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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

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Household Investor Expectations of Risk and Return on Stocks: Are Sharpe Ratios Countercyclical?

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  1. 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

  2. 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

  3. 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

  4. 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

  5. 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

  6. 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

  7. 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

  8. Expected stock returns, survey means Gallup/UBS 12-month ahead (own)vs. Michigan 3-yr(mkt) 8

  9. 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

  10. Gallup/UBS 12-mo. ER vs. log(D/P) • Literature: Positive coef. in regression using realized returns, low R-squares 10

  11. 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

  12. 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

  13. 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

  14. 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

  15. 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

  16. 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

  17. 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

  18. 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

  19. 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

  20. The End 20

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