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

2. 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; McInish, 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
NASM 2008 Conference

3. 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
NASM 2008 Conference

4. 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
NASM 2008 Conference

5. 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
NASM 2008 Conference

6. 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 risk-free 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
NASM 2008 Conference

7. AGGREGATE PORTFOLIO COMPOSITION
9.98%
20.73%
-5.12%
28.40%
24.50%
50.87%
70.63%
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NASM 2008 Conference

8. 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
June
NASM 2008 Conference

9. HISTORICAL EXCESS RETURNS
Time series statistics
Covariances and correlations (in italic)
Excess
Return (%)
Standard
Deviation (%)
Sharpe
Ratio (%)
Tangency Portfolios
Bonds
3.7295
8.7109
0.7891
0.3942
Stocks
5.3191
0.2109
0.0757
Real Wealth
3.4281
7.4082 -
0.5300 %
Bonds
Stocks
Real Wealth
0.7588
0.4089
3.1031
0.1253
0.3195
0.5488
June
NASM 2008 Conference

10. RESULTS Based on financial portfolios, no constraints
Based on financial and real 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)
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NASM 2008 Conference 10 10

11. Financial + real (total) wealth
AGGREGATE RRA
The representative agent holds the aggregate portfolio
95% confidence interval: from 1,000 block-bootstrap simulations over time series realizations
Financial wealth
Financial + real (total) wealth
Unconstrained
Constrained
RRA
4.7460
(2.8469, )
7.9193
(5.6451, )
2.2200
(0.0403, )
Wealth loss (%)
0.8936
(0.0103, )
0.8451
(0.1719, )
0.4489
(0.1361, )
June
NASM 2008 Conference

12. INDIVIDUAL RRA BY PORTFOLIO TYPE
Median values
Financial wealth
Financial + real
(total) wealth
Obs.
Uncon.
Const.
Deposits
= 0 51
5.4003
6.7630
1.7688
> 0
3582
6.0531
7.0667
2.6560
Bonds
= -real wealth 72
3.9676
4.6594
1.0280
> -real wealth
3561
6.1697
7.0656
2.6598
Stocks
1238
7.5624
4.1703
2395
5.1078
6.8653
2.0057
Real wealth
= primary residence
2196 -
6.8530
2.8931
> primary residence
1437
7.4109
2.2038
Binding constraints
At least one
2456
8.3244
6.9562
2.8088
No binding constraint
1177
5.2437
7.2491
3.8370
Whole sample
3633
5.9851
7.0262
2.6154
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NASM 2008 Conference

13. INDIVIDUAL RRA HETEROGENEITY
Financial + Real portfolio (constrained)
25th perc.
50th perc.
75th perc.
RRA
1.2253
2.6154
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NASM 2008 Conference

14. INDIVIDUAL RRA HETEROGENEITY
Financial + Real portfolio (unconstrained)
25th perc.
50th perc.
75th perc.
RRA
4.4449
7.0262
8.6028
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NASM 2008 Conference

15. INDIVIDUAL RRA HETEROGENEITY
Financial portfolio (unconstrained)
25th perc.
50th perc.
75th perc.
RRA
4.3145
5.9851
June
NASM 2008 Conference

16. OBSERVED PORTFOLIOS AND RRA
Portfolio weights
Constraint
Obs.
Deposits
Bonds
Stocks
Real
wealth
Primary residence
unconstrained financial and real (total) portfolio vs. unconstrained financial portfolio
RRA lower
1482
0.1486
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
2984
0.0851
0.2729
0.7331
0.5233
644
0.1652
0.1473
0.0838
0.6036
0.5215
constrained total portfolio vs. unconstrained total portfolio
3071
0.2761
0.7054
0.4897
562
0.1749
0.0280
0.0252
0.7718
0.7550
Whole sample
3781
0.0971
0.2446
0.7137
0.5231
June
NASM 2008 Conference

17. DETERMINANTS OF RISK AVERSION
Financial wealth
Financial + real (total) wealth
Method: OLS
Unconstrained
Constrained
Dependent variable: log(RRA)
Primary residence / Wealth - ** **
Wealth (millions USD)
***
0.0196***
0.0176***
***
***
(Wealth (millions USD))2
0.0002***
***
0.0001***
Age
***
0.0085
0.0104
0.0090
0.0110
Age2/100
0.0407***
0.0033
0.0012
0.0169
0.0148
Household size
0.0372 *
0.0140
0.0158
Female
0.0576
0.0119
0.0518
0.0790
Married
0.0053
0.0009
Non-white
0.0144
0.0076
0.0487
0.0769
College graduate
***
***
***
With financial advisor
0.0250
0.0156
Employee
0.1222 ** **
Self-employed
0.1106
0.0612
0.0493
0.0128
0.0006
Business industry: finance **
0.0759
Fair / poor health
0.0581
0.1368
0.1345
Constant
3.1876***
1.3673***
1.3386***
0.4335
0.4053
Minimum obs
2939
3631
3621
Mult. Imp. Minimum dof
38.7
16.4
18.2
95.2
45.3
Note: Robust std. errors in parentheses
June
NASM 2008 Conference

18. 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!
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NASM 2008 Conference 18 18