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I- Theoretical Framework

I- Theoretical Framework. Literature on Portfolio choice models. Static model (Arrow, 1965) : optimal portfolio choice theory Extensions : Inter-temporal model (Mossin, 1968) Inter-temporal consumption-portfolio choice model (Merton, 1969, Samuelson, 1969).

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I- Theoretical Framework

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  1. I- Theoretical Framework Risk management and demand for risky assets

  2. Literature on Portfolio choice models • Static model (Arrow, 1965) : optimal portfolio choice theory • Extensions : • Inter-temporal model (Mossin, 1968) • Inter-temporal consumption-portfolio choice model (Merton, 1969, Samuelson, 1969) Risk management and demand for risky assets

  3. Main hypothesis in Merton’s model Complete markets • No transaction or holding costs (fixed or proportional), no taxes, perfect divisibility of assets, short sales allowed • Perfect information (no information costs…) • Transactions made continuously in time Risk management and demand for risky assets

  4. Main results in Merton’s model • If u[c(t)], the instantaneous utility function, exhibits constant relative risk aversion (CRRA) and if assets prices are log-normally distributed (yields follow a wiener process) then :  portfolio choice is independant of consumption myopia is optimal (optimal portfolio does not depend of age). Risk management and demand for risky assets

  5. TheTwo funds separation theorem holds : one may consider only one risky asset (the risky mutual fund depends only on returns and covariance matrix) and the risk-free asset (portfolio are perfectly diversified) • Intertemporal portfolio choice may be analysed within a standard static portfolio choice model Risk management and demand for risky assets

  6. First « Puzzles » Porfolio are incomplete and very different Portfolio depend on age Risk management and demand for risky assets

  7. The standard static portfolio problem W :initial wealth w : fraction of wealth invested in risky assets Risk management and demand for risky assets

  8. Risk management and demand for risky assets

  9. Demand for risky assets • For small risk, taking a first order Taylor expansion of FOC is (also true for CRRA utility function and log-normality of assets price) : Risk management and demand for risky assets

  10. Risk management and demand for risky assets

  11. Predictions • The proportion of risky assets in wealth is constant with wealth if u(.) exhibits CRRA • The demand for risky assets is increasing according to wealth if u(.) is DARA Risk management and demand for risky assets

  12. “Equity Premium Puzzle” • In France : on the period 1896-1996 with annual data, we should obtain according to this model (same prediction in USA) : • - If g=1  w* = 160% (234%) • - If g=4  w* = 40% (58%) Risk management and demand for risky assets

  13. “Participation Puzzle” • In 2000 in France, only 15% of households own stocks directly (only stocks) and about 23% directly or indirectly (mutual funds included) •  How can we explain this fact in the standard portfolio choice model? Risk management and demand for risky assets

  14. How the model can explain why people holds so few stocks? Risk management and demand for risky assets

  15. Alternative hypothesis (I) Incomplete markets or more general utility 1) Existence of holding and transaction costs 2) There are other sources of risk (income, unemployment, health…) 3) Some individuals are liquidity constrained 4) Some individuals have more flexible labor supply 5) Utility function u(.) does not exhibit CRRA Risk management and demand for risky assets

  16. Alternative hypothesis (II) The role of other forms of wealth Human wealth : 2) Housing wealth : ratio H(T)/W(t) Risk management and demand for risky assets

  17. King and Leape (1998) and Arrondel and Masson (1990) introduce holding costs to explain why portfolio are incomplete • Gollier and Zeckhauser (1998) show that if risk tolerance (the inverse of risk aversion) is convex, then young households invest more in risky assets than old households (myopia is no longer optimal) • -if it is true, the fraction of wealth invested in wealth must increase with wealth Risk management and demand for risky assets

  18. Bodie, Merton and Samuelson (1992) study the impact of labor supply flexibility • Flavin and Yamashita (2002) or Cocco (2002) analyze the relation between housing and risky asset demand Risk management and demand for risky assets

  19. The optimal static portfolio composition with background risk • We assume now that initial wealth is random (Kimball, 1993): Risk management and demand for risky assets

  20. is exogenous, undiversifiable and uninsurable (it is independant of portfolio risk) • Let us define indirect utility function: for all W, where dF(y) is the distribution function of y. Risk management and demand for risky assets

  21. In consequence, portfolio choice problem can be rewritten as : The introduction of an independent risk is equivalent to the transformation of the original utility function u(.)into the indirect utility function v(.) Risk management and demand for risky assets

  22. Application of Arrow-Pratt theorem: - If we can rank the degree of concavity of these two functions, we can analyse changes in attitude towards portfolio risks PROPOSITION • Risk affects negatively the demand for stocks ifv(.) is more concave than u(.) Risk management and demand for risky assets

  23. Technically, this means that: Risk management and demand for risky assets

  24. Let us define: Main results Risk management and demand for risky assets

  25. I) The proposition is true if preferences are standard (Kimball, 1993): • -Standarness correspond to properness but with respect to a less restrictive set of risks (loss-aggravating risks) • Standarness correspond to more restrictive preferences than properness… Risk management and demand for risky assets

  26. II) The proposition is true if (Pratt and Zeckhauser (1987): for undesirable risk Risk management and demand for risky assets

  27. III) The proposition is true if (Gollier and Pratt, 1996) (for unfair risk): Risk management and demand for risky assets

  28. Standarness Properness Risk vulnerability DARA Risk management and demand for risky assets

  29. Risk management and demand for risky assets

  30. Prediction of the model on portfolio behavior • an increase in income risk (background risk) makes households less willing to bear a rate of return risk (risks are substitutes) even when the two risks are independent Risk management and demand for risky assets

  31. Borrowing constraints and Portfolio Choice • A Consumer who is subject to income risk and who anticipates to be constrained in the future will hold less risky securities. So borrowing constraints reinforce precautionary motives a is decreasing in wealth and concave Risk management and demand for risky assets

  32. II- The Data and the Variables • « Patrimoine 97 » INSEE household survey (10,207 households) • « Recto-verso » questionnaires (4,633 individuals - 2,954 households) • Table 1 Risk management and demand for risky assets

  33. Measuring Relative Risk Aversion • Barsky, Juster, Kimball and Shapiro (1997)R: current incomeContract A Risk management and demand for risky assets

  34. Yes No Contract A Contract C Contract B Risk management and demand for risky assets

  35. Rational consumer chooses a contract if:1/2 u(2C) + 1/2 u(lC) >= u(C) • Assumption : u(.) is CRRA • Tables 2a-2b-3 Risk management and demand for risky assets

  36. Table 2a : Risk aversion in France and in U.S.A. Risk management and demand for risky assets

  37. Does Measured Risk Aversion Predict Behavior? Risk management and demand for risky assets

  38. Earnings Uncertainty • Guiso, Japelli and Terlizzese (1992) • Within the next 5 years, your total household revenue (the rise in prices excluded) will have :-… increased by more than 25%-... increased by 10 to 25%-... increased by less than 10%-... Will be constant-... will have decreased by less than 10%-... will have decreased by 10 to 25%-... will have decreased by more than 25%-... will have marked ups and downs (indicate the minimum and maximum annual income) • You dispose of 100 points to be distributed among the 8 items, according to the degree to which you agree or you disagree with the relative statement. Risk management and demand for risky assets

  39. Table 4 : Frequency Distribution of the Ratio of the Subjective Standard Deviation to the Current Earning (s/y) • Average expected growth of income: around 1.5% • s2y= s2x y2t ; y is current income; x is expected growth of income Risk management and demand for risky assets

  40. The Probability of Being Liquidity Constrained • Guiso, Japelli and Terlizzese (1996) • Did you renounce to finance expenditures on durable goods (main residence, cars ...) or did you renounce to restore your home because you expected that bank or other financial intermediaries will refuse the loan or the mortgage? • Did you renounce to finance expenditures on durable goods (main residence, cars ...) or did you renounce to restore your home because bank or other financial intermediaries refused the loan or the mortgage? • 11,6% of households are constrained in total sample9,8% in sample of respondents Risk management and demand for risky assets

  41. III-Empirical Analysis of the Precau-tionary Motive in Wealth Behaviors Income Risk, Borrowing Constraints and Portfolio Choice (with exogenous income risk)A/F = g(s2,cl,X) + e  with endogenous job riskiness A/F = g(s2,cl,g,X) + e Risk management and demand for risky assets

  42. Previous Results • Demand for risky assets decreases with income variance in : • Italy: Guiso,Japelli and Terlizzese (1996) • USA: Vissing-Jorgensen (1999) • Demand for risky assets do not depend on income variance in : • Netherlands: Hochguertel (1998) Risk management and demand for risky assets

  43. Econometric Specification for Risky Assets Demand • Three definitions of risky assets: • Narrow definition: equities only • Broad definition I: equities, obligation or securities, mutual funds • Broad definition II: equities and mutual funds with equities Risk management and demand for risky assets

  44. Econometric Specification for Risky Assets Demand • Two econometric specifications (in Probit, conditional demand or Tobit) • I : income risk is assumed to be exogenous • II : income risk is assumed to be endogenous (estimated by IV); proxy for individual’s CRRA is introduced in estimation Risk management and demand for risky assets

  45. Table 5 and 7 : The demand for risky assets in France • The sign of the variance of income is positive and statistically significant in Probit model (and in Tobit model for the broad definition) Risks are not substitutes • Probability of being liquidity constrained in the future decreases demand for risky assets Risk management and demand for risky assets

  46. Table 6 and 8 : The demand for risky assets in France • Job riskiness depends positively on proxy for CRRA (see Table 3) • Demand for risky assets depends positively on proxy for CRRA (in Probit and Tobit models for the narrow and the broad definitions) • The coefficient of the variance of income is always positive Risk management and demand for risky assets

  47. IV-Conclusions • Empirical estimates using French data “Patrimoine 97” (INSEE) indicate that : • Borrowing constraints induce people to be more temperant in their portfolio • Households who are confronted to more risky income hold a greater proportion of their wealth in risky assets • Less risk averse households have more risky job and more risky assets in their portfolio Risk management and demand for risky assets

  48. Explanations • Consumers are not DARA + DAP • Risk are not independant: negative correlation between income risk and portfolio risk could explain the positive effect of the variance on risky portfolio (risky investment are considered like insurance) Risk management and demand for risky assets

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