MEASURING CHINESE RISK AVERSION

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1 MEASURING CHINESE RISK AVERSION --Based on Insuance Data Li Diao (Cental Univesity of Finance and Economics) Hua Chen (Cental Univesity of Finance and Economics) Jingzhen Liu (Cental Univesity of Finance and Economics)

2 MEASURING CHINESE RISK AVERSION Abstact In the liteatue isk avesion has been widely studied by many scholas. Howeve, little eseach is done about China s maket. In this pape we assume a model involves the data on popety/liability insuance and estimate the isk avesion in China. We use data fom 1997 to 2013 afte modifying by deflatos. The esult comes out to suppot ou hypothesis of inceasing elative isk avesion. I. Intoduction Thee is a consensus that absolute isk avesion deceases with wealth. It was established by Patt (1964) and Aow (1965), along with the measue of absolute and elative isk avesion. Many othe studies have tied to deive simila hypothesis about elative isk avesion, but thei esults vay widely. Such studies include Fiend and Blume(1975), Siegel and Hoban(1982), Moin and Suaez(1983), Szpio(1986), Blake(1996), etc. Szpio(1986) used the time seies data fom 1955 to 1975 on popety/liability insuance in the United States and concluded that elative isk avesion was constant and the degee was between about 1.2 to 1.8. In this pape we use simila model and analyze the isk avesion in China. Fist we assume a isk avesion function evolves some vaiables and paametes. We modify the time seies data 1 by deflatos and do nonlinea egession. Then we choose the paametes which have the minimum sum of squaed eos and evaluate the coefficient of China s isk avesion. Accoding to the esult, we conclude that the elative isk avesion in China inceases with wealth. Ou esult confoms to the hypothesis of IARA (inceasing elative isk avesion.). II. The model 1 The data in this pape have been modified by deflatos, so we think the esults ae compaable to those coss-section estimates.

3 We assume that the amount of insued assets has a fom like I W / W, (1) whee I is the insued assets, W is the individual s wealth, is the loading chaged by insuance companies, and W avesion. Denote P pi and Q qi donates the absolute isk espectively, because the amount insued assets I cannot be obtained diectly. Hee P is the total pemiums, p donates the pemium ate. Q is the total claims and q donates the claim ate. Then we get a couple of equations: P pw p / W,, (2) Q qw q / W. (3) We assume the isk avesion function has the fom / W h c W. (4) Substituting equation (4) into (2) and (3), we get 1 ( h ) ( h P t pw t p twt awt m twt ) c (5) 1 ( h ) ( h Q t qw t q twt bwt n twt ) c (6) We obtain the pemiums and claims data on popety/liability as P andq, afte eliminating pice fluctuation. We use GDP pe capital with fixed base as W and( P/ Q) 1as. By nonlinea egession we obtain the value of h, togethe with those fo a, m, b and n. The ange of h is fom -5 to 5. The step size is Moeove, thee ae some estiction conditions. The esults should subject to a 0, b 0, 2 m 0and n 0. 3 We choose the paametes which esults the minimum S.E.of egession and use them to evaluate the coefficient of elative isk avesion. III. Results 2 Because of a pand p stands fo the pemium ate, thee must be a 0. So doesb. 3 Geneally we agee that the coefficient of absolute isk avesion is positive. Then because of / W n. h c W >0, and ou esults pove h >0, so we have 0 c. m p / c, so m 0. So does

4 The data afte modified ae pesented in Table1. Table1--Data afte Modified 4 YEAR P Q W The minimum S.E.of egession is obtained fo hp 0.11and hq 0.18 using pemiums and claims as dependent vaiable. The signs of a and b ae positive and the signs of m and n ae negative, which meet the equiements. 5 Then we estimate the coefficient of elative isk avesion. cp c q a / m b / n The esults ae pesented in Table2. The changing tendency can be obseved by Chat1 and Chat2. Obviously, the coefficient of elative isk avesion inceases gadually with wealth. 4 We use five-yea moving aveages as poxies of annul pemiums and claims, so the data stat fom 2001, not 1997 as mentioned befoe. 5 Details ae in appendix.

5 TABLE2--RELATIVE RISK AVERSION 6 YEAR W p q CHART1 -- P WITH WEALTH 5 4,5 4 3,5 3 2,5 2 1,5 1 0,5 0 Rp W R R W c W, p 6 (1 h) A epesents the R using pemiums and q epesents the R using claims.

6 CHART2 -- q WITH WEALTH 4,5 Rq 4 3,5 3 2,5 2 1,5 1 0, W IV. Conclusion Inceasing elative isk avesion means that the wealthie the man, the moe isk-avesion he is. In this pape IRRA means that people get iche with the time. Moeove they puchase insuance in a much faste inceasing ate. We analyze the data on popety insuance and ty to explain the esults by the following easons fom the insuance point of view. The fist eason is the extenal uncetainty inceasing. In past two decades, geat changes have taken place in China. With the blooming of economy and technology, many kinds of new isk ae appeaing, and the degee of loss is also inceasing. Fo example, evey 100 families had only 0.34 cas on aveage in This numbe is inceased shaply to 16.9 in following 14 yeas. It is well known that moe vehicles mean moe possibilities of isk. Moeove, the accumulation of wealth also affects isk avesion coefficient. On one hand, the accumulation of pesonal popety, family popety and entepise popety suffes moe loss than in the past when some accident occus. On the othe hand, the influence of wealth on isk avesion coefficient can be classified. Some studies indicate that house popety has positive effect on isk avesion coefficient and financial popety has negative effect. Thus,

7 the moe house popety, the moe isk avesion. In china, the pice of house gew in incedible speed. Accoding to National Bueau of statistic, the aveage pice of commecial house was 2053 Yuan in 1999, but it was up to 6237 Yuan in People have to pay much moe fo house, which is about 22.7% of family income. The house popety inceased a lot, which means isk avesion coefficient is lage. Anothe eason may be the pefection of insuance industy in China. Since 1990s, China s insuance industy is developing apidly. It s becoming moe pofessional, intenational and standadized. The sots of insuance poducts have been divesified and specialized. Moeove, the quality of sevice has also been impoved. Now the insuance needs fo diffeent people can be met. What s moe, Chinese people s undestanding of isk is becoming compehensive and pofound. Now they think insuance is much moe impotant than in the past, as it is an effective way to potect them fom isk. Thee ae still some open poblems to be solved late. Fist we cannot detemine the specific easons that esult IRRA in China. Second we can t distinguish how much each facto has the effect. Finally it is necessay to do coss-section estimates to examine ou esults. Appendix The egession esult using pemiums as dependent vaiable is this: The egession esult using claims as dependent vaiable is this:

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