The dynamics of U.S. equity risk premia :
lessons from professionals’view
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Document de Travail
Alain Abou et Georges Prat
Université Paris X NanterreUMR 7166 CNRS
THE DYNAMICS OF U.S. EQUITY RISK PREMIA:
LESSONS FROM PROFESSIONALS’ VIEW
Abou Alain* and Prat Georges**
* Research Associate Professor, CNRS (Centre National de la Recherche Scientifique),
firstname.lastname@example.org, EconomiX, University of Paris Ouest Nanterre La Défense,
Bât G, 200 avenue de la République, 92001, Nanterre Cedex, France
** Research Professor, CNRS, corresponding author, email@example.com,
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
THE DYNAMICS OF U.S. EQUITY RISK PREMIA:
LESSONS FROM PROFESSIONALS’ VIEW
Abstract - Semi-annual surveys carried out by J. Livingston on a panel of experts have enabled us to
compute the expected returns over the time span 1-semester and 2-semesters ahead on a portfolio made
up of US industrial stocks. We calculated about 3000 individual ex-ante equity risk premia over the
period 1952 to 1993 (82 semesters) defined as the difference between these expected stock returns and
the risk-free 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 ex-ante premia. First, the mean values of
these premia are closer to the predictions derived from the consumption-based asset pricing theory than
the ones obtained for the ex-post premia. Second, the experts' professional affiliation appears to be a
significant criterion in discriminating premia. Third, in accordance with the Arbitrage Pricing Theory,
individual ex-ante 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
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 ex-ante) 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 ex-post equity premia) with
respect to the risk-free rate. However, as illustrated with the famous “equity premium puzzle”
debate initiated by Mehra and Prescott (1985), these historical averages (about 6-7% per year in
the US market) are much too large compared to the predictions from Lucas‟ consumption-based
asset pricing model (about 1-2% per year). Interestingly, Fama and French (2002) suggest an
explanation: because actual returns include “large unexpected gains”, the observed equity
returns over the past half-century 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 ex-ante
premium. This is a key point: contrary to the ex-post premium, the ex-ante premium is conditional on
the information available at time t when agents choose the structure of their portfolios. It may be viewed
as the premium that necessarily arises out from the actual decision-making process. Fama and French
provide empirical evidences using fundamentals based on the Gordon-Shapiro stock valuation
formula. This last one defines the ex-ante 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 risk-free bonds yield. For the 1951-2000 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 ex-post or
an ex-ante magnitude? If it is an ex-ante one, how to measure it? At what date it is observed? What is the
time-horizon 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 ex-ante premia at the individual level. This paper analyses
individual and time varying ex-ante risk premia worked out for an industrial portfolio in the US stock
market over the time span horizon 1-semester to 2-semesters ahead. These premia are defined by the
difference between the expected returns of this portfolio issued from surveys and the risk-free 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 ex-ante risk premia over
the 41-year period between 1952 and 1993, this paper analyses straightforwardly the factors that drive their
The structure of the paper is as follows. Part 2 provides a review of the literature that
investigates the concept of ex-ante risk premium and its empirical analysis. Part 3 deals with measuring
and describing the statistical properties of ex-ante 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 ex-ante premia. Concluding remarks follow in the final section
2 – Ex-ante 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 ex-post magnitudes. The third heading shows that equity risk premia may be viewed as either
long-term or short-term phenomena. The fourth heading describes the main empirical approaches and
results found in the literature related to ex-ante 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 ex-ante premium1 is greater
than the market excess return will sell stocks in order to buy the risk-free asset, whereas another agent
whose required premium is lower than the market excess return will sell the risk-free asset and buy
stocks. If stocks sellers and risk-free asset purchasers are more numerous than agents having opposite
positions, then the price of the stock will drop whereas the price of the risk-free asset will rise. This
implies both an increasing stock return and a decreasing risk-free rate, resulting in a higher market
excess return. Consequently, the number of stocks sellers goes down whereas the number of risk-free
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 risk-free asset, and prices
are such that the average of the individual required ex-ante risk premia equals the market excess return,
which then represents the ex-ante 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 ex-ante market premium using
the average of the ex-ante individual premia, and this suggests that our approach makes sense, although
our sample does not obviously represent all market participants.
2.2 – Ex-ante versus ex-post risk premia
Ex-ante market risk premia differ from ex-post risk premia mainly analysed in the literature.
Unlike ex-ante premia, ex-post premia are deduced from the return observed between t and t+1 and not
from the return expected between t and t+1. The ex-post representation implies both theoretical and
empirical limitations. On the theoretical ground, investors being unable to use ex-post premia to make
their financial choices at time t, this magnitude cannot be regarded as a decision-making 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 ex-post between time t and t+1. However, it is clear that there is no risk
premia in such a set-up, so that the ex-post excess return cannot be viewed as a risk premium.
Considering now the rational expectation hypothesis (REH), the ex-post premium appears to be the
rational ex-ante premium plus a white noise representing the ex-post forecasting error. In this instance,
because the rational return expectation is unknown, trying to measure ex-ante 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 ex-post 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 Mpacko-Priso (2001)). Moreover, experts‟
expected returns derived from Livingston‟s surveys convey systematic forecast errors (Abou and Prat
(1997)), suggesting to model ex-ante premia without assuming the REH.
2.3 – Equity risk premium: long-term view versus short-term view
Should equity risk premium be viewed as a long-term or a short-term phenomenon? Two points
must be distinguished. The first one relates to the relevant time-horizon 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 one-month time horizon and by 100% of stocks for a 10-year time horizon. This
result helps to understand why risk premia may be viewed both within a long-term time horizon and
within a short-term 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 long-term view refers to the well-known 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 asset-based general equilibrium model are far too low (about 1-2% 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 long-term 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 long-term investors typically adopt myopic behaviour when measuring the returns of their
portfolios. They found that long-term 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 short-term dynamics of premia makes sense even when long-term investors are involved,
which further clarifies the numerous studies found in the literature that analyse risk premia' short-term
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 short-term dynamics of premia by using a conditional multivariate Capital Asset
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 long-term and a short-term phenomenon. In this paper, these two aspects are taken
into account. Using the Livingston survey's semi-annual data to compute individual forward ex-ante
premia over the time span 1-semester and 2-semesters ahead, we examine over 41 years altogether the
long-term historical averages and variances, the discrepancy between agents and the factors of the
dynamics of the premia.
2.4 – Ex-ante market risk premium as measured in the literature: backward versus forward
Generally speaking, an ex-ante premium is defined by a given representation of the expected
return at time t for a future time horizon. Two ways of measuring ex-ante 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, short-term interest rate, payout ratio, term and default
spread, inflation rate, book-to-market 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 ex-ante equity risk premium is to extrapolate historical averages of the difference between
returns of the stock market portfolio and a risk-free debt rate. For example, Ibbotson Associates
(2006) consider that the relevant historical premium is 7.1% during the period 1926-2005. Siegel
(2005) shows that the premium was substantially lower during the periods 1802-1870 (3.17%)
and 1871-1925 (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
These difficulties led Fama and French (2002) to suggest another approach to measure the ex-
ante equity premium. These authors inferred ex-ante premia on the US stock market (S&P index) from
the present value model. They assume that at any time t, both the risk-free 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 well-known 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 consumption-based asset-pricing 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 ex-ante long term market risk premium for
US stocks (S&P 500) over the period 1982-98 (annual averages of monthly data). The authors
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 long-term 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 forward-looking 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 well-known limitation of approaches based on the DDM
is that it relies on the restrictive hypothesis that both the risk-free rate and the expected growth rate in
dividends (or earnings) remain unchanged over an infinite time horizon.
The second way of measuring ex-ante 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
surveys-based expected risk premia are of market views; in particular, these premia probably tell
us hoped-for 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 long-term growth for future
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 one-year
horizon, the consensus is 5.8% per year with a 2.4% standard deviation but that, in average,
short-term premia are lower than long-term premia. The academic profession appears not to have
a consistent opinion concerning whether the risk factors as size, book-market, price-earnings 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 one-year 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 10-year expected risk premium, the
one-year 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 cross-section of individual data, the authors also check if, as predicted by the
asset pricing theory, there is a positive trade-off between expected returns and ex-ante
volatility. They found no significant relation between expected returns and the variance at the
one-year horizon, but a strong positive relation at the ten-year 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 market-wide expectations may not be
In their paper dated 2005 (resp. 2007), Graham and Harvey examine over the period
June 2000 to June 2005 (resp. November 2006) the ex-ante US equity risk premium measured
over a 10-year horizon relative to a 10-year treasury bond. While the survey asks for both the
one-year and ten-year expected returns, authors focus on the ten-year 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 long-run expected risk premium was 3.9%, most values
ranging from 3.5% to 4.5%. Graham and Harvey also examined the discrepancies between
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 long-run risk premium. They found that, although
premia are not influenced by one-year ago stock returns and past price-earning ratios (S&P
500), there are positive correlations between the ex-ante 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 long-run expected return of stocks over government bonds. The experts are
global bond investors asked on future long-term 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 10-year 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‟ ex-ante 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 above-mentioned studies,
the main advantage of these survey data stands in that they have been conducted on a semi-annual
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 consumption-based asset pricing model (Lucas (1978)) helps to solve not
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
maximum-likelihood ». 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 consumption-based framework.
Obviously, these results led us to pay special attention to ex-ante premia as inferred from
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 ex-ante 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
group-level defined by experts' professional affiliation, and this approach is groundbreaking as regards
3 – Ex-ante individual equity risk premia in the US stock market using Livingston’
3.1 - Measuring individual ex-ante 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 semi-annual surveys processed
in June and December. From June 1952 to December 1989, these surveys gave the 1-semester 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 1987-89, 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 non-financial 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
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
Using Livingston‟s data, we consider the forward ex-ante risk premium
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 May-June and
November-December. 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
Over the 83 semesters during the 41-year period from December 1952 to December 1993, we
have computed 2981 individual forward premia held by 262 different experts, using the following
is the forward expected stock return,
t r the implicit forward risk-free market interest
t i E
the forward expected rate of change of the price of the industrial portfolio,
forward expected dividends given by this portfolio, and
, the price of the portfolio expected at
time t for t+1. All rates prevail at time t, relate to the future semester time-span [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
, the Livingston surveys give, for expert i, forecasts one and two
semesters ahead for the S&P 400 industrial index P , noted
, 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:
Note that the logarithm of the ratio between the two expected stock price indexes (
does not equal the forward expected logarithmic ratio between the two future indices (
whereas only this last magnitude theoretically represents the forward expected rate of change
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
, PEt i
1, PEt i
, 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.
, PEt i
1, PEt i
), their answers may be viewed as deriving from the following relations for the two
t it t i
)( ln)( ln
t it t i
)( ln)( ln
which result in the following equalities:
t i t i
As a result, the logarithm of the ratio between the two expected stock price indexes (
) accurately measures the forward expected rate of change (
(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:
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 ad-hoc hypothesis is not crucial since the
subsequent impact on the ratio
is largely dominated by
(iii) As regards the risk-free interest rate
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:
) 1 (
) 1 (
Any agent is bound to secure this rate at time t for the future time-span [t+1, t+2] by
simultaneously lending over two semesters and borrowing over one semester.
3.2 - Main empirical features of ex-ante 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 ex-post 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 ex-post premia values, both the ex-ante premia central values and their variances seem to accord
more with the predictions derived from the consumption-based asset pricing model.
Note that the magnitude of the ex-ante premia cross-section 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 ex-post premia is that, as can be seen on figure 2, none
of the three ex-ante premia components, namely, the expected stock prices rate of change, the expected
dividends yield and the risk-free rate, 11 are insignificant one compared to others.
[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 “Non-financial 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
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 Non-financial firm‟s experts” to 0.25 for the pair “Investments
banks experts and Non-financial 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 sub-samples 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 sub-period,
we will examine later this adequacy of this approach (see section 4.2).
[Insert figure 3 p.32]
[Insert table 2 p.35]
[Insert table 3 p.36]
4 – Explaining ex-ante 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 t-1 and t of any portfolio includes three
elements: (i) the return forecasted at time t-1 for t:
, (ii) the unexpected returns involved in
forecast errors associated to n independent common factors
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 ex-ante premium
tz , the weight j
representing the sensitivity
of the portfolio to factor
is the return on factor
tjF , and where
represents the j component of the risk
premium for the following period, namely the ex-ante risk premium of the portfolio if only the common
tjF is involved.
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 macro-factors determine the time-varying 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 time-varying 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 n-independent 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
jF by coefficient a
, the risk premium 1
tz may be written as a linear combination
of n independent variables, each of them weighted by the composite coefficient
at time t, any agent may refer to two types of “common factors”. The first ones will be called
“idiosyncratic common factors” (
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” (
jX ) and consists in
macroeconomic variables observable by all agents. Finally, the equation of the n-factors one period
ahead forward ex-ante risk premium required by expert i is as follows:
t ijjtjj t i
4.2 - Lessons from econometric analysis
With respect to equation , the econometric equation used to model forward premia is the
m t i
m t i
where j-indexed exogenous variables stand for macroeconomic common factors
jX (see table 1 for
notations of variables), where i-indexed exogenous variables represent idiosyncratic common factors
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.
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 three-dimensional (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  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
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  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
[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 time-span [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
expected inflation rate increases the likelihood of a smaller future real equity value, ending with a higher
required risk premium. For the second effect, long-lasting 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 well-known Taylor rule -
investors will anticipate a restrictive policy that will lead to higher required premia.
(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 group-centred 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  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  adequately explain the main part of the dynamics of the ex-ante market
[Insert figure 4 p.33]
Table 4 shows that heterogeneity across experts is captured in equation  both through the
that are group-dependent, 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 ex-ante 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
various models explaining the individual risk premia by adding in  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
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  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
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
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 ex-ante risk premium is defined as the spread between the expected return on a
portfolio of industrial stocks and the risk-free 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 time-horizon, whereas zero coupon bonds with maturities in step
with forecasts' time horizon give the risk-free rate. Using these variables, we computed about 3000
individual ex-ante risk premia over the period from 1952 to 1993. In respect of ex-post market premia
analysed in the literature, these ex-ante 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 ex-ante premia values are
closer to the predictions derived from the consumption-based asset pricing theory than the ones obtained
for the ex-post 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
required risk premia. Third, individual ex-ante 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 ex-ante and ex-post risk premia. This topic will be dealt with at length in a forthcoming study.
1955 1960 1965 1970 1975 1980 1985 1990
Figure 1 - Mean, median, and standard-error
of individual ex-ante risk premia
percent per year
1955 1960 1965 1970 1975 1980 1985 1990
Figure 2 - The three components of individual risk premia
expected rate of
change in stock prices
risk-free rate of interest
(implicit forward rate)
percent per year
1955 1960 1965 1970 1975 1980 1985 1990
Figure 3 - Individual ex-ante risk premia mean values
according to professional affiliation
percent per year
1955 1960 1965 1970 1975 1980 1985 1990
Figure 4 - Actual and fitted values of ex-ante risk premia
% per year
: Forward ex-ante risk premium at time t for the semester time span [t+1, t+2], related to
expert i pertaining to group G.
1 - Macroeconomic common factors
t S : Consumer Sentiment Index at time t (in log).
: Stock returns volatility: standard error over the four semester period [t, t-4].
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, t-1].
tI : Inflation Rate observed during the previous semester [t, t-1].
Crash : Impact of the October 1987 stock market crash: dummy variable with value 1 for the
December 1987 survey, and 0 otherwise.
2 – Idiosyncratic common factors
t i t i
[t, t+1] : spread between individual expectation and group G mean rate.
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
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.
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.
: Industrial production's growth rate expected at time t for the time span
1, 1, 1,
z,: mean, median and standard deviation
according to expert's professional affiliation
Individual ex-ante risk premia
December 1952 - December 1993
(% per year)
709 23.8 2.03 4.01
483 16.2 2.85 3.89 10.40
2981 100 2.27 4.04 11.86
R between mean values of ex-ante risk premia Coefficients of determination
according to expert's professional affiliation
December 1952 - December 1993
1 0.441 0.529 0.415 0.381
1 0.464 0.254 0.343
1 0.253 0.380
: Vector of risk premia mean values at time t for experts affiliated to group G, namely:
U: Universities, C: Commercial Banks, N: Non-financial firms, I: Investment Banks, A: Others.
Macroeconomic and idiosyncratic common factors of ex-ante risk premia for each group
OLS estimation of equation  over the period December 1953 – December 1993
m t im
m t i
I – MACROECONOMIC COMMON FACTORS
1 , t
II – IDIOSYNCRATIC COMMON FACTORS
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%
Factors of individual ex-ante risk premia
OLS estimation of equation  for each expert in a 26 agents sub-sample
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
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.
tI ; CRASH =
Crash ; EIP1 =
1,t iq ; EIPF =
t iq, ; EINF1 =
; EINFF =
t iI, ; C :
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1 For any stockholder, the risk premium required to hold stocks rather than a risk-free 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
be his/her demand for stocks and
his/her demand for the risk-free asset. These
magnitudes depend on the spread between his/her required ex-ante premium iz and the market excess return m
At any time,
are such that
the weight of agent i : the largeri is, the greater the amount is for the transactions for a given value of
>iz , agent i sells the risk-free asset and buys stocks (
) whereas when m
iz , agent i sells stocks and buys the risk-free asset (
). 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
. This last
equation leads to the equality between the market excess return and the weighted average of ex-ante individual
premia, that is
, which implies that, when the equilibrium is reached, the market excess
return equals the ex-ante market premium. Note that when all agents have the same weight (
), we obtain
: the market ex-ante premium is a simple arithmetic average of individual ex-ante 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.
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 1989-02 and the 1990-01 surveys, observed and expected indexes both relate to the
10 This premium may be viewed as the 1-semester 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 ex-post 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
13 We checked that, at the 10% level, the exogenous variables are not significantly correlated, which is a condition
for applying the APT.
44 Download full-text
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 ex-ante premia.