In an early psychology-free model of asset prices, De Long et al. (1990a) consider an economy with two assets, asset A and asset B, which are claims to the same cash-ow stream. Asset B diers from asset A in that it is traded in part by noise traders whose demand is subject to i.i.d. shocks. De Long et al. (1990a) show that, in equilibrium, asset Bs price is lower, and its average return higher, than those of asset A. The reason is that noise traders uctuating demand for asset B causes the price of that asset to be more volatile. This higher volatility is an additional risk for investors in asset B, one they are compensated for through a lower price and a higher average return.

Lee et al. (1991) use the De Long et al. (1990a) model to address a classic puzzle in nance: the fact that, on average, the shares of a closed-end fund trade at a discount to net asset value, the market value of the assets that the fund holds.29 The idea is that the assets held by closed-end funds correspond to asset A in the De Long et al. (1990a) 29A closed-end fund is a fund that, at inception, raises money from investors and allocates this money to stocks or other assets. From this point on, the funds shares are traded on an exchange investors wanting to buy or sell fund shares do so there at the prevailing market price. 49

Closed-end funds are more likely to be traded by unsophisticated retail investors than are the underlying fund assets; as such, the prices of closed-end fund shares are aected by the uctuating optimism and pessimism of these investors. This time-varying sentiment constitutes an additional risk for holders of fund shares. To compensate for this risk, closed-end funds trade at a discount to net asset value, just as, in the De Long et al. (1990a) framework, asset B trades at a discount to asset A.

Baker and Wurgler (2006, 2007) pursue a dierent psychology-free approach. Rather than using psychology to identify markers of misvaluation, they proceed empirically: they propose six measures of the extent to which stock market investors are displaying excessive exuberance, and combine these measures to create a sentiment index. The measures, computed on an annual basis, are: the number and average rst-day return of IPOs, stock market turnover, the closed-end fund discount, the equity share (the fraction of equity issues among all new issues), and the dividend premium (the relative valuation of dividend-paying rms as compared to non-dividend payers).