Expectations of equity risk premia, volatility and asymmetry

John R. Graham,

Fuqua School of Business, Duke University, Durham, NC 27708, USA

Campbell R. Harvey*

Fuqua School of Business, Duke University, Durham, NC 27708, USA National Bureau of Economic Research, Cambridge, MA 02912, USA

ABSTRACT

We present new evidence on the distribution of the ex ante risk premium based on a multi-year survey of Chief Financial Officers (CFOs) of U.S. corporations. We have responses from surveys conducted from the second quarter of 2000 through the second quarter of 2003. We find evidence that the one-year risk premium is highly variable through time, while the ten-year expected risk premium is stable and equal to approximately 3.8%. For one-year premia, after periods of negative returns, CFOs significantly reduce their market forecasts, and return distributions are more skewed to the left. We also examine an important prediction of asset pricing theory: a positive trade-off between ex ante returns and ex ante volatility. In a unique test, we examine this trade-off in a cross-section of individual respondents. We find that time horizon plays and important role. While there is little evidence of a significant relation between expected returns and variance at the one-year horizon, there is a strong positive relation at the ten-year horizon that is consistent with asset pricing theory.
______________________________________________________________________________ *Draft: July 7, 2003. Corresponding author, Telephone: +1 919.660.7768, Fax: +1 919.660.8030, Email address: cam.harvey@duke.edu. We thank the Financial Executives International (FEI) executives who took the time to fill out the surveys. We thank Michael Brandt, Alon Brav, Magnus Dahlquist, Wayne Ferson, Ken French, Ron Gallant, Eric Ghysels, Felicia Marston, Jim Smith, Paul Soderlind, Ross Valkanov, and Bob Winkler for their helpful comments, seminar participants at Boston College and the University of Michigan, participants at the NBER Corporate Finance Summer Workshop, as well as conference participants at the TIAACREF-Association of Investment Management Research research seminar and the Western Finance Association. Hai Huang and Krishnamoorthy Narasimhan provided research assistance. This research is partially sponsored by FEI but the opinions expressed in the paper are those of the authors and do not necessarily represent the views of FEI. Graham acknowledges financial support from the Alfred P. Sloan Research Foundation.
Expectations of Equity Risk Premia
1. Introduction The current market capitalization of U.S. equities is approximately $10 trillion. A shift in the equity risk premium by just one percent could add or subtract $1 trillion in market value. In addition, corporate investment decisions hinge on the expectations of the risk premium (via the cost of capital) as do both U.S. and international asset allocation decisions. Therefore, it is important for financial economists to have a thorough understanding of the expected risk premium and the factors that influence it. The expected market risk premium has traditionally been estimated using long-term historical average equity returns. Using this approach, in December 2002, the arithmetic average return on the S&P 500 over and above the U.S. Treasury bill was reported by Ibbotson Associates (2003) to be 8.21%. To many, this is a very high risk premium and it seems to have influenced the views of a great many academics [Welch (2000)]. Fama and French (2002) conclude that average realized equity returns are in fact higher than ex ante expected returns over the past half century because realized returns included large unexpected capital gains. If this is true, then using historical averages to estimate the risk premium is misleading. We use a different approach to estimate the expected risk premium and offer a number of new insights. We base our estimate on a multiyear survey of Chief Financial Officers (CFOs), designed to measure their expectations of risk premia over both short and long horizons. Our survey is unique in that we obtain a measure of each respondents risk premium distribution, rather than just the expected value (mean). That is, our survey captures both market volatility and asymmetries implicit in the respondents probability distributions. In addition, we shed light on how recent stock market performance impacts the ex ante risk premium, volatility and asymmetries. We also study the relation between expected risk and expected return. There are many methods to estimate the equity risk premium and we cannot tell which method is the best because the variable of interest is fundamentally unobservable. The average of past returns is the method with the longest tradition. However, there are other timeseries methods that use measures like dividend yield to forecast returns. These models are

A similar argument is made in Poterba and Summers (1995) survey of CEOs.
based on firm characteristics. We also have limited ability to link forecasts from one quarter to the next and are able to verify consistency in a given CFOs forecast. We have conducted surveys representing over 3,000 total responses, from the second quarter of 2000 through the second quarter of 2003. Our results, summarized in Table 1, indicate that the one-year risk premium averages between 1.3 and 6.6 percent depending on the quarter surveyed. The ten-year premium is much less variable and ranges between 2.9 and 4.7 percent (also see Fig. 1).3 The standard deviation of the quarterly ten-year means is 0.52% while the same measure for the one-year means is 1.52%. We also find that the CFOs assessment of market volatility is much lower than popular alternative measures, suggesting that CFOs are very confident in their opinions (i.e., their individual distributions for the market risk premium are tight). We show that the recent performance of the S&P 500 has a significant effect on the shortterm expected risk premium as well as on forecasted volatility. Recent stock market performance also has a pronounced effect on CFO's ex ante skewness. In general, when recent stock market returns have been low, the one-year expected risk premium is low, its distribution has a relatively fat left tail, and expected market volatility is high. Our study has implications for asset pricing theory. We revisit the debate about the relation between expected excess returns and expected volatility. Our data provides us with a unique opportunity to test the relation between risk and expected return in a cross-section of individual respondents. While the evidence is mixed at the one-year horizon, we document a positive relation between risk and expected excess returns at the ten-year horizon. Our results support the idea that time horizon is important when examining the relation between risk and the risk premium. Finally, one of our surveys was delivered via FAX during the morning of September 10, 2001. Given the events of the next day, we are able to see how respondents assessments of risk and expected return change after a shock to systematic risk.
Pooling the individual responses, the standard deviation of the one-year premia is 4.27%. The standard deviation of the ten-year premia is 2.34%.
The paper is organized as follows. The second section details the methodology and the sampling procedure. The results are presented in the third section. An analysis conditional on firm characteristics is also outlined in the third section. Some concluding remarks are offered in the final section.
2. Methodology 2.1 Design The quarterly survey project is a joint effort with Financial Executives International (FEI). FEI has approximately 14,000 members that hold policy-making positions as CFOs, Treasurers, and Controllers at 8,000 companies throughout the U.S. and Canada. Every quarter, Duke University and FEI poll these financial officers with a short survey on important topical issues (Graham and Harvey, 1996-2003). The usual response rate for the quarterly survey is 5%-8%. Fig. 2 details the exact questions that we currently ask regarding the equity premium and some firm characteristics that we collect every survey.

2.2 Delivery and response In the early years of the survey, FEI faxed approximately 4,000 surveys to a sample of their membership. The executives returned their completed surveys by fax to the third-party data vendor, Office Remedies Inc. Using a third party ensures that the survey responses are anonymous, although we knew a number of firm-specific characteristics, as discussed below. FEI changed the delivery mechanism to the Internet as of the December 4, 2001 survey. Among other things, we now collect the respondents IP addresses (though not their identity or company) and are able examine consistency of responses across different surveys. On the day of delivery, the survey contains information about the yield on the ten-year Treasury bond at the close of the previous business day, and the respondents are given approximately four business days to return the survey. Each survey is time stamped upon receipt. This allows us to examine if recent equity returns impact the CFOs responses when
they fill out the survey. Usually, two-thirds of the surveys are returned within two business days. We also conducted a survey at the North Carolina CFO Symposium on August 22, 2000. In this case, we were able to obtain a response from nearly every executive in the room. By comparing these responses with the other quarterly survey responses, we are able to examine whether the response rate on the quarterly survey affects the CFO predictions about the equity market risk premium. (For example, perhaps predominantly optimists respond to the quarterly survey.) We find that the responses for the North Carolina CFO survey are consistent with those from the quarterly survey indicating that there is no obvious nonresponse bias.4
2.3 The survey instrument and summary statistics The risk premium questions are a subset of a larger set of questions in the Duke-FEI quarterly survey of CFOs. Copies of the surveys can be found on the Internet. We ask respondents for their one- and ten-year forecasts of the S&P500 given the current ten-year Treasury bond rate [see Fig. 2]. The CFOs also complete the following statement: During the next year, there is a 1-in-10 chance that the actual [S&P 500] return will be greater than ___% as well as the analogous question for the lower equity return. This allows us to examine each respondents distribution of expected returns. We can recover a measure of volatility as well as skewness from each individuals responses. While the survey is anonymous, we ask questions about seven firm characteristics: industry, sales revenue, number of employees, headquarters location, ownership (public or private), proportion of foreign sales and whether they pay dividends. Fig. 3 summarizes our sample information for three of these characteristics.

There are three other reasons why we are not overly concerned with the response rate. First, our response rate is within the range that is documented in many other survey studies. Second, in Graham and Harvey (2001), we do standard tests for non-response biases (which involve comparing the results to those that fill out the survey early to ones that fill it out late) and find no evidence of bias. Third, in Brav, Graham, Harvey and Michaely (2003), we perform a captured sample survey at a national FEI conference in addition to an Internet survey. The responses for the captured survey (where nearly everyone responded) are qualitatively identical to those for the Internet survey (where 8% responded), indicating that response bias did not significantly affect the results.
3. The market risk premium and volatility 3.1 Risk premium For the ex ante one and ten-year risk premia, we calculate a histogram for each quarters survey.5 The complete set of histograms is available on the Internet. Fig. 4 focuses on two quarters histograms: March 12, 2001 and March 11, 2002. These two quarters are chosen on the basis of past equity market performance. The 2001 survey followed a substantial downward move in the equity market (the S&P 500 lost 12% in the month prior to the survey). The 2002 survey followed a substantial upward move in the market (the S&P 500 gained 6% in the month prior to the survey). The one-year premium is presented in panel A of Fig. 4. The mean premium from the 2001 survey following poor market performance is 1.3%. The mean premium from the 2002 survey following positive market performance is 4.8% (a difference of 3.5% from 2001 to 2002). The one-year premium histograms suggest that respondents assessments of future returns are potentially influenced by past returns. In panel B of Fig. 4, the ten-year risk premium is more stable. The survey that followed the negative market episode suggests a mean premium of 4.4% whereas the survey following positive returns had a mean premium of 2.9% (a difference of -1.5% from 2001 to 2002). This preliminary look at the data suggests that the longer-term expectations are influenced by different factors. The ten-year expectations are consistent with the idea that if the market has risen (fallen), expected returns are lower (higher) the notion of mean reversion in expectations. Of course, other economic conditions may have been different at these two dates. We explore this possibility below.
3.2 Past returns and the risk premium Fig. 4 examines only two quarters. In Fig. 5, we use mean premiums from each of the quarterly surveys to examine whether the past market performance affects the average risk

We trim the data by removing the two highest and two lowest forecasted returns. This is roughly equivalent to a one percent trim. The untrimmed results are available on request.
premium. There is an open question as to the definition of past. Andreassen (1990), Andreassen and Kraus (1990) and Klibanoff, Lamont and Wizman (1998) address the issue of the salience of information in forming investors reactions to news. Hence, we look at multiple definitions of past returns. However, our analysis does not address the possibility that respondents vary their look-back period in forming their expectations. Fig. 5 presents the analysis of the one-year premium relative to four different measures of lagged excess returns: the one-week, one-month, two month, and one-quarter past return on the S&P 500. In each graph, there is a positive relation between the past returns and the expected returns. For the one and two month lag returns, 61% and 75% of the variation in the one-year premium can be explained by lagged returns. In contrast, there is a modest negative relation between the past returns and the ten-year risk premium (graphs available on request). While CFOs assessments of the one-year risk premium appear strongly positively influenced by recent returns, the expectations of ten-year premium appear modestly negatively influenced by past returns. Table 2 presents regressions that use all of the data (rather than the means of the surveys which are presented in Fig. 5 for the one-year premia). We estimate weighted least squares regressions, where the weights are the inverse of each quarters standard deviation. Consistent with the graphical analysis, recent realized returns significantly positively impact the respondents forecasts of the one-year premium using each of the four measures of past returns.6 The regression for the ten-year premium shows a significant (at the 5% level) negative relation only with the previous months return (not the other three measures of lagged returns). Even using the one-month lagged return, the economic influence is much smaller for the ten-year premium. For example, a 10% return in the previous month increases the one-year premium by 211 basis points. We also present the OLS estimates. The inferences are consistent across the OLS and WLS estimates.
This is also consistent with Welch (2000, 2001) who shows in a survey of economists that the mean one-year premium in 1998 was 5.8% (near the peak of the stock market) and only 3.4% in 2001 (after a sizable retreat in the market).

A quadratic function explains 58% of the variance.
between ex post standard deviation and our measure of ex ante standard deviation. Finally, we also look at past values of the VIX and test whether there is information in the VIX that is relevant for future ex ante volatility. We find weak positive relation between past values of VIX and disagreement.
3.6 Asymmetry in distributions We use the information in the survey to form a simple measure of skewness in each respondents distribution. We look at the difference between each individuals 90% tail and the mean forecast and the mean minus the 10% tail. Hence, if the respondent's forecast of the risk premium is 6% and the tails are -8% and +11%, then the distribution is negatively skewed with a value of -9% (=5%-14%). As with the usual measure of skewness, we cube this quantity and standardize by dividing by the cube of the individual standard deviation. Panel B of Fig. 7 presents histograms of this asymmetry measure for the same 2001 and 2002 surveys featured before. In both of these surveys, the average asymmetry is negative. Indeed, we see negative average asymmetry in all of the quarterly surveys. However, the histograms suggest more negative asymmetry after negative returns.10 Following our analysis of disagreement, we can also examine the cross-sectional skewness of the distribution of risk premia, every quarter. For example, in panel A of Fig. 4, the crosssectional skewness of risk premia for the March 12, 2001 survey is 0.42. Fig. 9 finds a significant positive relation between recent returns and this measure of skewness for one-year forecasts. There is no significant relation between past returns and cross-sectional skewness at the ten-year horizon.
3.7 Asset pricing implications Given that we have new measures of expected (rather than realized) returns and ex ante volatility, we can say something about the link between expected returns and expected variance a fundamental component of asset pricing theory. We have two unique angles.
A complete set of histograms is available on the Internet.
First, we are able to test this relation in a cross-section of individual respondents. Second, previous research exclusively relies on statistical measures of both the mean and variance based on historical data whereas we directly observe a measure of expectations. The literature is evenly split on whether there is a positive relation or a negative relation between the mean and volatility. For example, using a GARCH framework, French, Schwert and Stambaugh (1987) and Campbell and Hentschel (1992) estimate a positive relation while Campbell (1987), Breen, Glosten, and Jagannathan (1989), Nelson (1991) and Glosten, Jagannathan and Runkle (1993) find a negative relation between the realized mean and volatility. Scruggs (1998) argues that Glosten, Jagannathan and Runkle results hide a positive partial relation once you control for other factors. Asset pricing theory implies a positive partial, not simple, relation. Harrison and Zhang (1999) use a semi-nonparametric method and find a positive relation. Brandt and Kang (2003) use a latent VAR technique and document a strong negative correlation. Goyal and Santa-Clara (2003) find a positive relation between the average on individual stock variances and expected returns. Ghysels, Santa-Clara and Valkanov (2003) combine daily data with monthly data and find a significantly positive relation. Harvey (2001) uses a combination of nonparametric density estimation and GARCH models and finds that the relation depends on the instrumental variables chosen. Both Harvey (2001) and Brandt and Kang (2003) document a distinct counter-cyclical variation in the ratio of mean to volatility.11 Evidence on the relation between risk and expected returns has important economic implications. For example, Pstor and Stambaugh (2001) have recently presented a Bayesian analysis of long-horizon risk premia. They find that the risk premium in the 1990s is 4.8% which is roughly consistent with our results. However, a critical component of their analysis involves tying their prior to a positive relation between the premium and volatility. If Pstor and Stambaugh instead chose a diffuse prior relation between volatility and the premium,

We focus on the relation between variance and risk premium. There is a considerable literature that investigates the asset pricing implications of heterogeneous beliefs. See Abel (1989), Basak (2000), Constantinides (1982), Constantinides and Duffie (1996), Detemple and Murthy (1994), Heaton and Lucas (1995), Williams (1977), and Zapatero (1998). Diether, Malloy and Scherbina (2002) and Anderson, Ghysels and Juergens (2003) use the dispersion of analysts forecast to proxy for disagreement.
their estimate of the risk premium in June 1999 rises dramatically to 27.7%.12 Our results below support the prior they impose. First, we examine aggregated data. Panels A, C, and E of Fig. 10 show that there is a negative relation between the one-year mean premium and disagreement, individual variance, and total variance. However, in panels B, D, and F, we find that the opposite is true for the ten-year premium the relation is positive. It is also interesting to note that the bulk of the total variance comes from the average individual variance not the disagreement. The graphical analysis only uses one observation per quarter. Given that we have individual estimates of the risk premium, variance and skewness, it is possible to examine whether there is a positive trade-off between expected return and risk in the cross-section of respondents. Table 4 provides quarter-by-quarter estimates of this relation. Panel A examines the relation between risk and the one-year premium. In 10 of the 13 quarters, this relation is positive. The average slope coefficient 0.33 with a Fama-MacBeth tratio of 1.8. When a skewness term is included, it has a negative sign in 11 of 13 quarters and is significantly negative when aggregated. Asset pricing theory suggests that higher positive skewness would be associated with lower expected returns. Given the possibility that the regressions could be influenced by extreme observations, we re-estimate the relation with various levels of trimming. The inference is the same. A weak positive relation between expected returns and variance and a significant negative relation with skewness. However, the intercepts in all of the regressions are significantly positive, which provides evidence against the specification. Panel B of Table 4 focuses on the ten-year premium. In the six quarters of data that are available, there is a positive relation between expected returns and individual variances in each of the quarters. The average slope coefficient is 2.33 with a t-ratio of 2.7. The slope is often interpreted as a measure of relative risk aversion and a value of 2.33 appears reasonable. When skewness is added to the specification, the significance and magnitude of the variance

b. During the next year, I expect the S&P 500 return will be: Worst Case: There is a 1-in-10 chance the actual return will be less than: % a. Industry Retail/Wholesale Mining/Construction Manufacturing Transportation/Energy Communications/Media b. Sales Revenue Less than $25 million $25-99 million $100-499 million Tech [Software/Biotech] Banking/Finance/Insurance Service/Consulting Other Best Guess: I expect the return to be: % Best Case: There is a 1-in-10 chance the actual return will be greater than: %
11. Please check one from each category that best describes your company:
Fig. 2. Risk premium and firm characteristic questions from March 2003 survey
$500-999 million $1-4.9 billion Over $5 billion c. Number of Employees Fewer than 100 100-499 500-999 1000-2499 d. Headquarters Northeast Mountain Midwest South Central South Atlantic Pacific e. Ownership Public, NYSE Public, NASDAQ/AMEX Private f. Foreign Sales 0% 1-24% 25-50% Over 50% g. Dividend Payments Yes No

Click here to finish

2500-4999 5000-9999 Over 10,000

A. Industry

45% 40%

B. Revenue ($ millions)

30% 30% 20% 15% 10%
0% Retail/ Wholesale Mining/ Construct Manufacture Transport/ Energy Commu./ Media Tech (Software/ Bio Tech) Banking/ Finance/ Insurance Other
0% < 25 25-99 100-499 500-999 1000-4900 > 5000

C. Employment

0% < 100 100-499 500-999 1000-2499 2500-4999 5000-9999 > 10000
Fig. 3. Sample firm characteristics. Based on respondents to the FEI/Duke CFO Outlook Surveys from June 2000 to June 2003. While the survey is anonymous, information on seven firm characteristics is collected. We report industry, sales revenue and employment. Other characteristics, such as headquarters location, ownership, percentage of foreign sales, and whether the firm pays dividends are available on request. The exact questions are listed in Fig. 2.

A. One-year risk premium

35 Percentage of responses 20 March 12, 0 <-20 -20 -18 -16 -14 -12 -10 -8 -6 -4 -18 more March 11, 2002

Average premium 1.33% (2001), 4.49% (2002). Median premium 0.7% (2001), 3.4% (2002). Risk free 4.3% (2001), 2.6% (2002). Standard deviation 5.43% (2001), 3.26% (2002). Skewness -0.42 (2001), 0.66 (2002). Responses 124 (2001), 225 (2002). Previous month's S&P 500 excess return 11.77% (2001), 4.92% (2002).

B. Ten-year risk premium

35 Percentage of responses 0
--<20 ----m or e -8 -6 -4 -18
March 12, 2001 March 11, 2002
Average premium 4.41% (2001), 2.90% (2002). Median premium 4.1% (2001), 2.7% (2002). Risk free 4.9% (2001), 5.3% (2002). Standard deviation 2.52% (2001), 2.01% (2002). Skewness 0.28 (2001), 0.06 (2002). Responses 136 (2001), 229 (2002). Previous month's S&P 500 excess return 11.77% (2001), 4.92% (2002).
Fig. 4. Distributions of the one-year and ten-year risk premia. Based on responses to the FEI/Duke CFO Outlook Surveys in March 2001 and March 2002. Histograms for the other surveys are available on the Internet. We also report summary statistics of these two survey's cross-sectional distributions. Standard deviation is the standard deviation of the individual risk premium forecasts. We refer to this measure as the disagreement. Skewness is the skewness of the individual risk premium forecasts. We refer to this as the cross-sectional skewness. The number of responses on the one-year and ten-year premium questions may differ because individual respondents may choose not to answer some questions.
7 Mean one-year premium 0

-6 -4 -10

6 Mean one-year premium Excess S&P 500 return in previous week y = 0.149x + 3.4382 R2 = 0.115
y = 0.2021x + 3.5301 R2 = 0.6132
Excess S&P 500 return in previous month
7 Mean one-year premium Mean one-year premium 0 -15 -10 -15 Excess S&P 500 return in previous two months y = 0.1666x + 3.4556 R2 = 0.7518
-20 -15 -10 -Excess S&P 500 return in previous quarter y = 0.1141x + 3.7353 R2 = 0.5049
Fig. 5. The influence of past market performance on expected one-year risk premia. Based on responses to the 13 FEI/Duke CFO Outlook Surveys from June 2000 to June 2003. For each graph symbol, the vertical axis represents the mean percentage premium across all respondents in one particular quarter. The horizontal axis is the excess S&P 500 return in the previous week, month, two months and one quarter, measured up to the day before the survey is released. The arrow denotes the most recent survey observation.

y = -0.0338x + 6.4513

Mean one-year premium

R2 = 0.0407

-y = -0.1226x + 3.6448 R2 = 0.0187
University of Michigan Index of Consumer Confidence C.
Lagged four quarter real GDP growth D.

Mean ten-year premium

y = 0.0286x + 1.R2 = 0.2511
-3 y = 0.2239x + 3.3418 R2 = 0.5 6
University of Michigan Index of Consumer Confidence
Lagged four quarter real GDP growth
Fig. 6. Expected and current economic conditions and one and ten-year risk premia. Based on responses to the 13 FEI/Duke CFO Outlook Surveys from June 2000 to June 2003. For each graph symbol, the vertical axis represents the mean percentage premium across all respondents in one particular quarter. The horizontal axis is either the most recent value of the University of Michigan Index of Consumer Confidence or the previous four quarters' real GDP growth. The arrow denotes the most recent survey observation.
A. Respondents' one-year risk premium distribution volatility
Percentage of respondents 0 <20 more Volatility Average 6.75 (2001), 4.83 (2002); median 5.66 (2001), 3.77 (2002); standard deviation 3.61 (2001), 3.25 (2002); one month prior VIX 35.29 (2001), 22.02 (2002). Previous month's S&P excess return -11.77% (2001), 4.92% (2002). March 12, 2001 March 11, 2002
B. Respondents' one-year risk premium skewness
Percentage of responses more Skewness Average -0.814 (2001), -0.646 (2002); median -0.260 (2001), -0.054 (2002); standard deviation 1.613 (2001), 1.473 (2002). Previous month's S&P excess return -11.77% (2001), 4.92% (2002). <-6 -4 -2
Fig. 7. Volatility and skewness of repondents' risk premium distributions. Based on responses to the FEI/Duke CFO Outlook Surveys in March 2001 and March 2002. Histograms for the other surveys are available on the Internet. For each respondent, we calculate the standard deviation of their individual one-year risk premium distribution based on Davidson and Cooper (1976). We also report a measure of the skewness of their individual distribution. We also report summary statistics of these two survey's cross-sectional distributions. In panel A, standard deviation represents the standard deviation of the respondent's individual volatilities. In panel B, it represents the standard deviation of the individual skewness measures. We also report the one-month prior implied volatility on the S&P 100 index option (VIX) as well as one-month prior S&P 500 prior returns.
A. Disagreement over the one-year premium and past returns
7 Disagreement over the one-year premium 0 -15
y = 0.0195x2 + 0.0293x + 3.3967 R2 = 0.5776
y = -0.0565x + 3.9647 R2 = 0.1445
Past one-month excess S&P 500 return
B. Disagreement over the ten-year premium and past returns

3.78 91.21 -0.009 -1.67 0.001 3135
3.76 88.48 -0.006 -1.42 0.000 3135
3.80 47.71 0.166 6.27 0.013 2865
3.75 49.02 0.226 15.81 0.080 2865
3.62 47.45 0.170 17.71 0.098 2865
4.03 51.04 0.120 15.20 0.074 2865
3.79 89.88 -0.005 -0.37 0.000 3135
3.79 90.77 -0.023 -2.96 0.003 3135
3.80 90.74 -0.008 -1.45 0.000 3135
3.79 87.75 -0.004 -0.93 0.000 3135
Table 3 Economic determinants of the risk premium Based on the responses from the FEI/Duke CFO Outlook Surveys from June 2000 to June 2003. The dependent variable is each respondent's assessment of the risk premium. The independent variable is either the most recent value of the University of Michigan Index of Consumer Confidence or the previous four quarters' real GDP growth. Panel A reports weighted least squares regressions where the responses in each quarter are weighted by the standard deviation of the risk premium forecasts in that quarter. Panel B reports ordinary least squares regressions. The number of observations from the one-year and tenyear regressions differs because some respondents choose not to fill out some questions. A. WLS
One-year premium Consumer Previous year real Confidence GDP growth 10-year premium Consumer Previous year real Confidence GDP growth
Intercept in % T ratio Economic indicator T ratio Adj. R2 Observations B: OLS Intercept in % T ratio Economic indicator T ratio Adj. R2 Observations
7.61 8.87 -0.043 -4.53 0.007 2865
4.07 29.70 -0.151 -2.96 0.003 2865
1.53 3.17 0.025 4.66 0.007 3135

10-year premium

3.35 49.64 0.208 7.87 0.019 3135
7.81 8.49 -0.045 -4.42 0.006 2865
4.04 29.05 -0.132 -2.49 0.002 2865
1.28 2.69 0.028 5.34 0.009 3135
3.33 47.16 0.219 8.15 0.021 3135
Table 4 Quarterly estimates of the relation between the expected risk premium and risk In each quarter, two regressions are estimated. The first is the individual risk premiums on the individual variance estimates. In the second regression, the specification is augmented with the individual skewness estimate. We report the intercept (which should be zero according to asset pricing theory) and the slope estimates. The t-ratio reported in the average column is the Fama-MacBeth t-ratio for the time-series of slopes. The smaller number of survey quarters for the 10-year risk premium reflects the fact that the variances have only been available for the past six surveys. A. One-year risk premium Quarter: 00q3 Intercept 0.023 T ratio 5.45 Individual variance T ratio Adj. R Observations

00q4 0.029 11.58 0.185 1.21 0.003 158
01q1 0.025 6.96 0.240 0.70 -0.003 195
01q2 0.014 1.96 -0.196 -0.23 -0.008 118
01q3 0.024 5.76 0.244 0.41 -0.006 142
01q4 0.024 4.00 -0.915 -1.62 0.012 133
02q1 0.044 10.29 0.484 1.82 0.012 185
02q2 0.042 13.92 1.481 3.00 0.046 169
02q3 0.029 13.72 0.814 2.63 0.019 303
02q4 0.030 12.91 0.889 3.25 0.027 344
03q1 0.051 19.73 0.647 1.89 0.010 267
03q2 0.031 9.02 0.121 0.38 -0.005 177
03q3 Average 0.062 0.033 22.33 9.02 0.772 3.21 0.0.323 1.82

-0.564 -1.49 0.008 159

Intercept T ratio Individual variance T ratio Individual skewness T ratio Adj. R Observations
0.026 6.02 -0.790 -2.08 -0.0041 -2.77 0.048 159
0.030 11.74 0.170 1.12 -0.0015 -1.57 0.012 158
0.026 7.24 0.103 0.30 -0.0019 -1.99 0.013 195
0.009 1.22 -0.721 -0.88 -0.0103 -3.30 0.071 118

0.028 6.67 -0.449 -0.74

0.028 4.85 -1.413 -2.56
0.044 10.64 0.293 1.13 -0.0056 -3.92 0.084 185
0.042 13.76 1.601 3.12 0.0015 0.86 0.044 169
0.029 12.91 0.796 2.55 -0.0005 -0.44 0.017 303
0.030 12.72 0.914 3.25 0.0004 0.39 0.025 344
0.050 19.19 0.576 1.63 -0.0011 -0.80 0.008 267
0.029 8.11 0.060 0.19 -0.0019 -1.59 0.004 177
0.061 21.76 0.732 3.02 -0.0018 -1.38 0.029 344
0.033 9.04 0.144 0.63 -0.003 -3.12
-0.0046 -0.0102 -3.54 -3.85 0.0.106 133
Table 4 (continued) B. Ten-year risk premium Quarter: 02q2 02q3 02q4 03q1 03q2 03q3 Average Intercept 0.029 0.029 0.037 0.029 0.032 0.038 0.032 T ratio 17.10 16.96 26.74 16.52 15.12 26.83 18.85 Individual variance T ratio Adj. R Observations

0.256 0.34 -0.004 207

1.831 3.19 0.028 315

2.410 4.82 0.059 352

6.063 5.97 0.113 272

2.971 3.35 0.055 176

0.464 1.38 0.003 352

2.332 2.70

0.029 16.89 0.192 0.25 -0.0009 -0.79 -0.006 207
0.029 16.91 1.863 3.07 0.0002 0.17 0.025 315
0.037 27.05 2.773 5.39 0.0027 2.66 0.076 352
0.029 16.50 6.166 5.90 0.0005 0.43 0.111 272

0.032 14.94 2.994 3.35

0.038 25.36 0.536 1.51