) and the riskless rate are
inferred from historical mean values of dividends (earnings) and interest rate, respectively. For the period
extending from 1951 to 2000, Fama and French found a mean premium around 2.5% a year, a value
which is close to the one predicted by the consumptionbased assetpricing model. Study by Harris and
Marston (2001) is particularly original since the authors introduce in the DDM model the
expected earnings issued from surveys to estimate an exante long term market risk premium for
US stocks (S&P 500) over the period 198298 (annual averages of monthly data). The authors
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considered the five years ahead expected growth in earnings per share issued from financial
analysts as a proxy of the long run expected growth rate in dividends. The average market risk
premium is found to be 7.14% above yields on longterm US government bonds. This value
seems to be too high since it joins the equity premium puzzle. However, the period is not large
enough to allow a reliable conclusion on this point. Interestingly, the authors show strong
evidence that the risk premium change over time. A significant part of these dynamics may be
explained either by the level of interest rates or by readily available forwardlooking proxies for
risk as the spread of interest rates, the consumer confidence index reported by the Conference
Board, the degree of discrepancy between financial analysts' forecasts, or the implicit volatility
issued from options prices. However, a wellknown limitation of approaches based on the DDM
is that it relies on the restrictive hypothesis that both the riskfree rate and the expected growth rate in
dividends (or earnings) remain unchanged over an infinite time horizon.
The second way of measuring exante premia avoids this restriction since it is based on
a forward looking approach using experts‟ forecast survey data for stock prices to measure
expected stock returns.6 Within a finite time horizon framework, this approach is not based on
historical excess stock returns, but on excess returns expected for a given horizon. Although ex
ante premia may be viewed as a decisional concept, one can always question how representative
surveysbased expected risk premia are of market views; in particular, these premia probably tell
us hopedfor excess returns as much as required returns. However, with respect of the backward
looking approach, the forward looking one is less restrictive since it consists in getting rid of the
arbitrary hypothesis concerning how expectations are formed. Moreover, in comparison with the
DDM approach reviewed above, it does not assume a constant longterm growth for future
dividends.
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In this perspective, the paper by Welch (2000) intends to measure the consensus
(average) of the expected equity risk premium in the academic profession (finance professors) at
October 1997, for time horizons of 1, 5, 10 and 30 years. This measurement is given by the
difference between the mean of 226 academic financial economists' forecasts in stock returns
(S&P 500) and the equivalent horizon bonds yields. The author found that, for the oneyear
horizon, the consensus is 5.8% per year with a 2.4% standard deviation but that, in average,
shortterm premia are lower than longterm premia. The academic profession appears not to have
a consistent opinion concerning whether the risk factors as size, bookmarket, priceearnings or
momentum are likely to be useful for portfolio selection in the future. Another interesting result
comes from the question asked whether economists believe or not in arbitrage opportunities – i.e.
the ability to make money without risk. Apparently, the respondents did pay attention and
marked a strong view in favor of the absence of arbitrage opportunities. Our approach to identify
risk premia factors will keep in mind this result. Welch (2001) extends these results to a survey
(dated August 2001) of 510 finance and economics professors. He found that the consensus
forecast for the oneyear equity premium ranges from 3% to 3.5%, that is considerably lower
than the results exhibited by Welch (2000) for the October 1997 survey, suggesting that equity
risk premium is a time varying phenomenon.
Graham and Harvey (2001, 2003, 2005, 2007) present a set of studies about the
expected equity premia defined as the difference between the experts' mean expected stock
returns and an equivalent horizon bonds yields. These studies are based on quarterly surveys
conducted since June 2000 by Duke University and CFO Magazine. It concerns stock market
returns expected by about 270 anonymous Chief Financial Officers (CFOs) of U.S.
corporations. In their paper dated 2001 (resp. 2003), authors consider the values of premia from
the second quarter 2000 (resp. second quarter 2003) through the third quarter of 2001 (resp.
third quarter 2004). They found that, in contrast with the 10year expected risk premium, the
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oneyear risk premium is highly erratic through time (averages between 1.3 and 6.6%
depending on the quarter surveyed). This confirms the results obtained by Welch. In the context
of the capital asset pricing model, the market risk premium should reflect the price of risk (the
market risk aversion) and the amount of risk (the stock market volatility). Accordingly, the
surveys ask questions designed to determine CFO‟s assessment of market volatility. It finally
appears to be much lower than usual alternative measures.
In a crosssection of individual data, the authors also check if, as predicted by the
asset pricing theory, there is a positive tradeoff between expected returns and exante
volatility. They found no significant relation between expected returns and the variance at the
oneyear horizon, but a strong positive relation at the tenyear horizon that is consistent with
asset pricing theory. To check if there are systematic differences in expectations based on
firms‟ characteristics, they use information on each respondent‟s industry, size, number of
employees, headquarters location, ownership and percentage of foreign sales. They conclude
that the null that firms‟ characteristics have no impact on marketwide expectations may not be
rejected.
In their paper dated 2005 (resp. 2007), Graham and Harvey examine over the period
June 2000 to June 2005 (resp. November 2006) the exante US equity risk premium measured
over a 10year horizon relative to a 10year treasury bond. While the survey asks for both the
oneyear and tenyear expected returns, authors focus on the tenyear premium. The average
risk premia ranges between a minimum of 2.88% and a maximum of 4.65 % per year (mean
4.68% and standard deviation 0.52%). These outcomes conform to the study by O‟Neil, Wilson
and Masih (2002) who used a survey conducted in July 2002 by Goldman Sachs for its global
clients: they found that the average longrun expected risk premium was 3.9%, most values
ranging from 3.5% to 4.5%. Graham and Harvey also examined the discrepancies between
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individual premia measured by the standard deviation across experts for each quarter: over the
study period they found a mean of 2.35% with a standard deviation of 0.25%. Finally, the
authors examine the determinants of the longrun risk premium. They found that, although
premia are not influenced by oneyear ago stock returns and past priceearning ratios (S&P
500), there are positive correlations between the exante risk premium in one hand, and both the
real interest rates (as reflected in Treasury Inflation Indexed Notes) and the implied volatility on
the S&P 100 index options, on the other hand. However, as underlined by these authors, with
only 20 observations, it is difficult to consider these results to be robust.
Ilmanen (2003) makes his own survey in April 2002 to explore several issues
concerning the longrun expected return of stocks over government bonds. The experts are
global bond investors asked on future longterm equity market returns. For the United States the
author found a mean forecast of 7.6% over the next decade. Compared with the bond yields
(5.2% in average), this implies a mean risk premium of 2.4 % per year. This result is in line
with Graham and Harvey who found a 10year ahead risk premium of 2.7 % at the second
quarter 2002, and this convergence between risk premia exhibited by different surveys at the
same date is reassuring concerning the significance of the surveys approach.
Park (2006) used stock price forecasts issued from surveys conducted by J. Livingston to
construct experts‟ exante equity risk premia on the US market. As far as we know, no other study in the
literature uses these data to analyze equity premia. By comparison with the abovementioned studies,
the main advantage of these survey data stands in that they have been conducted on a semiannual
frequency basis since 1952. The author refers to the previous contribution by Cechetti et al.
(2000), which relate to the debate about the “equity premium puzzle”. What Cechetti et al.
(2000) demonstrated was that, in contrast with what ensues from REH, introducing distorted
expectations in the consumptionbased asset pricing model (Lucas (1978)) helps to solve not
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only this puzzle, but also the “volatility puzzle” and other well known stylised facts on stock
returns or risk premia. Cechetti et al. (2000) justify the distorted expectations hypothesis due to
the cost involved in processing information, leading rational agents to sidestep the relevant
method for making forecasts, as « individuals find it too costly to acquire the skills to do
maximumlikelihood ». Accordingly, agents tend to use a less accurate but cheaper predicting
method: « instead, they respond by using rules of thumb ». Assuming a CRRA utility function
with reasonable values for the risk aversion coefficient (<10) and for the discount rate, and
using expectations from the Livingston panel, the authors showed that agents are pessimistic
during periods of prosperity (i.e. expected stock returns are lower than their values under REH),
and optimistic during periods of recession (i.e. expected stock returns are greater than their
values under REH). Using expected stock returns calculated from the Livingston survey, which
show biases similar to those exhibited by Cechetti et al. (2000), Park (2006) confirmed that
distorted expectations solve the equity premium puzzle. He showed that the theoretical values of
Sharpe's ratios based on the Cechetti et al. (2000) model have the same statistical properties as
those worked out from the Livingston panel.7 Note that it is not the case with the Campbell and
Cochrane (1999) model, which integrates habits in the Lucas consumptionbased framework.
Obviously, these results led us to pay special attention to exante premia as inferred from
Livingston‟s surveys.
While Park‟s approach is based on the analysis of the first moment of the distribution of
equity premium, Prat (1996, 2001) focused on how to explain time series of aggregate exante premia
derived from Livingston‟s consensus relating to stock price expectations. Prat‟ study showed that
aggregate premia are influenced by macroeconomic variables such as inflation, production growth and
consumer sentiment. In the present study, we aim to broaden this last approach by evaluating the relative
impact on risk premia for various levels of explanation, i.e. the macro and micro levels, as well as the
grouplevel defined by experts' professional affiliation, and this approach is groundbreaking as regards
the literature.
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3 – Exante individual equity risk premia in the US stock market using Livingston’
surveys
3.1  Measuring individual exante risk premia
We consider individual stock market premia for a panel of experts who have answered the
surveys managed by Joseph Livingston since 1952 with the support of the Philadelphia Federal Bank.8
Premia are those associated with the US Standard and Poor‟s 400 Industrial stock price index. For a
given agent, the expected return of this equity portfolio is inferred from semiannual surveys processed
in June and December. From June 1952 to December 1989, these surveys gave the 1semester and 2
semesters ahead forecasts for the S&P 400 industrial index.9 Beginning with the survey dated June 1990,
the questions refer to the S&P 500 composite index that includes the 400 industrial securities. As these
two indexes are highly correlated with a stable regression coefficient over the years 198789, it is
possible to link up the 500 index values over the period from June 1990 to December 1993 to the 400
index values by using a stable coefficient of proportionality for both observed and expected indexes.
Each sample reports the answers given by 50 to 70 economic and financial experts belonging
to various professional affiliations that are divided into five groups: universities (identified by the letter
"U"), commercial banks ("C"), investment banks ("I") and nonfinancial firms ("N"). A last group ("A")
stands for experts belonging to various administrations (US government, Unions, etc.).
Assuming that experts' opinions reflect without bias investors' opinions is presumably a rather
strong hypothesis. However, various reasons suggest that it is safe to say that their answers provide a
proxy for investor‟s opinions. First, we must only assume that for a given expert, the expected stock
returns constructed from the "disclosed opinion” i.e. the expert‟s answer  equals the “true opinion”,
namely the one that would prevail without agency or conflict of interest problems, plus a white noise.
This hypothesis is less restrictive than the equality between both magnitudes and, using pooled data, the
biases between individuals for each survey may be offset. Second, the Livingston panel represents
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leading institutions that influence other major operating agents significantly intervening in the volume of
transactions in the US stock market (see Lakonishok (1980), p.922). This lessens the problems that may
arise from an agency bias. Third, a specific bias may arise from conflicts of interest since any expert
should give strategic answers that do not disclose his own opinions. However, interestingly, each
individual answer remains confidential and does not significantly affect the consensus, as the average
weight of each expert in the whole sample is less than 2%. Fourth, Abou and Prat (2000) have specified
a model combining the traditional extrapolative, regressive and adaptive processes that may represent
individual stock price expectations as revealed by Livingston's surveys. Although these expectations do
not conform to the rational expectation hypothesis (see Abou and Prat (1997)), they nevertheless appear
to be generated by an identifiable process. This result points to consistent behaviour at work behind the
experts‟ opinions. On the whole, these arguments will probably attenuate the question of measurement
biases.
Using Livingston‟s data, we consider the forward exante risk premium
f
i t
z, defined as the
premium relating to an industrial portfolio required by expert i at time t for the future time span [t+1,
t+2].10 This forward specification  noted by exponent f  precludes measurement errors that might occur
if premia for the time span [t, t+1] were considered. As a matter of fact, this last specification would
involve knowing the precise value of the S&P 400 index (i.e. the base index) involved by forecasters at
the time they make their forecasts. Unfortunately, because the June and December survey questionnaires
are sent in early May and November, individual answers come in dribs and drabs between MayJune and
NovemberDecember. As a result, we cannot know for sure when each answer were given, so that
individual base indexes remain unidentified. Those loose ends explain why we will consider a forward
specification.
Over the 83 semesters during the 41year period from December 1952 to December 1993, we
have computed 2981 individual forward premia held by 262 different experts, using the following
formulae:
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f
t
f
,
t i
f
,
i
rREz
t
)(
[1]
with:
)(
)(
100)()(
1,
t i
,
,,
PE
DE
ERE
f
t i
f
t i
f
t i
[2]
where
)(
,R
t i
Ef
is the forward expected stock return,
f
t r the implicit forward riskfree market interest
rate,
)(
,
f
t i E
the forward expected rate of change of the price of the industrial portfolio,
)(
,D
t i
Ef
the
forward expected dividends given by this portfolio, and
)(
1,PEt i
, the price of the portfolio expected at
time t for t+1. All rates prevail at time t, relate to the future semester timespan [t+1, t+2] and are
expressed in percentage per year.
The variables involved in risk premia measurement are calculated on the basis of the
following assumptions:
(i) Concerning
)(
,R
t i
Ef
, the Livingston surveys give, for expert i, forecasts one and two
semesters ahead for the S&P 400 industrial index P , noted
)(
1,PEt i
and
)(
2
, PEt i
, respectively. The
forward expected rate of change in the price of the industrial portfolio at semester t for period [t+1, t+2]
is then defined as:
)(
)(
ln 200)(
1,
t i
2,
,
PE
PE
E
t i
f
t i
[3]
Note that the logarithm of the ratio between the two expected stock price indexes (
)(
)(
ln
1,
t i
2
,
PE
PE
t i
)
does not equal the forward expected logarithmic ratio between the two future indices (
) (ln
1
2
,
P
P
Ef
t i
),
whereas only this last magnitude theoretically represents the forward expected rate of change
)(
,
f
t i
E
.
However, both from a theoretical and an empirical point of view, it seems reasonable to assume that the
relevant magnitude for stockholders is the return rather than the price of equities. Consequently,
supposing than experts forecast the stock return and not the price, the relevant variables are not
)(
2
, PEt i
Page 19
18
and
)(
1, PEt i
but
)(
2
,t i
E
and
)(
1,t i
E
, respectively for 2 semesters and 1 semester ahead time spans. In
this context, when experts were asked to disclose their forecasts concerning stock prices in level (i.e.
)(
2
, PEt i
and
)(
1, PEt i
), their answers may be viewed as deriving from the following relations for the two
time horizons:
))( exp()(
2
,
2
,
t it t i
EPPE
=>
)( ln)( ln
2
,
2
,
t it t i
EPPE
))( exp()(
1,
t i
1,
t it
EPPE
=>
)( ln)( ln
1,
t i
1,
t it
EPPE
which result in the following equalities:
)(
)(
ln
1
t i
,
2
,
PE
PE
t i
=
)( ln
2
,
PEt i

)( ln
1
,
PEt i
=
f
,
t i
t i t i
,
EEE
1,2
)()(
As a result, the logarithm of the ratio between the two expected stock price indexes (
)(
)(
ln
1,
t i
2
,
PE
PE
t i
) accurately measures the forward expected rate of change (
)(
,
f
t i
E
).
(ii) As regards the expected dividends, we assume that any expert builds his forecast for the
following semester by extrapolating the rate of change observed during the previous semester:
)exp()(
,
tt
f
t i
dDDE
with
)(1
1
t
tt
DDnd
i [4]
where
t D are the dividends per share distributed over the previous year by the 400 industrial firms
included in the S&P 400 industrial stock price index. This adhoc hypothesis is not crucial since the
subsequent impact on the ratio
)(
)(
1,
t i
,
PE
DE
f
t i
is largely dominated by
)(
1,PEt i
.
(iii) As regards the riskfree interest rate
f
tr , we apply the implicit forward rate inferred from
the zero coupon treasury bonds reaching maturity after 1 and 2 semesters, which is in keeping with the
stock returns expectations time horizon:
Page 20
19
2
~
1
) 1 (
) 1 (
1
t
2
1
t
2
t
t
f
t
rr
r
r
r
i [5]
Any agent is bound to secure this rate at time t for the future timespan [t+1, t+2] by
simultaneously lending over two semesters and borrowing over one semester.
3.2  Main empirical features of exante premia
Table 1 provides the definitions for all the variables used in this paper. For every survey
covering the period from December 1952 to December 1993, figure 1 depicts the central values and the
standard deviation across experts, which represents the discrepancy between individual premia
for a given date. During that period, the median of individual premia is about 4 % a year and the mean
about 2.2%; the central values per date range from +15% to –8% a year, with about 20% of negative
premia. These values clearly differ from those obtained for expost market premia that range from 63%
to +64% (48% of values are negative) with a 5.3% mean (median: 7.1%), and confirm for a long period,
the outcomes of the literature using survey data. Moreover, the 2.2% mean observed during the period
from 1952 to 1993 within the finite horizon approach using survey data compares significantly with the
average of 2.5% obtained by Fama and French (2002) during the period from 1951 to 2000 (still with
the S&P index) within the Gordon model. Within the famous equity premium puzzle debate, compared
to the expost premia values, both the exante premia central values and their variances seem to accord
more with the predictions derived from the consumptionbased asset pricing model.
Note that the magnitude of the exante premia crosssection standard deviations, ranging from
5 to 15 % a year over the period, warrants a micro data approach to explain the degree of heterogeneity
which is time varying. Another difference with expost premia is that, as can be seen on figure 2, none
of the three exante premia components, namely, the expected stock prices rate of change, the expected
dividends yield and the riskfree rate, 11 are insignificant one compared to others.
Page 21
20
[Insert table 1 p. 34]
[Insert figure 1 p.30]
[Insert figure 2 p.31]
Figure 3 and table 2 show that agents' professional affiliation is a weak but discriminating
criterion for premia. For instance, table 2 shows that over the 42 years covered by the whole sample
period, the median value for experts belonging to the “Nonfinancial firms ” is 3.9 % a year, whereas it
is 4.6 % for experts from “Investments banks”. The relative discriminative power of experts‟
professional affiliation is illustrated by table 3 which provides the
2
R coefficients between the mean
premia per date according to that criterion: the coefficients range from 0.53 (significant at the 5% level)
for the pair “University‟s experts and Nonfinancial firm‟s experts” to 0.25 for the pair “Investments
banks experts and Nonfinancial firm‟s experts”.
These results tend to show that the information used by experts to determine their required
premia depends on their skills and concerns according to their professional affiliation. However, these
statistics incorporate the resulting effect of two factors that are the professional affiliation and the
sample period characteristics. The reason is that the survey participation is free: at semester t a given
expert may cancel its membership without being substituted by another one pertaining to the same
group. Consequently, over a long period, not only the respondent but also the relative weight of each
professional group in the sample may vary from date to date.
The overall effect is that besides a specific group effect, the discrepancies between medians,
means and correlations partly reflect a time effect. Unfortunately, because of the short temporal
overlapping between subsamples for each expert, we could not build any consistent full panel in order
to control for time and group effects.12 This is why we worked with pooled individual data for each
group of experts. By studying a full panel of experts that answered the survey over a same subperiod,
we will examine later this adequacy of this approach (see section 4.2).
Page 22
21
[Insert figure 3 p.32]
[Insert table 2 p.35]
[Insert table 3 p.36]
4 – Explaining exante individual risk premia
4.1  Theoretical framework
Our approach derives from the Arbitrage Pricing Theory (APT, Ross (1976)). Let us recall
that the APT is based on two general hypotheses. The first one is that at any time, the condition of
absence of arbitrage opportunity prevails on the market: with a null initial wealth, any riskless
investment leads to a zero expected return. One remembers that this hypothesis is in accordance with
Welch (2000) who put into evidence that experts have a strong view in favor of absence of
arbitrage. The second hypothesis is that the return R between t1 and t of any portfolio includes three
elements: (i) the return forecasted at time t1 for t:
][
1
1REt
, (ii) the unexpected returns involved in
forecast errors associated to n independent common factors
tjF :
n
j
j
t
t
j
j
t
t
FEFRER
1
1
1
1
1
)()(
,
and (iii) the unexpected returns resulting from the unexpected components of specific factors. These
hypotheses allow expressing the risk premium relating to the portfolio by a linear combination of the n
factors, each contributing to explain the exante premium
1
tz , the weight j
representing the sensitivity
of the portfolio to factor
tjF :
))(()(
1
t
1
t
1
1
t
1
t
1
tj
n
j
j
rRErREz
[6]
Where R
j
is the return on factor
tjF , and where
))((
1
t
1
tj
rRE
represents the j component of the risk
premium for the following period, namely the exante risk premium of the portfolio if only the common
factor
tjF is involved.
Page 23
22
According to this approach, the common factors of risk premia will not be identified by the
theory, but by empirical analysis. Most studies concerned with APT estimate unconditional risk premia
and put into evidence the influence of macroeconomic factors such as industrial production growth rate,
spread of interest rates and stock market returns (among others, see Roll and Ross (1980), Chen, Roll
and Ross (1986) and Elton, Gruber and Mei (1994)). Using a conditional APT, Kryzanowski, Lalancette
and To (1997) confirm that several macrofactors determine the timevarying premia for a set of 130
mutual funds equities on the Canadian market: these factors are a composite index of leading indicators,
the exchange rate between the Canadian and US dollars, exports, lagged industrial production, shape of
the interest rates term structure and the market factor. Supposing REH, the first step in the estimation
procedure consists to estimate the
j coefficients by regressing the innovations of returns  i.e. their
unexpected values  on the innovations of the macroeconomic factors. The second step consists in
regressing time varying excess returns on the values of
j with timevarying parameters representing
risk premia related to each factor. According to this approach, the risk premium is endogenously
determined at any date by summing the effects of the nindependent factors.
With respect to this approach, one advantage of survey forecasts is that they provide an
exogenous measure of the risk premium per date a priori not bounded to an expectational hypothesis,
and particularly to the REH. Consequently, it becomes possible to identify directly the common factors
and to estimate their relative weight. Supposing each component j of the risk premium to be proportional
to a given variable
t
jF by coefficient a
j
, the risk premium 1
tz may be written as a linear combination
of n independent variables, each of them weighted by the composite coefficient
ab
jjj
. Moreover,
at time t, any agent may refer to two types of “common factors”. The first ones will be called
“idiosyncratic common factors” (
t i
jY,) and express expert' opinions about the future state of the
economy through expected macroeconomic variables. From a more standard perspective, the second
type of common factors will be called “macroeconomic common factors” (
t
jX ) and consists in
macroeconomic variables observable by all agents. Finally, the equation of the nfactors one period
ahead forward exante risk premium required by expert i is as follows:
Page 24
23
m
j
n
mj
t ijjtjj t i
zYbXb
11
,
1
,
[7]
4.2  Lessons from econometric analysis
With respect to equation [7], the econometric equation used to model forward premia is the
following:
m
j
t i
,
f
,
t i
I
m t i
I
m
f
,
t i
q
m t i
q
m
tt
jj
f
,
i
Cbbbb CrashKXbz
t
1
4
1,
32
1,
1
[8]
where jindexed exogenous variables stand for macroeconomic common factors
t
jX (see table 1 for
notations of variables), where iindexed exogenous variables represent idiosyncratic common factors
t i
jY, consisting in individual forecasts in production growth and inflation, and where C is an intercept
which may capture a systematic bias in expectations measurement or/and a constant structural effect.
t
Crash is a dummy variable introduced to capture the specific impact of the October 1987 stock market
crash, so that K represents the impact of the crash on the premium.
The threedimensional (agents, variables, dates) matrix that reports the answers given by the
262 experts over the 83 semesters during the sample period has 83% of missing values. This is because
that over the 42 years covered, there is a natural attrition phenomenon concerning experts since some
enter the panel whereas others leave it. Although recent econometric methods would help deal with
incomplete panel data, the number of missing values is here far too high to apply them accurately. That
is why we have estimated equation [8] using OLS on pooled individual data for each group of experts.
However, the OLS method with pooled data may induce biases due to correlations between individual
error terms. To address this question, we have attempted to measure these correlations for a subsample
of experts observed during the same time period. To do so we have selected the longest full panel data 
i.e. with no missing value  we could set up over the whole sample period. We found that 12 experts
Page 25
24
with various professional affiliations regularly responded to all the surveys over the 32 semesters
covering the period from December 1952 to December 1968. For each of the 12 files reporting expert's
data, we made an OLS estimation of equation [8] and retrieved the 12 residual vectors. We then
computed the correlation between the 66 different pairs of these 12 time series. The mean coefficient of
correlation is about 0.19 and only 8% of these coefficients appeared to be significantly different from
zero at the 5% level. Therefore, controlling for time and individual effects, the correlations between
residuals appears to be rather weak. Consequently, to all intents and purposes, we can infer that there is
no serious estimation bias induced by pooling individual data.
For a given group of experts selected according to professional affiliation, Table 4 shows that
the forward risk premia depend both on idiosyncratic and macroeconomic common factors as defined
above.13
[Insert table 4 p.37]
In keeping with experts‟ personal forecasts, the following four idiosyncratic common factors
concern industrial production and inflation:
(i) Forecasts about the industrial production growth rate: the one semester ahead growth rate
has an intuitive negative influence on the premia since it generates a transitory increase in corporate
profits and households‟ real income. Conversely, the forward expected rate  i.e. for timespan [t+1,
t+2]  appears to have a positive influence on premia. This result suggests that a high and sustained
economic expected growth induces a rising uncertainty about the duration of this trend, so that beyond a
certain threshold, a downward turning point is likely.
(ii) Expectations about the inflation rate: contrary to what happens with industrial production,
the one semester ahead expected rate has no significant impact on risk premia. But the forward expected
inflation rate appears to have a significant positive influence. This result may be interpreted according to
two mechanisms: a wealth effect and a monetary policy effect. In the first instance, an increasing
Page 26
25
expected inflation rate increases the likelihood of a smaller future real equity value, ending with a higher
required risk premium. For the second effect, longlasting inflation may increase the likelihood of a
restrictive monetary policy, which drives up premia.
Let us turn now to the significant macroeconomic common factors:
(i) Indicators expressing uncertainty make up the first set of variables. Firstly, with the
expected negative influence, the Consumer Sentiment Index (devised by the Survey Research Centre at
the University of Michigan) put into evidence the significant effect of household's economic and
financial confidence. Secondly, the volatility of stock returns has the expected positive sign. Thirdly, the
positive influence of the stock price expectations heterogeneity indicator suggests that for a given agent,
the more he/she perceives a high dispersion within other agents' forecasts, the more likely he/she will be
to consider his/her own expectations to be uncertain, inducing a higher required value for the risk
premium. This last result suggests that, at the individual level, experts are influenced by other agents„
forecasts, suggesting a mimetic behaviour.
(ii) A second set of variables is made up of indicators describing macroeconomic situation,
namely, inflation and production growth rate observed over the previous semester. The negative impact
of the industrial production growth rate is in line with the influence of one semester ahead individual
expectations: the higher the previous semester growth rate, the lower the required premia. A same but
weaker effect is found for inflation: the higher the previous semester inflation rate, the lower the
required premia. We also have introduced the squared value of the inflation rate to represent the optimal
inflation hypothesis, that is an inflation rate minimizing the risk premium, all other effects being given.14
At the 10% level, this hypothesis only applies to the whole sample: when inflation exceeds 5.5% a
year,15 the required premia increase, while under that threshold, increasing inflation leads to a decrease
in premia. This may be interpreted in the light of the monetary policy: if expected inflation exceeds the
target set by the Central Bank, and if its reaction function is known  e.g. the wellknown Taylor rule 
investors will anticipate a restrictive policy that will lead to higher required premia.
Page 27
26
(iii) Finally, a dummy variable, taking the value 1 for the December 1987 survey and 0
otherwise, captures the major stock market Crash that occurred in October 1987. The negative impact of
the crash seems rather intuitive: according to the financial press, with experts stating that stock prices
were much above their fundamental value, a crash was likely. After it occurred, experts thought that
stock prices had gone back to their fundamental value, which made a future decrease of stock price
unlikely, and this finally led them to lower their required risk premia.
Since the linear combination involving the macroeconomic common factors plus the
intercept implicitly gives the fitted values of mean risk premia per date, we also estimate an equation
explaining groupcentred risk premia by only the idiosyncratic common factors. It appeared
that the coefficients of theses factors are not significantly different from those given on table 4.
This result indirectly confirms that the macroeconomic common factors taken into account in
equation [8] give a valuable representation of the mean premia. Figure 4 shows that the fitted
values of the mean risk premia for the full sample depict satisfactorily the actual values. If the market
behaviour were similar to Livingston‟ experts behaviour, this result would mean that the
macroeconomic variables in [8] adequately explain the main part of the dynamics of the exante market
risk premia.
[Insert figure 4 p.33]
.
Table 4 shows that heterogeneity across experts is captured in equation [8] both through the
coefficients b
j
that are groupdependent, and through the idiosyncratic common factors that are agent
dependent. We will see later (cf. table 5) that the estimated coefficients of the macroeconomic and
idiosyncratic common factors notably vary among experts themselves, and these results broaden our
understanding of the sources behind exante premia heterogeneity. As mentioned earlier (see 3.2), a
question arise: does discrepancies between groups of experts mainly result from the fact that
differently affiliated agents might be clustered in different periods of time or are they mainly
tied to the heterogeneity across experts? To answer this question, we made estimations of
Page 28
27
various models explaining the individual risk premia by adding in [8] dummies representing a
time effect (date of the survey) and dummies supposed to capture a specific additive group
effect. Results obtained on the full sample showed these dummies not to be significant at the
standard 5% level. This suggests that discrepancies observed between professional affiliations
is not due to a time effect and confirm that the group effect operate through the idiosyncratic
common factors.
Overall, the significant differences between estimates according to experts' affiliation
appositely show that macroeconomic and idiosyncratic factors join together in accounting for
heterogeneity from professional affiliation, as can be seen in figure 3. In addition, the influence of the
same set of factors over the different groups explains the correlation between groups' mean premia, as
shown on table 3.
Finally, to investigate more deeply the factors explaining the heterogeneity between experts'
premia, we selected the 26 agents (10% of the total) who uninterruptedly replied to the Livingston
survey for at least 15 years. After that, we estimated equation [8] on each of the 26 corresponding
individual time series data reporting the answers for at least 30 semesters. The results given on table 5
show large discrepancies between estimates. As has been stated before, heterogeneity (see standard
errors on figure 1) may be partly explained by discrepancies between experts' price and production
expectations. Another major source of heterogeneity is that agents vary in their responsiveness to the
same given information. An extreme case arises when the coefficient related to variables
tjX or
variables
t ijY, is null for one agent but is highly significant for another one: having various skills,
experts use different types of information depending on its respective cost and accessibility. For most of
the 26 agents, only a few variables summarise this information, generally two or three indicators
selected from the previous set of variables. Among them, the prevalent ones are expected production
trends  i.e. for semester t survey, forward growth rate over the time span [t+1, t+2]  the Consumer
Page 29
28
Sentiment Index, and typically, two indicators measuring market risk: stock returns volatility and stock
price expectations heterogeneity.
[Insert table 5 p.38]
Compared with the previous studies using the APT quoted above, our results confirm the
influence of inflation and industrial production growth, represented both by “idiosyncratic common
factors” and “macroeconomic common factors”. Moreover, the significant influence of the “Consumer
Sentiment Index”, which is classified as a leading indicator by the NBER, confirms the role of the
leading indicators composite index that Kryzanowski et al. (1997) put into evidence.16
5 – Concluding remarks
The equity exante risk premium is defined as the spread between the expected return on a
portfolio of industrial stocks and the riskfree rate. The expected return on industrial stocks in the US
stock market (S&P400 industrial index) is inferred from surveys carried out by J. Livingston on a panel
of experts for one and two semester's timehorizon, whereas zero coupon bonds with maturities in step
with forecasts' time horizon give the riskfree rate. Using these variables, we computed about 3000
individual exante risk premia over the period from 1952 to 1993. In respect of expost market premia
analysed in the literature, these exante premia offer three main advantages: (i) they are based on
forecasts that use information available at the time of the actual financial decisions; (ii) they do not
require any assumption about the expectations' formation process; and (iii) they enable to analyse
experts' behaviours at the individual level.
Three main conclusions may be drawn from our study. First, these exante premia values are
closer to the predictions derived from the consumptionbased asset pricing theory than the ones obtained
for the expost premia. Second, professional affiliation, which is linked to experts' skills and concerns,
appears to be a significant variable in sorting out the information used by forecasters to assess the
Page 30
29
required risk premia. Third, individual exante premia depend both on macroeconomic and idiosyncratic
common factors: the former are represented by a set of macroeconomic variables observable by all
agents, and the latter by experts‟ personal forecasts about the future state of the economy, as defined by
expected inflation and industrial production growth rate. Each of these factors partly explains
heterogeneity due to experts' professional affiliation, and more generally, heterogeneity among agents.
These results shed light on the relevant sources of heterogeneity that must be taken into
account to model the interdependence between investors operating on the stock market. Finally, our
conclusions call for further investigations, especially in order to identify the dynamic relationship
between exante and expost risk premia. This topic will be dealt with at length in a forthcoming study.
Page 31
30
10
5
0
5
10
15
20
1955 1960 1965 1970 1975 1980 1985 1990
Figure 1  Mean, median, and standarderror
of individual exante risk premia
mean
median
standarderror
percent per year
Page 32
31
10
5
0
5
10
15
20
1955 1960 1965 1970 1975 1980 1985 1990
Figure 2  The three components of individual risk premia
mean values
expected rate of
change in stock prices
(mean value)
expected dividend
price ratio
(mean value)
riskfree rate of interest
(implicit forward rate)
percent per year
Page 33
32
20
15
10
5
0
5
10
15
1955 1960 1965 1970 1975 1980 1985 1990
Figure 3  Individual exante risk premia mean values
according to professional affiliation
investment banks
commercial
banks
others
nonfinancial
firms
universities
percent per year
Page 34
33
10
5
0
5
10
15
1955 1960 1965 1970 1975 1980 1985 1990
Figure 4  Actual and fitted values of exante risk premia
mean values
% per year
actual values
fitted values
Page 35
34
TABLE 1
Notations
Dependant variable
)(
zf
i t
: Forward exante risk premium at time t for the semester time span [t+1, t+2], related to
expert i pertaining to group G.
Exogenous variables
1  Macroeconomic common factors
t
t S : Consumer Sentiment Index at time t (in log).
: Stock returns volatility: standard error over the four semester period [t, t4].
,G
jX
t
1 , t : Stock prices expectations heterogeneity indicator: at time t, ratio between the cross standard
deviation and the consensus (mean) of stock price expectations one semester ahead.
t q : Industrial production's growth rate observed during the previous semester [t, t1].
tI : Inflation Rate observed during the previous semester [t, t1].
Crash : Impact of the October 1987 stock market crash: dummy variable with value 1 for the
December 1987 survey, and 0 otherwise.
t
2 – Idiosyncratic common factors
(
Eq
t i t i
[t, t+1] : spread between individual expectation and group G mean rate.
)()(
,
,,
qEqEq
tG
t it i
: Forward industrial production's growth rate, expected at time t for the time
span [t+1, t+2]: spread between individual expectation and group G mean
rate.
)()(
IEIEI
tG
t it i
: Inflation rate expected at time t for the time span [t, t+1]: spread between
individual expectation and group G mean rate.
)()(
,
,,
IEIEI
tG
t it i
: Forward inflation rate expected at time t for the time span [t+1, t+2]:
spread between individual expectation and group G mean rate.
t i
jY,
)()
1,
G
1,1,
qEq
t
: Industrial production's growth rate expected at time t for the time span
fff
1, 1, 1,
fff
Page 36
35
TABLE 2
f
i t
z,: mean, median and standard deviation
according to expert's professional affiliation
Individual exante risk premia
December 1952  December 1993
(% per year)
Group
N
Frequency
(%)
Mean
(m)
Median
( )
Standarddeviation
( )
12.26
12.08
Universities
709 23.8 2.03 4.01
Commercial
Banks
Non
Financial
Firms
Investment
Banks
Others
Total
772
25.9
2.34
4.03
598
20.0
2.50
3.88
10.82
419
14.1
1.55
4.60
13.66
483 16.2 2.85 3.89 10.40
2981 100 2.27 4.04 11.86
Page 37
36
TABLE 3
R between mean values of exante risk premia Coefficients of determination
2
according to expert's professional affiliation
December 1952  December 1993
)(Uzf
t
)(Czf
t
)(Nzf
t
)(Izf
t
)(Azf
t
)(Uzf
t
1 0.441 0.529 0.415 0.381
)(Czf
t
1 0.464 0.254 0.343
)(Nzf
t
1 0.253 0.380
)(Izf
t
1 0.432
)(Azf
t
1
)(Gzf
t
: Vector of risk premia mean values at time t for experts affiliated to group G, namely:
U: Universities, C: Commercial Banks, N: Nonfinancial firms, I: Investment Banks, A: Others.
Page 38
37
TABLE 4
Macroeconomic and idiosyncratic common factors of exante risk premia for each group
OLS estimation of equation [8] over the period December 1953 – December 1993
m
m t im
tt
jj
qb CrashKXb
t
1
j
t i
,
f
,
t i
I
m t i
I
m
f
,
t i
q
f
,
i
Cbbbz
4
1,
32
1,
1
I – MACROECONOMIC COMMON FACTORS
t
jX
tS
t
1 , t
tq
tI
2
tI
t
Crash
constant
term C
49.11
(1.8)
64.24
(2.6)
46.57
(2.1)
45.46
(1.1)
59.14
(2.3)
54.8
(4.5)
U
11.65
(1.9)
14.53
(2.7)
10.81
(2.2)
9.52
(1.1)
14.04
(2.5)
12.58
(4.7)
0.05
(1.3)
0.06
(1.5)
0.12
(3.3)
0.09
(1.4)
0.05
(1.3)
0.07
(3.7)
0.44
(3.1)
0.16
(1.0)
0.38
(2.6)
0.17
(0.8)
0.62
(4.0)
0.31
(4.3)
0.21
(3.8)
0.21
(3.6)
0.19
(3.5)
0.10
(1.1)
0.11
(2.0)
0.17
(6.4)
0.40
(1.2)
0.22
(0.7)
0.45
(1.5)
0.22
(0.5)
0.18
(0.6)
0.22
(1.6)
0.04
(1.4)
0.004
(0.1)
0.03
(1.1)
0.06
(1.3)
0.04
(1.1)
0.02
(1.7)
12.73
(4.0)
4.15
(1.9)
14.29
(6.5)
13.7
(3.0)
9.80
(3.5)
9.56
(7.8)
C
N
I
A
Full sample
II – IDIOSYNCRATIC COMMON FACTORS
t i
jY,
GROUP
1,t iq
f
t iq,
1,t iI
f
t iI,
2
R
RMSE
%
N
U
0.01
(0.1)
0.98
(9.8)
0.03
(0.2)
0.53
(2.4)
0.239
0.134
0.230
0.119
0.199
10.70
708
C
0.03
(0.3)
0.57
(4.7)
0.01
(0.0)
0.34
(1.0)
0.43
(1.3)
11.25
771
N
0.02
(0.3)
0.91
(8.3)
0.72
(4.7)
0.73
(7.7)
0.36
(1.4)
0.70
(1.9)
0.08
(0.4)
9.49 597
I
0.07
(0.5)
0.31
(3.9)
1.02
(2.7)
0.46
(2.1)
12.84
418
A
9.31 482
Full sample
0.09
(2.5)
0.79
(17.3)
0.03
(0.3)
0.31
(2.7)
0.101
10.24
2976
Notes: Student values are reported in brackets under estimates. The estimation based on the full sample of individual
risk premia including dummy variables capturing a specific additive group effect was non significant at the 5%
level.
Page 39
38
TABLE 5
Factors of individual exante risk premia
OLS estimation of equation [8] for each expert in a 26 agents subsample
ECON GROUP FIRST NOBS LCS VOL4 DISP1 OIP1 OINF1 OINF**2 CRASH EIP1 EIPF EINF1 EINFF CST RSQ ECON GROUP FIRST NOBS LCS VOL4 DISP1 OIP1 OINF1 OINF**2 CRASH EIP1 EIPF EINF1 EINFF CST RSQ RMSE
RMSE
14 A 52.2 59 20.73 0.18 14 A 52.2 59 20.73 0.18  0.03
. 2.17 3.65 . . . 2.59 . . 4.52 . . 2.11 . . . 2.17 3.65 . . . 2.59 . . 4.52 . . 2.11 . .
0.03  0.09 0.09  0.35 0.10 . 0.35 0.10 .  0.02 0.46 0.02 0.46  0.45 0.45  0.41 0.41  92.71 0.52 4 92.71 0.52 4.53.53
27 A 52.2 49 27 A 52.2 49  14.28 0.01 0.15 14.28 0.01 0.15  0.07 0.07  0.34 0.34  0.01 . 0.01 .  0.25 0.04 0.09 0.21 69.67 0.07 5.80.25 0.04 0.09 0.21 69.67 0.07 5.85 5
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
94 A 54.2 35 94 A 54.2 35  49.18 0.08 1.96 0.15 49.18 0.08 1.96 0.15  2.34 0.06 .
. . . 2.47 . . . . . 2.90 . . . . . . . . 2.47 . . . . . 2.90 . . . . .
2.34 0.06 .  0.35 2.16 0.35 2.16  0.71 0.71  0.23 208.23 0.54 12.50 0.23 208.23 0.54 12.50
187 A 71.2 40 187 A 71.2 40  4.98 0.07 0.11 0.05 4.98 0.07 0.11 0.05  0.73 0.04 0.73 0.04  3.56 3.56  0.79 0.42 0.16 0.14 24.25 0.36 4.37 0.79 0.42 0.16 0.14 24.25 0.36 4.37
. . . . . . . . 2.92 1.66 . . . . . . . . . . . . . 2.92 1.66 . . . . .
22 C 52.2 34 22 C 52.2 34  1.52
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.52  0.43 1.81 0.43 1.81  0.10 0.10  2.10 0.68 . 0.10 2.10 0.68 . 0.10  1.36 2.03 1.36 2.03  2.47 2.47  15.87 0.33 12.9515.87 0.33 12.95
64 C 52.2 36 64 C 52.2 36  53.69 0.04 53.69 0.04  0.01 0.01  0.18 0.81 0.18 0.81  0.17 . 0.25 0.74 0.17 . 0.25 0.74  0.41 0.65 246.95 0.45 7.56 0.41 0.65 246.95 0.45 7.56
. 1.84 . . . . . . . 1.93 . . 1.83 . . . 1.84 . . . . . . . 1.93 . . 1.83 . .
72 C 52.2 40 14.61 72 C 52.2 40 14.61  0.06 0.06  0.57 0.57  0.46 0.46  0.59 0.17 . 0.59 0.17 .  0.15 0.78 0.72 0.98 0.15 0.78 0.72 0.98  57.96 0.19 15.6157.96 0.19 15.61
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
87 C 53.2 38 87 C 53.2 38  57.74 0.20 0.62 0.26 57.74 0.20 0.62 0.26  1.69 0.00 . 1.69 0.00 .  0.50 0.15 0.28 0.01 259.04 0.28 10.760.50 0.15 0.28 0.01 259.04 0.28 10.76
. 1.65 . . . . . . . . . . . . . . 1.65 . . . . . . . . . . . . .
116 C 59.1 45 116 C 59.1 45  14.07 0.11 0.53 14.07 0.11 0.53  0.27 1.15 0.27 1.15  0.08 .
. . . . 1.90 . . . 2.67 2.45 . . . . . . . . . 1.90 . . . 2.67 2.45 . . . . .
136 C 62.2 54 136 C 62.2 54  8.80 0.25 0.19 8.80 0.25 0.19  0.30 0.30  1.04 0.04 1.04 0.04  5.32 0.36 1.30 0.32 1.50 40.95 0.46 6.67
0.08 .  1.08 1.20 0.47 1.08 1.20 0.47  1.28 57.93 0.61 6.461.28 57.93 0.61 6.46
5.32 0.36 1.30 0.32 1.50 40.95 0.46 6.67
. . 2.79 . . . . . . 1.94 . . . . . . . 2.79 . . . . . . 1.94 . . . . .
57 I 52.2 31 57 I 52.2 31  25.38 0.55 25.38 0.55  1.06 0.33 1.19 1.06 0.33 1.19  0.32 .
. . 2.12 . . . . . . 1.90 . . . . . . . 2.12 . . . . . . 1.90 . . . . .
97 I 55.2 34 97 I 55.2 34  28.38 0.22 28.38 0.22  0.20 0.20  0.16 0.16  0.62 0.62  0.11 .
0.32 .  0.36 1.14 0.82 0.45 121.43 0.48 11.040.36 1.14 0.82 0.45 121.43 0.48 11.04
0.11 .  0.17 1.61 0.17 1.61  1.89 2.94 134.51 0.58 6.931.89 2.94 134.51 0.58 6.93
. . . . . . . . . 3.02 . 2.21 . . . . . . . . . . . . 3.02 . 2.21 . . .
134 I 62.2 34 134 I 62.2 34  6.29 0.09 0.35 0.09 6.29 0.09 0.35 0.09  2.55 0.23 . 0.74 0.06 0.40 0.01 33.66 0.36 6.962.55 0.23 . 0.74 0.06 0.40 0.01 33.66 0.36 6.96
. . . . . . 1.87 . 1.81 . . . . . . . . . . . . 1.87 . 1.81 . . . . . .
28 N 52.2 73 28 N 52.2 73  30.22 0.17 0.31 30.22 0.17 0.31  0.07 0.07  0.76 0.05 0.76 0.05  20.38 0.06 1.65 20.38 0.06 1.65  0.49 0.38 135.51 0.59 8.81 0.49 0.38 135.51 0.59 8.81
. 1.91 1.83 . . . . 3.39 . 6.29 . . 1.86 . . . 1.91 1.83 . . . . 3.39 . 6.29 . . 1.86 . .
58 N 52.2 30 58 N 52.2 30  54.87 54.87  0.38 0.30 0.21 0.38 0.30 0.21  0.07 0.07  0.18 .
. . . . . . . . . 1.73 . . . . . . . . . . . . . . 1.73 . . . . .
104 N 57.1 46 104 N 57.1 46  41.74 0.11 41.74 0.11  0.75 0.75  0.10 0.10  1.48 0.10 1.48 0.10  17.84 0.48 0.25 0.42
0.18 . 0.11 0.11  1.27 1.27  4.17 0.13 244.14 0.30 10.394.17 0.13 244.14 0.30 10.39
17.84 0.48 0.25 0.42  0.57 203.35 0.60 7.78 0.57 203.35 0.60 7.78
51 U 52.2 34 51 U 52.2 34  37.22 0.13
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
53 U 52.2 34 53 U 52.2 34  81.80 81.80  0.93 2.21 0.17 0.93 2.21 0.17  1.37 1.37  0.10 .
. 2.34 . . . . . 2.27 . . . . 2.41 . . . 2.34 . . . . . 2.27 . . . . 2.41 . .
37.22 0.13  0.88 0.88  0.07 0.43 0.07 0.43  0.13 . 0.04 0.47 0.13 . 0.04 0.47  1.33 1.87 181.41 0.31 7.90 1.33 1.87 181.41 0.31 7.90
0.10 .  1.07 1.59 2.30 2.03 344.00 0.62 15.951.07 1.59 2.30 2.03 344.00 0.62 15.95
. . 2.09 . . . . . 2.04 2.41 . . . . . . . 2.09 . . . . . 2.04 2.41 . . . . .
75 U 52.2 58 4.12 0.09 1.55 75 U 52.2 58 4.12 0.09 1.55  0.24 0.24  1.59 0.14 . 1.59 0.14 .  0.60 0.31 0.60 0.31  0.31 1.30 0.31 1.30  33.86 0.51 8.6933.86 0.51 8.69
101 U 55.2 42 101 U 55.2 42  23.22
. . . 3.64 . 2.06 . . 2.15 . . . . . . . . . 3.64 . 2.06 . . 2.15 . . . . . .
23.22  0.01 0.28 0.01 0.28  0.21 1.49 0.21 1.49  0.18 . 0.18 .  0.24 0.24  0.28 0.28  1.24 1.24  0.39 105.27 0.21 11.030.39 105.27 0.21 11.03
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
106 U 57.1 41 3.00 0.01 106 U 57.1 41 3.00 0.01  0.49 0.49  0.47 0.47  3.61 0.09 . 3.61 0.09 .  0.43 0.02 0.08 0.43 0.02 0.08  1.44 13.43 0.46 8.91 1.44 13.43 0.46 8.91
. .
118 U 59.1 49 5.06 118 U 59.1 49 5.06  0.14 0.43
. . . 2.58 1.91 . . . . . . . . . . . . 2.58 1.91 . . . . . . . . .
0.14 0.43  0.27 0.75 0.27 0.75  0.06 . 0.06 .  0.10 0.20 0.00 0.10 0.20 0.00  0.58 0.58  24.85 0.09 8.9924.85 0.09 8.99
.
126 U 61.1 53 23.65 0.03 0.79 126 U 61.1 53 23.65 0.03 0.79  0.26 0.62 0.02
. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
0.26 0.62 0.02  6.21 6.21  0.45 0.05 0.45 0.05  0.54 1.00 0.54 1.00  109.09 0.29 7.80109.09 0.29 7.80
.
156 U 67.1 33 1.83 0.04 156 U 67.1 33 1.83 0.04  1.11
. . . 1.90 . . . . 1.69 . . . . . . . . 1.90 . . . . 1.69 . . . . . .
1.11  0.23 0.23  1.49 0.21 . 1.49 0.21 . 0.15 0.93 0.15 0.93  0.54 0.82 10.00 0.45 7.570.54 0.82 10.00 0.45 7.57
. . . . . . 1.66 . . 1.91 . . . . . . . . . . . 1.66 . . 1.91 . . . . .
171 U 70.1 44 171 U 70.1 44  28.92 28.92  0.10 0.11 0.10 0.11  0.10 0.48 0.10 0.48  0.04 0.04  12.48 0.27 0.86 0.56 0.59 125.86 0.42 8.4312.48 0.27 0.86 0.56 0.59 125.86 0.42 8.43
. 1.73 . . . . . 1.98 . 2.01 . . . . . . 1.73 . . . . . 1.98 . 2.01 . . . . .
173 U 70.1 41 173 U 70.1 41  43.96 0.19 0.75 0.18 43.96 0.19 0.75 0.18  3.48 0.26
. 1.70 . . . . . . 1.88 . . . . . .
3.48 0.26  12.46 12.46  0.83 0.00 0.83 0.00  1.26 1.26  1.73 192.42 0.56 10.67 1.73 192.42 0.56 10.67
. 1.70 . . . . . . 1.88 . . . . . .
Note: Student values are reported in brackets only under estimates significant at the 10% level.
Legend: ECON: Expert's number; GROUP: Expert‟s professional group; FIRST: first observation (“year  semester”) for
expert's survey participation; NOBS: number of observations; LCS =
t S ; VOL4 =
t ; DISP1 =
1 , t; OIP1 =
t q ;
OINF1 = t I ; OINF1**2 =
constant term ; RSQ =R**2 ; RMSE : root of mean square error.
2
tI ; CRASH =
t
Crash ; EIP1 =
1,t iq ; EIPF =
f
t iq, ; EINF1 =
1,t iI
; EINFF =
f
t iI, ; C :
Page 40
39
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NOTES
1 For any stockholder, the risk premium required to hold stocks rather than a riskfree asset classically depends
both on the agent‟s risk aversion and on his/her appreciation of how uncertain the state of the nature is.
2 For investor i , let
)(sQi
be his/her demand for stocks and
)(rQi
his/her demand for the riskfree asset. These
magnitudes depend on the spread between his/her required exante premium iz and the market excess return m
z
.
At any time,
)(sQi
and
)(rQi
are such that
)(
)()(
imi
ii
zz
dt
rdQ
dt
sdQ
, where
0
i
represents
the weight of agent i : the largeri is, the greater the amount is for the transactions for a given value of
im
zz
.
When m
z
>iz , agent i sells the riskfree asset and buys stocks (
0
)(
; 0
)(
dt
r dQ
dt
s dQ
ii
) whereas when m
z
<
iz , agent i sells stocks and buys the riskfree asset (
0
)(
;0
)(
dt
r dQ
dt
s dQ
ii
). If N investors having the
same weight intervene on the market, the equilibrium, reached when for the two assets, supply matches demand at
the aggregate level, is defined by the condition
0
)(
1
N
i
i
dt
s dQ
or, equivalently,
N
i
imi
zz
1
0)(
. This last
equation leads to the equality between the market excess return and the weighted average of exante individual
premia, that is
N
i
ii
N
i
im
zz
11
, which implies that, when the equilibrium is reached, the market excess
return equals the exante market premium. Note that when all agents have the same weight (
i
i
), we obtain
N
i
im
z
N
z
1
1
: the market exante premium is a simple arithmetic average of individual exante premia.
3 See Cochrane (1999).
4 See papers by Kocherlakota (1996), Cochrane (1997) and Siegel and Thaler (1997), which provide
comprehensive surveys of the macroeconomics and finance literature about the equity premium puzzle.
Page 44
43
5 For instance, according to the naive process hypothesis, the expected return equals the return observed during the
last period. However, as suggested by Abou and Prat (2000), the three traditional expectation processes:
extrapolative, adaptive or regressive, may also be assumed in a more general model mixing them.
6 In the book on the equity risk premium edited by Mehra (2006), historical excess returns remain largely the
dominant approach, but some rare studies using survey data are mentioned and are reviewed in the present paper.
7 The Sharpe ratio is defined as the ratio between the mean risk premium over the period and the standard
deviation of the expected return of stocks. To check the distorted expectation hypothesis for the Livingston panel
data, the observed Sharpe ratio has to be greater than the corresponding theoretical value.
8 After the death of J. Livingston in 1989, the Philadelphia Federal Bank managed the survey. Croushore (1997)
provides a survey of studies using the Livingston panel.
9 Cf. the online documentation from the Bank of Philadelphia Bank website, August 1992, page 5, and July 1997,
p.2, (variable SPIF). For the 198902 and the 199001 surveys, observed and expected indexes both relate to the
S&P400 index.
10 This premium may be viewed as the 1semester ahead expected premium corresponding to a portfolio of
industrial stocks held for one semester. The existence of a forward market for such a portfolio increases the
relevance of the forward premium since the difference between the expected portfolio price and its forward price
also defines the forward risk premium.
11 For the expost premium, the variance of the stock prices rates of change is quite high compared to the
dispersion of the two other components.
12 As a consequence, we cannot test if discrepancies between groups (moments, correlations, parameters…) are
statistically significant.
13 We checked that, at the 10% level, the exogenous variables are not significantly correlated, which is a condition
for applying the APT.
Page 45
44
14 See Lintner (1973).
15 We have: 0.22 / (2* 0.02) = 5.5 (% a year).
16 Among the “macroeconomic common factors”, we found that the interest rates term structure is not significant at
the 5% level. Concerning the stock market returns, our results show that the volatility of returns, rather than the
returns themselves, is a relevant factor explaining exante premia.
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