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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

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household investor expectations of risk and return on stocks are sharpe ratios countercyclical

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

1

motivation 1 what drives cyclicality of returns
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)

2

motivation 1 cont
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?

3

motivation 2 broader q what influences investor beliefs
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

4

previous studies survey beliefs stock market
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

5

road map summary of results
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

6

data michigan survey special supplement
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

7

gallup ubs 12 mo er vs cay
Gallup/UBS 12-mo ERvs.CAY
  • (+) coef. in realized return regressions (so L-L are on to something, but their interpretation contradicts that of actual consumers)

9

gallup ubs 12 mo er vs log d p
Gallup/UBS 12-mo. ER vs. log(D/P)
  • Literature: Positive coef. in regression using realized returns, low R-squares

10

next step relating expected return mich survey to expected economic conditions
Next step: Relating Expected Return (Mich. survey) to expected economic conditions
  • BUS5. Looking ahead, which is more likely -- continuous good timesduring the next 5 years, or periods of widespread unemployment or depression, or what? [coded -2,-1,0,1,2]
  • 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?

Business cycle

Near-term “news”

Own Prospects

11

expected return regressions 3 yr er
Expected ReturnRegressions (3-yr ER)
  • (1) Procyclical ER; Past return (+); gender effect
  • (2) Consensus effect even stronger
  • Findings identical for half of sample w/ largest equity holdings

Regressors

Coefficient (t-stat)

Good times, next 5 yrs [2, -2]

0.28 (5.8)

1.52 (8.2)

Good times-survey mean

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)

12

measuring perceived risk volatility
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.)

13

regressors to explain perceived risk
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

14

expected risk regressions dependent variable uncertainty prob r r e 2
Expected Risk RegressionsDependent Variable: Uncertainty = Prob |R − Re|>2%
  • Specification (3) excludes 50-50 answers
  • Better conditions/times reduces perceived risk
  • Better own prospects reduce market risk
  • Representativeness
    • 10% discrepancy raises uncertainty 6.1%
  • Confidence, knowledge lowers uncertainty

(2) all obs. (2069)

(3) Prob≠50 (1413)

Good times, next 5 yrs

-0.70 (2.4)

-1.03 (3.0)

-0.25 (0.4)

Better conditions next 12 months

-0.14 (0.3)

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

15

can reported er and explain actual behavior
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

16

portfolio choice regressions samuelson model
Portfolio choice regressions: Samuelson model
  • Expected return, risk significant; signs consistent with theory
  • Coefficients small compared to theory
  • Not shown: sluggish adjustment (yrs invest experience matters)

17

conclusions
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”

18

conclusions cont d
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?

19