قیمت گذاری دارایی با زیان گریزی
|کد مقاله||سال انتشار||مقاله انگلیسی||ترجمه فارسی||تعداد کلمات|
|10904||2008||22 صفحه PDF||سفارش دهید||11794 کلمه|
Publisher : Elsevier - Science Direct (الزویر - ساینس دایرکت)
Journal : Journal of Economic Dynamics and Control, Volume 32, Issue 10, October 2008, Pages 3253–3274
The use of standard preferences for asset pricing has not been very successful in matching asset price characteristics, such as the risk-free interest rate, equity premium and the Sharpe ratio, to time series data. Behavioral finance has recently proposed more realistic preferences such as those with loss aversion. Research is starting to explore the implications of behaviorally founded preferences for asset price characteristics. Encouraged by some studies of Benartzi and Thaler [1995. Myopic loss aversion and the equity premium puzzle. The Quarterly Journal of Economics 110 (1), 73–92] and Barberis et al. [2001. Prospect theory and asset prices. Quarterly Journal of Economics CXVI (1), 1–53] we study asset pricing with loss aversion in a production economy. Here, we employ a stochastic growth model and use a stochastic version of a dynamic programming method with an adaptive grid scheme to compute the above mentioned asset price characteristics of a model with loss aversion in preferences. As our results show using loss aversion we get considerably better results than one usually obtains from pure consumption-based asset pricing models including the habit formation variant.
Consumption based asset pricing models with time separable preferences, such as power utility, have been shown to encounter serious difficulties in matching financial market characteristics, such as the risk-free interest rate, the equity premium and the Sharpe ratio, with time series data. In those models, even if the coefficient of relative risk aversion in the power utility function is raised significantly, neither the risk-free rate nor the mean equity premium and nor the Sharpe ratio fit the observed data. The former is usually too high and the latter two are much too low in the model when compared to the data. One important concern has been that asset pricing models have often used models with exogenous dividend streams.1 The difficulties of matching stylized financial statistics may have come from the fact that consumption was not endogenized. There is a tradition in asset pricing that is based on the stochastic growth model which endogenizes consumption, see Brock and Mirman (1972) and Brock, 1979 and Brock, 1982. The Brock approach extends the asset pricing strategy beyond endowment economies to economies that have endogenous state variables including capital stocks that are used in production. Authors, building on this tradition,2 have argued that it is crucial how consumption is endogenized. In stochastic growth models, the randomness occurs in the production function of firms and consumption and dividends are derived endogenously. Yet, models with production have turned out to be even less successful. Given a production shock, consumption can be smoothed through savings and, thus, asset market features are even harder to match.3 Recent developments in asset pricing have focused attention on extensions of intertemporal models, conjecturing that the difficulties in matching real and financial time series characteristics may be related to the simple structure of the basic model. In order to better match the asset price characteristics of the model to the data, economic research has explored numerous extensions of the baseline stochastic growth model.4 An enormous effort has been invested in models with time non-separable preferences,5 such as habit formation models, which allow for adjacent complementarity in consumption. This type of habit specification gives rise to time non-separable preferences and time varying risk aversion. Risk aversion falls with rising surplus consumption and the reverse holds for falling surplus consumption. A high volatility in surplus consumption will lead to a high volatility in the growth of marginal utility and thus to a high volatility in the stochastic discount factor (SDF). Such habit persistence was introduced in asset pricing models by Constantinides (1990) in order to account for high equity premia. Asset pricing models along this line have been further explored by Campbell and Cochrane (2000), Jerman (1998) and Boldrin et al. (2001). As the literature has demonstrated6 one needs not only habit formation but also adjustment costs of investment in order to reduce the elasticity of the supply of capital to generate a higher equity premium and Sharpe ratio. Yet, a habit formation model can only slightly improve the equity premium and Sharpe ratio. It also does not generate enough covariance of consumption growth with asset returns so as to match the data.7 Current research has focused on prospect theory which moves away from consumption based asset pricing models. The new strategy is to look for the impact of wealth fluctuation on households’ welfare. Here, the decision on a portfolio is impacted by both preferences over a consumption stream as well as by changes in financial wealth. In the preferences there will be thus an extra term representing the change of wealth. Furthermore, as prospect theory has taught us, an investor may be much more sensitive to losses than to gains. This is known as loss aversion. Loss aversion, in particular, seems to hold if there have been prior losses already. Therefore, past gains and losses may be relevant as well. By extending the asset pricing model in this direction one does not need to raise the covariance of consumption growth and asset returns, a feature not found in the data.8 Not only low variance of consumption growth, but also a higher mean and volatility of asset returns, might be achieved by a time varying risk aversion arising from the fluctuation of asset value. The idea is that after an asset price boom the agents may become less risk averse because their gains may dominate any fear of losses. On the other hand, after an asset price fall, the agents become more cautious and more risk averse. This way, the variation of risk aversion would allow the asset returns to be more volatile than the underlying pay-offs, the dividend payments, a property that Shiller (1991) has studied extensively. Generous dividend payments and an asset price boom makes the investor less risk averse and drives the asset price still higher. The reverse can be predicted to happen if large losses occur. This may give rise to some waves of optimism and pessimism and associated asset price movements. Habit formation models attempt to increase the equity premium and Sharpe ratio by constructing a time varying risk aversion arising from the change of consumption. Loss aversion models do not rely on surplus consumption, as in the habit formation model, but rather on the fluctuation in asset value affecting the SDF. This is likely to produce a high volatility of returns and a substantial equity premium and Sharpe ratio, yet it allows for a low covariance of the growth rate of consumption and asset returns. The basic idea of loss aversion as developed in the context of prospect theory goes back to Kahneman and Tversky (1979) and Tversky and Kahneman (1992). It was further developed for applications in asset pricing by Benartzi and Thaler (1995), although their work is set in the context of a single period portfolio decision model. Barberis et al. (2001) have extended it to an intertemporal model of an endowment economy.9 Yet, without the asymmetry in gains and losses, whereby prior losses will play an important role, the risk aversion will be constant over time and the theory cannot contribute to the explanation of the equity premium.10 Although Barberis et al. (2001) make use of an Euler equation, augmented by an effect arising from loss aversion, there model and solution technique are still static. Furthermore, their model represents an endowment economy. We go beyond their work by studying asset pricing with loss aversion in a production economy. The most interesting and challenging feature of the loss aversion model in a production economy is the feedback effect of asset value – and changes of wealth – on preferences on the one hand, and the choice of consumption path on asset value, on the other hand. This creates a complicated stochastic dynamic optimization problem. We propose to solve this problem by a dynamic programming algorithm as presented in Grüne and Semmler (2004) which at least allows us to numerically approximate solutions to such models. Since the accuracy of the solution method is an intricate issue for models with more complicated decision structures, confidence in its accuracy is essential. In Grüne and Semmler, 2004 and Grüne and Semmler, 2007 a stochastic dynamic programming method with flexible grid size is used to solve such models. In that method an efficient and reliable local error estimation is undertaken and used as a basis for a local refinement of the grid in order to deal with regions of steep slopes or non-smooth properties of the value function (such as non-differentiability). This procedure allows for a global dynamic analysis of deterministic as well as stochastic intertemporal decision problems.11 This dynamic programming method is the one used in this paper. A model of loss aversion, as proposed by Benartzi and Thaler (1995) and Barberis et al. (2001), is reformulated for a production economy and numerically solved.The paper is organized as follows. Section 2 presents the model. Section 3 illustrates the expected results in a simpler setting. Section 4 introduces the stochastic dynamic programming method. Section 5 studies our model of loss aversion and reports numerical results. Section 6 interprets the results. Section 7 evaluates the results in the context of other recent asset pricing models with production. Section 8 concludes the paper. Appendix A presents the details of the algorithm used in this paper.
نتیجه گیری انگلیسی
Extensive research has recently been devoted to the study of asset price characteristics, such as the risk-free interest rate, the equity premium and the Sharpe ratio, arising from the stochastic growth model of the Brock–Mirman type. The failure of the basic model to match the empirical characteristics of asset prices and returns has given rise to numerous attempts to extend the model by allowing for different preferences and technology shocks, adjustment costs of investment, the effect of leverage on asset prices, and heterogenous households and firms.36 In this paper we have gone beyond the consumption based asset pricing model and have studied asset price characteristics when a consumption stream as well as the fluctuation of the agent's value of assets affect the utility of the agent. We have assumed, as recently proposed that agents become even more loss averse when they have prior experiences with large losses in asset value and are again hit by a decline in their asset value in the current period. This gives rise, as we have shown in Section 2 of the paper, to a new form of an SDF pricing the income stream in a production economy. In the context of this model, the agents do not have to experience large losses in consumption in order to induce them to change asset holdings.37 In our model, as one finds in time series data, consumption growth is de-linked from asset prices booms and busts and the covariance of consumption growth and asset returns can, as the empirical data show, be allowed to be weak. Thus one might want to design empirical estimation strategies that accept a de-linked relationship of consumption growth and asset returns.38 The next step would be to integrate more frictions, such as habit formation and adjustment costs of investment, into the loss aversion model with production studied here.