RISK AVERSION AND PORTFOLIO CHOICE NASM 2008 Conference

RISK AVERSION AND PORTFOLIO CHOICE NASM 2008 Conference June 21 2008 • Alessandro Bucciol University of Padua, Italy • Raffaele Miniaci University of Brescia, Italy

GOAL • Estimate the individual coefficient of relative risk aversion (RRA) from observations on household portfolios • Several works already do this (Cohn et al. , 1975; Friend and Blume, 1975; Mc. Inish, 1982; Siegel and Hoban, 1982; Morin and Suarez, 1983; Riley and Chow, 1992; …) § We include both financial and real assets in the definition of portfolio § We incorporate constraints on portfolio weights § We compare observed and mean-variance efficient portfolios § Our RRA estimate minimizes the monetary loss incurred with sub-optimal portfolio allocations June 21 2008 NASM 2008 Conference 2

THE FRAMEWORK • One risk free asset with constant return • n risky assets § Expected excess returns and covariance matrix • Expected utility function with a portfolio • For a given RRA, the optimal portfolio allocation maximizes the expected utility function conditional to the constraints June 21 2008 NASM 2008 Conference 3

COMPENSATING VARIATION • For a given RRA, we determine the “wealth loss” as the fraction of initial wealth that is not needed to obtain with the optimal portfolio the same expected utility as with the observed portfolio : June 21 2008 NASM 2008 Conference 4

IMPLICIT RRA • We estimate the RRA coefficient by choosing the value that minimizes the wealth loss: • In general, the solution is implicit in the equation • If there are no constraints, June 21 2008 NASM 2008 Conference 5

DATA: HOUSEHOLD PORTFOLIOS • US Survey of Consumer Finances (SCF) § wave 2004 • Consider two definitions of portfolio § Financial: Deposits, Bonds, Stocks § Financial and real: Deposits, Bonds, Stocks, Real wealth • Drop households whose portfolio contains only riskfree deposits (infinite RRA in our model) § 13. 36% of the sample • Our final data set consists of 3, 633 observations on household socio-demographic and economic characteristics June 21 2008 NASM 2008 Conference 6

AGGREGATE PORTFOLIO COMPOSITION 9. 98% 20. 73% -5. 12% 28. 40% 24. 50% 50. 87% 70. 63% June 21 2008 NASM 2008 Conference 7

DATA: ASSET TIME SERIES • Risk free asset § 3 -month T-Bill yields • Financial asset (source: Datastream) § Merrill Lynch US Corp. & Govt. Master Index § MSCI USA Stock Index • Real asset (source: MIT-CRE) § MIT-CRE Transaction-based Index of Real Estate Investment Available only quarterly, since 1985 • We extend our time series length using the method in Stambaugh (1997) • Our time series consists of 100 observations on yearly returns covering quarterly the period 1980 -2004 June 21 2008 NASM 2008 Conference 8

HISTORICAL EXCESS RETURNS • Time series statistics Bonds Stocks Real Wealth Excess Return (%) 3. 7295 5. 3191 3. 4281 Standard Sharpe Deviation Ratio (%) 8. 7109 42. 8143 17. 6156 30. 1956 7. 4082 46. 2749 Tangency Portfolios 0. 7891 0. 2109 - 0. 3942 0. 0757 0. 5300 • Covariances and correlations (in italic) % Bonds Stocks Real Wealth 0. 7588 0. 4089 0. 1253 26. 6493 3. 1031 0. 3195 19. 4222 24. 4837 0. 5488 June 21 2008 NASM 2008 Conference 9

RESULTS • Based on financial portfolios, no constraints • Based on financial and real portfolios, with constraints • Constraints: § § Deposits ≥ 0 (short-selling prohibited) Stocks ≥ 0 (short-selling prohibited) Bonds ≥ -Real wealth (mortgage lower than real wealth) Real wealth ≥ Residential housing (residential wealth is illiquid) June 21 2008 NASM 2008 Conference 10

AGGREGATE RRA • The representative agent holds the aggregate portfolio Financial wealth Financial + real (total) wealth Unconstrained Constrained RRA 4. 7460 (2. 8469, 7. 8833) 7. 9193 2. 2200 (5. 6451, 14. 0299) (0. 0403, 9. 6379) Wealth loss (%) 0. 8936 (0. 0103, 3. 3890) 0. 8451 (0. 1719, 2. 6502) 0. 4489 (0. 1361, 1. 5222) § 95% confidence interval: from 1, 000 block-bootstrap simulations over time series realizations June 21 2008 NASM 2008 Conference 11

INDIVIDUAL RRA BY PORTFOLIO TYPE Median values Financial wealth Obs. Deposits =0 >0 Bonds = -real wealth > -real wealth Stocks =0 >0 Real wealth = primary residence > primary residence Binding constraints At least one No binding constraint Whole sample June 21 2008 Financial + real (total) wealth Uncon. Const. 51 3582 5. 4003 6. 0531 6. 7630 7. 0667 1. 7688 2. 6560 72 3561 3. 9676 6. 1697 4. 6594 7. 0656 1. 0280 2. 6598 1238 2395 11. 5720 5. 1078 7. 5624 6. 8653 4. 1703 2. 0057 2196 1437 - 6. 8530 7. 4109 2. 8931 2. 2038 2456 1177 3633 8. 3244 5. 2437 5. 9851 6. 9562 7. 2491 7. 0262 2. 8088 3. 8370 2. 6154 NASM 2008 Conference 12

INDIVIDUAL RRA HETEROGENEITY • Financial + Real portfolio (constrained) RRA June 21 2008 25 th perc. 50 th perc. 75 th perc. 1. 2253 2. 6154 11. 1858 NASM 2008 Conference 13

INDIVIDUAL RRA HETEROGENEITY • Financial + Real portfolio (unconstrained) RRA June 21 2008 25 th perc. 50 th perc. 75 th perc. 4. 4449 7. 0262 8. 6028 NASM 2008 Conference 14

INDIVIDUAL RRA HETEROGENEITY • Financial portfolio (unconstrained) RRA June 21 2008 25 th perc. 50 th perc. 75 th perc. 4. 3145 5. 9851 11. 1046 NASM 2008 Conference 15

OBSERVED PORTFOLIOS AND RRA Portfolio weights Obs. Deposits Bonds Stocks Constraint Real wealth Primary residence unconstrained financial and real (total) portfolio vs. unconstrained financial portfolio RRA lower 1482 0. 1486 -0. 4426 0. 0352 1. 2588 0. 9374 RRA higher 2151 0. 0783 0. 0859 0. 3210 0. 5148 0. 3719 constrained total portfolio vs. unconstrained financial portfolio RRA lower 2984 0. 0851 -0. 0911 0. 2729 0. 7331 0. 5233 RRA higher 644 0. 1652 0. 1473 0. 0838 0. 6036 0. 5215 constrained total portfolio vs. unconstrained total portfolio RRA lower 3071 0. 0859 -0. 0674 0. 2761 0. 7054 0. 4897 RRA higher 562 0. 1749 0. 0280 0. 0252 0. 7718 0. 7550 Whole sample 3781 0. 0971 -0. 0554 0. 2446 0. 7137 0. 5231 June 21 2008 NASM 2008 Conference 16

DETERMINANTS OF RISK AVERSION Financial wealth Method: OLS Dependent variable: log(RRA) Primary residence / Wealth (millions USD) -0. 0534*** 2 (Wealth (millions USD)) 0. 0002*** Age -0. 0467*** 2 Age /100 0. 0407*** Household size 0. 0372 Female 0. 0576 Married -0. 0237 Non-white 0. 0144 College graduate -0. 1736*** With financial advisor -0. 0078 Employee 0. 1222 Self-employed 0. 1106 Business industry: finance -0. 1733** Fair / poor health 0. 0581 Constant 3. 1876*** Minimum obs Mult. Imp. Minimum dof 2939 38. 7 Financial + real (total) wealth Unconstrained Constrained 0. 0196*** -0. 0001*** 0. 0085 0. 0033 -0. 0371 -0. 0148 0. 0053 -0. 0201 -0. 0423 0. 0250 -0. 1251** 0. 0612 0. 0759 -0. 0028 1. 3673*** -0. 0070** 0. 0176*** -0. 0001*** 0. 0104 0. 0012 -0. 0354* 0. 0119 0. 0009 0. 0076 -0. 0282 0. 0156 -0. 1257** 0. 0493 0. 0612 -0. 0050 1. 3386*** -0. 0357*** 0. 0001*** 0. 0090 0. 0169 0. 0140 0. 0518 -0. 0507 0. 0487 -0. 4135*** -0. 0962 -0. 1033 0. 0128 -0. 1018 0. 1368 0. 4335 -0. 0071** -0. 0378*** 0. 0001*** 0. 0110 0. 0148 0. 0158 0. 0790 -0. 0551 0. 0769 -0. 3992*** -0. 1058 -0. 1040 0. 0006 -0. 1169 0. 1345 0. 4053 3631 16. 4 3631 18. 2 3631 95. 2 3621 45. 3 Note: Robust std. errors in parentheses June 21 2008 NASM 2008 Conference 17

RISK AVERSION AND PORTFOLIO CHOICE • More in the paper: § an individual estimate of the wealth loss “lower bound”, i. e. , the minimum wealth loss achieved with our RRA coefficient § a study on the link between this lower bound and risk aversion § a robustness check using different time series returns Thank you for your attention! June 21 2008 NASM 2008 Conference 18