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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 : secretariat-economix@u-paris10.fr

Document de Travail

Working Paper

2009-25

Alain Abou et Georges Prat

EconomiX

http://economix.u-paris10.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@u-paris10.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@u-paris10.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 - 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

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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 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

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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

dynamics.

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

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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

(Part 5).

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,

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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

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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

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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 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

approaches

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

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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

premium”.

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

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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 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

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 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

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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

rejected.

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

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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 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

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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

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

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 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

the literature.

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