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OVERCONFIDENCE 1187 have a limited effect on the size of the bubble or on price volatility. Since a Tobin tax will no doubt also deter trading generated by fun- damental causes that are absent from our model,the limited impact of the tax on the size of the bubble and on price volatility cannot serve as an endorsement of the Tobin tax.The limited effect of transaction costs on the size of the bubble is also compatible with the observation of Shiller (2000)that bubbles have occurred in the real estate market, where transaction costs are high. The existence of the option component in the asset price creates potential violations to the law of one price.Through a simple example, we illustrate that the bubble may cause the price of a subsidiary to be larger than that of its parent firm.The intuition behind the examplc is that if a firm has two subsidiaries with fundamentals that are perfectly negatively correlated,there will be no differences in opinion,and hence no option component on the value of the parent firm,but possibly strong differences of opinion about the value of a subsidiary.In this example,our model also predicts that trading volume on the subsidiaries would be much larger than on the parent firm.This nonlinearity of the option value may help explain the "mispricing"of carve-outs that oc- curred in the late 1990s such as the 3Com-Palm case. The paper is structured as follows.In Section Il,we present a brief literature review.Section III describes the structure of the model.Sec- tion IV derives the evolution of agents'beliefs.In Section V,we discuss the optimal stopping time problem and derive the equation for equi- librium option values.In Section VI,we solve for the equilibrium.Sec- tion VII discusses several properties of the equilibrium when trading costs are small.In Section VIII,we focus on the effect of trading costs. In Section IX,we construct an example in which the price of a subsidiary is larger than that of its parent firm.Section X concludes the paper with some discussion of implications for corporate finance.All proofs are in the Appendix. Ⅱ.Related Literature There is a large literature on the effects of heterogeneous beliefs.In a static framework,Miller (1977)and Chen,Hong,and Stein (2002)an- alyze the overvaluation generated by heterogeneous beliefs.This static framework cannot generate an option value or the dynamics of trading. In contrast,Federal Reserve Chairman Alan Greenspan seems to believe that the low turnover induced by the high costs of transactions in the housing market are an imped- iment to real estate bubbles:"While stock market turnover is more than 100 per cent annually,the turnover of home ownership is less than 10 per cent annually-scarccly tinder for speculative conflagration"(quoted in Financial Times [April 22,2002]).The results in this paper suggest otherwisc. Reproduced with permission of the copyright owner.Further reproduction prohibited without permission.Reproduced with permission of the copyright owner. Further reproduction prohibited without permission
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