Taking the stock market as a whole object, we assume that prior losses and gains are two different factors that can influence risk preference separately. The two factors are introduced as separate explanatory variables into the timevarying GARCHM (TVRAGARCHM) model. Then, we redefine prior losses and gains by selecting different reference point to study investors’ timevarying risk preference. The empirical evidence shows that investors’ risk preference is time varying and is influenced by previous outcomes; the stock market as a whole exhibits house money effect; that is, prior gains can decrease investors’ risk aversion while prior losses increase their risk aversion. Besides, different reference points selected by investors will cause different valuation of prior losses and gains, thus affecting investors’ risk preference.
Many studies suggest that investors’ risk preference changes over time. When investors make decision under uncertainty in financial markets, prior outcomes of investors’ can influence their risk preference, which can cause their decisionmaking behaviors to change. Studies as discussed in [
However, there is no agreement on what effects will prior outcomes have on investors’ risk preference, which attracts an increasing number of scholars to study it. Early studies mainly focused on disposition effect which reflects the tendency to sell assets that have gained value and keep assets that have lost value. In other words, investors tend to be risk seeking with losses and risk averse with gains. Some scholars [
When studying what effects will the prior outcomes have on the investors’ risk preference, the selection of the reference point is critical. Kahneman and Tversky [
The above literatures’ analysis shows that, on the one hand, the research of what effects prior losses and gains have on investors’ risk preference has not achieved agreement. Under the background of professional trading, Coval and Shumway [
In view of previous studies about the effect of prior losses and gains on investors’ risk preference and about the selection of reference price being insufficient and inadequate, this paper utilizes ten worldwide representative indexes and uses prior losses and gains as separate explanatory variables to explore their overall effects on current risk preference in the entire market on the basis of TVRAGARCHM model. Then, we choose the historical high price, the historical low price, the 5day average price, the 20day average price, the 30day average price, and the memoryadjusted price as the reference point, respectively, to further test investors’ risk preference. On the one hand, this paper has overcome the demerits of the psychological experiments of Frino et al. [
This paper is organized as follows: the second part presents the model analysis; the third part provides the empirical study which includes the sample selection and the empirical result; the fourth part is the conclusion.
It should be pointed out that the reference price is a critical factor to the judgments of gains and losses. If the stock price exceeds the reference price, investors get gains or otherwise obtain losses. Reference price, as a kind of investors’ psychological price, is different with personal evaluation criteria, and it is hard to determine which reference price is the most reasonable. Many researchers believe that investors usually take the average and extreme price as their reference points.
Many researchers found that investors usually were affected by the historical highest or lowest price when measuring gains and losses. For example, studies as discussed in [
Anderson [
Kopalle and LindseyMullikin [
In GARCHM model, the risk premium coefficient in the mean equation represents the required compensation for each unit of risk. The larger the risk premium coefficient, the greater the compensation required by investors and the stronger the tendency to be risk averse. So the risk premium coefficient can be used to measure investors’ risk preference [
Psychological experiments suggested that people’s decisions exhibit asymmetry when facing gains and losses. Thaler and Johnson [
Hypothesized effects of prior loss and gain on current risk preference.
Based on the TVRAGARCHM model, we further qualitatively distinguish the prior loss and prior gain:
In essence, if we only take the prior loss and the prior gain as values with different signs, but do not estimate them as separate explanatory variables in a model, it is impossible to test the house money effect (
Consequently, the following timevarying risk compensation coefficient model is derived on the basis of the above analysis to further test the house money effect and loss aversion simultaneously. We build the model called TVRASGARCHM model as follows:
In this paper, the sample data are the composite indexes of the top 10 market values in the global stock markets in 2011, including NYSE (USA), NASDAQ (USA), N225 (Japan), the FTSE 100 (UK), SSE (China), HSI (China), TSX (Canada), BOVESPA (Brazil), AORD (Australia), and DAX (Germany). The time span is from October 15, 2002, to October 15, 2012. All data are from Yahoo finance (http://finance.yahoo.com/). The return is expressed in logarithmic return
Descriptive statistics of returns.
Statistic/index  Mean  Std.  Skewness  Kurtosis  JB statistic  Number 

NYSE  −0.020146  1.379473  0.386855  12.76570  10072.59  2519 
NASDAQ  −0.034578  1.456799  0.178026  8.740239  3471.719  2519 
N225  0.001421  1.548458  0.547135  11.61059  7697.198  2452 
FTSE  −0.013400  1.265248  0.102467  10.37660  5729.256  2525 
SSE  −0.013083  1.656866  0.246740  6.634653  1412.133  2519 
HSI  −0.032618  1.605285  −0.037799  12.15559  8749.820  2505 
TSX  −0.025141  1.214611  0.680644  13.14799  10544.64  2414 
BOV  −0.078359  1.861404  0.084820  8.040546  2623.075  2475 
AORD  −0.016793  1.072880  0.553147  8.880106  3781.326  2535 
DAX  −0.033998  1.539663  −0.038525  8.105775  2773.715  2553 
According to the skewness, kurtosis, and JB statistic of each index shown in Table
Based on previous studies, investors’ different reference points will affect the judgment of prior losses and gains, thus affecting investors’ risk preference. Therefore, we select six reference points on the basis of the analysis in Section
Tables
Results of TVRAGARCHM model (MAX).
Index/parameter  NYSE  NASDAQ  N225  FTSE  SSE  HSI  TSX  BOV  AORD  DAX 


0.129 
−0.055 
−0.033 
−0.317 
0.008** 
−0.061 
−0.091 
0.248 
−0.130 
−0.070 

−0.815*** 
−0.406 
−0.985*** 
−0.707*** 
0.979*** 
−0.501 
0.376 
−0.979*** 
−0.696 
−0.984*** 

−2.503*** 
−1.184 
−0.549 
−3.251*** 
0.066*** 
−1.213* 
−1.162 
−0.492 
−1.572 
−0.759* 
Likelihood  −3574.632  −3988.067  −4083.697  −3533.477  −4436.532  −4083.826  −3298.369  −4688.108  −3153.892  −4137.287 
Note: ***, **, and * in all tables denote that the parameter is significant at 1%, 5%, and 10% level, respectively.
Results of TVRAGARCHM model (MIX).
Index/parameter  NYSE  NASDAQ  N225  FTSE  SSE  HSI  TSX  BOV  AORD  DAX 


0.291*** 
0.154 
0.070 
0.349*** 
−0.002 
0.109 
0.098 
0.385*** 
0.088 
0.046 

−0.798*** 
−0.473 
−0.995*** 
−0.746*** 
0.982*** 
−0.534 
0.265 
0.987*** 
−0.758*** 
−0.987*** 

−3.098*** 
−1.302 
−0.409 
−3.800*** 
0.056*** 
−0.623 
−1.437 
−0.601* 
−2.587** 
−0.614* 
Likelihood  −3572.507  −3987.908  −4083.661  −3531.389  −4434.745  −4085.042  −3298.805  −4686.645  −3152.282  −4136.812 
Note: ***, **, and * in all tables denote that the parameter is significant at 1%, 5%, and 10% level, respectively.
Results of TVRAGARCHM model (
Index/parameter  NYSE  NASDAQ  N225  FTSE  SSE  HSI  TSX  BOV  AORD  DAX 


0.008 
0.060 
−0.001 
0.075 
0.271*** 
0.003 
−0.004 
0.051 
−0.007 
0.001 

0.668*** 
−0.173 
0.728** 
0.898** 
−1.003*** 
0.833*** 
0.742*** 
0.577** 
0.761*** 
0.674*** 

−1.735*** 
−2.270* 
−0.698 
−0.164 
0.229*** 
−0.401 
−1.800*** 
−1.137** 
−0.708 
−1.062** 
Likelihood  −3598.082  −4019.787  −4145.145  −3598.893  −4518.374  −4143.122  −3344.253  −4758.705  −3197.032  −4211.978 
Note: ***, **, and * in all tables denote that the parameter is significant at 1%, 5%, and 10% level, respectively.
Results of TVRAGARCHM model (
Index/parameter  NYSE  NASDAQ  N225  FTSE  SSE  HSI  TSX  BOV  AORD  DAX 


0.064 
0.054 
0.0279 
0.105 
0.002*** 
0.040 
−0.008 
0.080 
−0.053 
0.005 

−0.556** 
−0.265 
−0.889*** 
−0.736*** 
0.986*** 
−0.604 (0.31) 
0.415 (0.18) 
0.277 (0.6) 
−0.786*** 
−0.984*** 

−4.623*** 
−2.211* 
−1.939** 
−4.914*** 
0.112*** 
−1.227 (0.13) 
−2.155** 
−1.139 (0.18) 
−2.752** 
−0.768* 
Likelihood  −3587.015  −4008.689  −4102.625  −3549.934  −4447.889  −4102.110  −3309.123  −4707.524  −3165.369  −4162.044 
Note: ***, **, and * in all tables denote that the parameter is significant at 1%, 5%, and 10% level, respectively.
Results of TVRAGARCHM model (
Index/parameter  NYSE  NASDAQ  N225  FTSE  SSE  HSI  TSX  BOV  AORD  DAX 


0.012 
−0.990*** 
−0.028 
0.026 
0.002** 
0.018 
−0.072 
0.297* 
−0.086 
−0.012 

−0.775*** 
0.010*** 
−0.896*** 
−0.791*** 
0.983*** 
−0.687 (0.2) 
−0.773*** 
−0.983*** 
−0.739** 
−0.984*** 

−2.807*** 
27.024*** 
−1.448** 
−3.771*** 
0.049*** 
−0.999* 
−2.595*** 
−0.499 (0.2) 
−2.089** 
−0.738* 
Likelihood  −3557.889  2334.177  −4064.561  −3515.359  −4413.490  −4071.417  −3282.155  −4671.547  −3142.182  −4116.618 
Note: ***, **, and * in all tables denote that the parameter is significant at 1%, 5%, and 10% level, respectively.
Results of TVRAGARCHM model (MP).
Index/parameter  NYSE  NASDAQ  N225  FTSE  SSE  HSI  TSX  BOV  AORD  DAX 


0.006 
0.012 
−0.001 
0.105 
0.118 
0.001 
−0.004 
0.026 
−0.023 
0.001 

0.777*** 
0.670*** 
0.821*** 
−0.671*** 
−0.070 
0.883*** 
0.857*** 
0.757*** 
−0.489 
0.807*** 

−3.119*** 
−2.003* 
−1.236 
−3.418** 
−0.962 
−0.693 
−2.690*** 
−1.475** 
−3.007 
−1.605** 
Likelihood  −3572.617  −3986.930  −4084.460  −3535.877  −4444.961  −4084.119  −3296.610  −4686.938  −3153.422  −4140.519 
Note: ***, **, and * in all tables denote that the parameter is significant at 1%, 5%, and 10% level, respectively.
As is shown in the above tables, among the TVRAGA0RCHM model estimation results with MAX, MIN,
Further observation shows that though the ten composite indexes as a whole show the house money effect, there are still some differences. For all indexes, when selecting different reference points, the same index does not have consistent value for
With the empirical study described in Section
Results of TVRASGARCHM model (MAX).
Index/parameter  NYSE  NASDAQ  N225  FTSE  SSE  HSI  TSX  BOV  AORD  DAX 


−57.180*** 
−32.726*** 
−26.952*** 
−55.843*** 
1.239** 
−20.389*** 
−39.102*** 
−19.859*** 
−43.328*** 
−37.310*** 

−0.990** 
−0.410 
−0.343 
−1.892*** 
0.030* 
−0.397 
−1.091*** 
−0.065 
−0.391 
−0.705** 
Likelihood  −3541.543  −3970.803  −4074.049  −3503.489  −4433.837  −4077.932  −3280.496  −4675.261  −3132.791  −4111.405 
Note: ***, **, and * in all tables denote that the parameter is significant at 1%, 5%, and 10% level, respectively.
Results of TVRASGARCHM model (MIN).
Index/parameter  NYSE  NASDAQ  N225  FTSE  SSE  HSI  TSX  BOV  AORD  DAX 


−1.422*** 
−0.766 
−0.048 
−2.029*** 
0.763** 
−0.166 
−1.047** 
−0.445 
−1.446 
−1.386** 

−27.106*** 
−27.806*** 
−4.567** 
−38.036*** 
−21.988*** 
−11.127*** 
−33.931*** 
−19.841*** 
−27.990*** 
−13.520*** 
Likelihood  −3563.113  −3972.361  −4084.628  −3514.580  −4436.957  −4082.474  −3287.054  −4676.344  −3141.543  −4136.597 
Note: ***, **, and * in all tables denote that the parameter is significant at 1%, 5%, and 10% level, respectively.
Results of TVRASGARCHM model (
Index/parameter  NYSE  NASDAQ  N225  FTSE  SSE  HSI  TSX  BOV  AORD  DAX 


−2.591** 
−3.778** 
−0.895 
−0.115 
0.240*** 
−0.409 
−2.992*** 
−1.690* 
−1.203 
−2.486** 

−0.734 
−0.453 
−0.601 
−0.222 
0.195*** 
−0.396 
−0.577 
−0.531 
−0.072 
0.127 
Likelihood  −3597.464  −4019.031  −4145.122  −3598.876  −4504.463  −4143.122  −3343.164  −4758.322  −3196.579  −4210.430 
Note: ***, **, and * in all tables denote that the parameter is significant at 1%, 5%, and 10% level, respectively.
Results of TVRASGARCHM model (
Index/parameter  NYSE  NASDAQ  N225  FTSE  SSE  HSI  TSX  BOV  AORD  DAX 


−5.448*** 
−1.709 
−2.752** 
−7.127*** 
2.640*** 
−1.553 (0.2) 
−3.250** 
−0.521 (0.3) 
−3.549* 
−0.848 (0.2) 

−3.549*** 
−2.769** 
−0.866 (0.3) 
−2.390* 
−2.309*** 
−0.639 (0.5) 
−0.844 (0.2) 
−0.843 (0.14) 
−2.075 (0.18) 
−0.770* 
Likelihood  −3586.786  −4008.609  −4100.709  −3549.149  −4458.122  −4102.049  −3308.176  −4708.183  −3165.194  −4162.036 
Note: ***, **, and * in all tables denote that the parameter is significant at 1%, 5%, and 10% level, respectively.
Results of TVRASGARCHM model (
Index/parameter  NYSE  NASDAQ  N225  FTSE  SSE  HSI  TSX  BOV  AORD  DAX 


−4.933*** 
19.093*** 
0.709 (0.4) 
−3.365** 
0.053** 
0.670 
−2.840* 
0.178 (0.7) 
−2.637 (0.12) 
−1.123 (0.12) 

−1.131 (0.2) 
17.579*** 
−1.639 (0.16) 
−4.008*** 
0.043* 
−2.747*** 
−2.424** 
−0.852* 
−1.728 (0.17) 
−0.633 (0.2) 
Likelihood  −3556.580  2302.776  −4063.584  −3515.318  −4413.475  −4069.571  −3282.142  −4670.078  −3142.121  −4116.474 
Note: ***, **, and * in all tables denote that the parameter is significant at 1%, 5%, and 10% level, respectively.
Results of TVRASGARCHM model (MP).
Index/parameter  NYSE  NASDAQ  N225  FTSE  SSE  HSI  TSX  BOV  AORD  DAX 


−4.051*** 
−5.176*** 
−4.207** 
−3.337** 
−0.672 
−3.300** 
−3.888*** 
−1.743 
−6.061** 
−4.664*** 

−1.887 
1.389 
0.761 
−2.176* 
1.097* 
1.682 
−1.607 
1.186 
1.772 
2.884 
Likelihood  −3571.901  −3984.559  −4082.694  −3532.935  −4442.370  −4083.135  −3295.887  −4687.562  −3151.470  −4138.233 
Note: ***, **, and * in all tables denote that the parameter is significant at 1%, 5%, and 10% level, respectively.
The above tables (from Table
In addition, the values for
This paper, based on previous studies about investors’ risk preference, selects ten representative samples of the world’s composite indexes and adopts six different reference points and builds the TVARSGARCHM model to further explore how prior losses and gains affect investors’ risk preference. First of all, the data in this paper are large enough, are easy to get, and are not affected by individual investor sentiments, so the results are more convincing. Secondly, this paper takes prior losses and gains as separate explanatory variables in the TVRAGARCHM model, overcoming the offsetting effect that the changes in prior gains and losses have on investors’ current risk preference. That is, if we do not distinguish prior losses from gains, and when equal amounts of prior losses and prior gains have opposite but equivalent effects on the current risk preference, as shown in Figure
Through the research, the following conclusions can be made. Firstly, from the overall stock market, investor’s risk preference is time varying and can be affected by the prior outcome. Secondly, the stock market as a whole shows house money effect; namely, prior gains reduce the current risk aversion while prior losses push up the current risk aversion. Thirdly, the selection of different reference points affects the judgment of prior loss and gain, causing certain influence on the investors’ risk preference.
The authors declare that there is no conflict of interests regarding the publication of this paper.
This work was supported in part by the Natural Science Foundation of China (no. 71171024, no. 71371195, and no. 71221061). The authors gratefully acknowledge the helpful work of postgraduate Mengxian Tao, who has made great contribution to this paper.