Household Investor Expectations of Risk and
Return on Stocks:
Are Sharpe Ratios Countercyclical?
Gene Amromin and Steven Sharpe
Chicago Fed and the Federal Reserve Board
January 2, 2009
paper & remarks reflect our own views, and not necessarily those of
the Board of Governors or the Federal Reserve System
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Motivation 1: What drives cyclicality of returns
 Huge literature on predictability of stock returns
 Grown from findings that macro variables “predict” equity returns/premium
 Fama and French (1989) – D/P, other “business cycle” factors
 Lettau and Ludvigson (2001) – CAY, consumption-wealth ratio, evokes cycle
story:
• “When excess returns are expected to be higher, forward-looking investors will
react by… allowing consumption to rise above its common trend w/ wealth”
• Rational story, still leaves question, why expected (required) returns vary
Lead to…
 New theories of household risky asset demand (Cochrane 2005)
 Time-varying risk aversion: Campbell and Cochrane (1999)
 Time-varying risk: Constantinides and Duffie (1996)
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Motivation 1 (cont)
Which has led to…
 New studies of household-level behavior
 Household portfolio dynamics -- Brunnermeier and Nagel (2008)
 Evidence on habit formation -- Dynan (2000) Ravina (2005)
So we step back, consider…
 What could we learn if we could ask relevant households about
their beliefs?
 How do their expected equity returns vary with perceptions of business
cycle? (especially the most influential--the more sophisticated or wealthy)
 How do their perceptions of risks in equity returns vary with the cycle?
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Motivation 2: Broader Q: What influences investor beliefs?
 Controlling for perceptions of economy, how do perceptions of
RETURN & RISK vary:
 Demographic characteristics
 Education
 Past experience
 Measured in cross section, but also potential time series interp.
 The relevance of survey-reported perceptions relevant:
 Related to respondent portfolio decisions?
 Wish granted: In 1999, devised insert to Michigan survey of
consumer sentiment
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Previous studies: Survey beliefs & stock market
 Individual investor expectations for returns
 Fisher and Statman, 2002 Vissing-Jorgensen, 2003;
• UBS-Gallup Survey: Persistence of past returns; Effect of wealth
 Dominitz and Manski, 2003, 2005 (Michigan survey)
• “Probability typical mutual fund will increase” (related to expected return, also risk)
• Document effects of expected business conditions, cross-sectional heterogeneity,
extrapolation; gender & education effects
 CFO expectations: Graham & Harvey (2003); G&H with Ben-David
(2007)
• Expected Returns & Risk: ST forecasts show persistence, no risk-return relation
• Evidence of overconfidence: tighter return distribution --> aggressive corp. policies
 Studies of Consumer Confidence Index (Michigan) & stock returns
 Qui and Welch (2006) – “sentiment” & actual returns
 Lemmon and Portniaguina (2006) – “sentiment” vs. fundamentals
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Road map & Summary of results
 Expected returns
 Measures contradict inferences of predictability studies (D/Y, CAY)
• Gallup-UBS survey data
 Expected returns are procyclical
• positively related to expected business conditions
• expected by self and by “consensus” (so not expected news)
 Determinants of perceived risk
 Uncertainty varies inversely with expected economic conditions;
• Given above, implies procyclical Sharpe ratios
 Individual characteristics, heuristics have strong affect perceived risk
 Portfolio allocations consistent with beliefs?
 Reported portfolio equity shares (+) in returns and (−) in risk
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Data – Michigan Survey special supplement
 Criterion household needs to pass: Equity ≥ $5000
 35%-45% of respondents
 150-250 respondents per survey month
 22 irregularly spaced surveys, Sept. 2000 – Oct. 2005
 Data quality filters
 Response to all 3 questions on ER
 Survey-giver’s codes indicating low quality responses
 Analysis in appendix
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Expected stock returns, survey means
Gallup/UBS 12-month ahead (own) vs. Michigan 3-yr (mkt)
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Gallup/UBS 12-mo ER vs. CAY

(+) coef. in realized return regressions (so L-L are on to something, but
their interpretation contradicts that of actual consumers)
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Gallup/UBS 12-mo. ER vs. log(D/P)
 Literature: Positive coef. in regression using realized returns, low
R-squares
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Next step: Relating Expected Return (Mich.
survey) to expected economic conditions
 BUS5. Looking ahead, which is more likely -Business
continuous good times during the next 5 years, or
cycle
periods of widespread unemployment or depression,
or what? [coded -2,-1,0,1,2]
Nearterm
“news”
 BEXP. A year from now, do you expect that in the
country as a whole, business conditions will be better,
or worse than at present, or about the same?
 What do you think chances are your family income
will increase by more than the rate of inflation in the
next five years or so?
Own
Prospects
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Expected Return Regressions (3-yr ER)
Regressors
Good times, next 5 yrs [2, -2]
Coefficient (t-stat)
0.28 (5.8)
Good times-survey mean
1.52 (8.2)
Good times-deviation from mean
0.23 (4.6)
Better Conditions-12 mos.
+ (3.1)
+ (2.9)
Chance own income > inflation
+ (4.3)
+ (4.0)
Past S&P return (time-series)
+ (10.2)
+ (9.3)
Gender=male
+ (2.7)
+ (2.9)

(1) Procyclical ER; Past return (+); gender effect

(2) Consensus effect even stronger

Findings identical for half of sample w/ largest equity holdings
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Measuring perceived risk (volatility)
The survey asks for confidence interval around ER:
“… what is the chance that the average return over the next 10 to 20
years will be within 2 percentage points of your [expected return]…?”
Define uncertainty as inverse: 100 – probability in interval
with distributional assumption, can map uncertainty  σ (std. dev.)
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Regressors to explain Perceived Risk
 Measures of expected economic conditions
 Confidence in own ability to predict (uncertainty)
 Knowledge: Higher education / years of investment experience
 Gender: male (Beyer, 1990)
 Representativeness (Tversky & Kahneman, 1982)
 Outcomes “representative” of available evidence may seem more
likely
 If event (Return being close to ER) consistent with “salient” available
evidence (past recalled S&P returns), put higher probability on event
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Expected Risk Regressions
Dependent Variable: Uncertainty = Prob |R − Re|>2%
(2)
all obs.
(2069)
(3)
Prob≠50
(1413)
 Specification (3)
excludes 50-50 answers
Good times, next 5
yrs
-0.70
(2.4)
-1.03
(3.0)
Better conditions
next 12 months
-0.14
(0.3)
-0.25
(0.4)
 Better conditions/times
reduces perceived risk
Chance own income
> inflation
-0.10
(6.5)
-0.12
(5.3)
Abs [Expected R –
Recalled R]
0.61
(9.5)
0.94
(6.5)
Male
-4.27
(5.1)
-5.69
(4.6)
College Degree
-6.69
(6.0)
-9.06
(4.8)
Pseudo R-squared
0.106
0.143
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 Better own prospects
reduce market risk
 Representativeness
 10% discrepancy raises
uncertainty 6.1%
 Confidence, knowledge
lowers uncertainty
Can reported ER and σ explain actual behavior?
 Are expectations summarized earlier relevant to
portfolio decisions?
 Survey question: Fraction of financial wealth in stocks
five discrete buckets {<10, 10-25, 25-50, 50-75, >75}
 Classic Samuelson portfolio (CRRA preferences)
 Portfolio fraction = (R i - rf) / γ i σi 2
 For regression: log (fraction) = log (R − rf) − log σ2 − log γ
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Portfolio choice regressions: Samuelson model
Dependent Variable: Log portfolio fraction in stocks
(Table 7)
Log expected excess returns
0.04 (3.4)
0.15 (2.9)
Log expected returns
Log expected volatility
Adjusted R-squared
-0.09 (7.0)
-0.09 (7.3)
0.042
0.046
 Expected return, risk significant; signs consistent with theory
 Coefficients small compared to theory
 Not shown: sluggish adjustment (yrs invest experience matters)
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Conclusions
 Summary of results
 Expected returns vary (+) with expected macro conditions
(procyclical)
 Uncertainty (risk) varies (-) with expected macro conditions
 Uncertainty varies (-) with individual’s knowledge, self-confidence,
“Representativeness” of prospective period
 Investor portfolios reflect these beliefs
 Results not just for dummies, investors with small portfolios
 Implications/interpretations
 ER appears to covary negatively with usual conditioning vars
 Sharpe ratios are procyclical – HH investors do not appear to
expect a premium in bad times, hold less equity
 Other types of investors need higher returns to “take up slack”
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Conclusions (cont’d)
 Implications for equilibrium asset prices?
 Equity valuations lower during recession – and subsequent returns
higher – because HH investors overly pessimistic (extrapolating too
much)
 Individual investors presumably ‘expropriated’ by smart
(institutional) investors
 But presumably rational investors do not entirely offset systematic
irrational trading by HH investors
• Limits to arbitrage
• Active “smart” traders profit by “riding the bubble” – positive feedback trading
• Observe countercyclical returns – Given these facts, what is simplest explanation?
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The End
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