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* I would like to thank Frank Dobbin, Christopher Marquis, Peter ...

* I would like to thank Frank Dobbin, Christopher Marquis, Peter ...

ENDNOTES 1

ENDNOTES 1 Instrumentally rational action (zweckrational) is social action by purposive actors who, based upon expectations of the behavior of other actors and objects, calculate an expedient means to achieve rationally pursued end goals. Value-rational action (wertrational) is social action by purposive actors who strive to achieve end goals oriented towards an “ethical” standard valued for its own sake. Action may be instrumentally rational in the choice of means, but value-rational in the choice of end goals (Weber [1922] 1978:24-36). 2 I have altered the original notations in the economic models to present a consistent set of notations throughout this paper. P refers to price, superscript * refers to predictions, nonsuperscripted P are observed prices, subscript t refers to time period, subscript or superscript R and S refer to rational and sentiment investors, respectively; p or P() refers to probability; R refers to returns; Q refers to quantity; δ refers to sentiment; and ε to uncorrelated disturbance terms. 3 Subjective expected utility (SEU) describes how rational actors choose between decision � alternatives; formally, actors maximize SEU value ����� ��� � ���� ������� where U(.) is the individual’s utility function, xi is the vectors of goods in the i th state of the world, and pi is the probability of the i th state of the world occurring. Savage ([1954] 1972) demonstrated that preferences should adhere to seven axioms for SEU maximization to occur. Bayes’ theorem relates the conditional probabilities of events A and B: ���É�� � ���É������ . Rational actors ���� should update their probability of B occurring when receiving new information A based on Bayes’ theorem. 4 Formally: ���� �� ���� � ��� ��� � �� ����� ���� � �� ���� � ��� �� where Rf is the risk free rate, Km is the market rate of return, SMB (small minus big) and HML (high minus low) are the differences in returns between portfolios by market capitalization and book-to-market (value) ratios, and the relevant coefficients are firm-specific exposures to such risks (market, size, and value risk). 5 Discounted cashflow analysis derives stock valuations by estimating the stream of dividends accruing to shareholders over the entire future life-course of the company and discounting that stream of payments back to the present. Intrinsic value is equal to the discounted present value (DPV) of future dividends. Formally for discrete cash flows: ��� � �� ��� ; or for � ������ ��� continuous cash flows: ��� � � �����������. � 6 Formally, rational investors initially value a company based on the DPV of its future dividend � � stream: ��� ����� while sentiment investors value the same company: ��� �������; where δ represents investor sentiment and DPV1 is the correct discounted present value of future dividends at time=1. At time=2, new information is revealed and rational investors correctly � update their price expectations: ��� ����������� ��� while sentiment investors incorrectly � update their price expectations: ��� ����������� where ξ * is the expected change to future dividends revealed and ½ < θ < 1 represents the underweighting of such information by �� � � sentiment investors. Demand for shares is: �� ��S�������� ������� where ������� and ψ is the risk tolerance factor for that type of investor (rational or sentiment). At low sentiment � � � levels [δ < z0 < 0 such that ��� ���� ���È��], sentiment investors withdraw from the market � � and rational investors determine prices: �� ���� ���È��. At high sentiment levels [δ > z1 > 0 44

� � � such that ��� ���� ���È��], rational investors are driven from the market due to short-sale � � constraints and sentiment investors determine pricing: �� ���� ���È��. At intermediate � � � � � sentiment levels [z0 < δ < z1 such that ��� ���È������ ���� ���È��], rational and sentiment investors jointly determine price, which approximates a risk-tolerance weighted average of price expectations: �� ����È��� ��� � � � � � � ����� ��� È�� �� ����� ���È��� ����. 7 Formally, the first-day close price for the issuer’s shares fully incorporating sentiment � � investors’s expectations is: �� ��� ����where �� is the rational predicted price and ��� is the intensity of noise trader sentiment at t=1 and is a random variable uniformly distributed on �������� so �����É���� ���� [integrating Baker and Stein’s formulation in footnote 6 to Derrien’s model, if δ < z0 then sentiment investors withdraw from the market, ��� ��, and � �� ��� ; if δ > z0, P1 is strictly increasing with increasing δ]. The underwriters set the offer price POPR by maximizing fees earned against the cost of price support activities post-IPO. Total fees are the gross spread times the offer price: �����, where f is the gross spread. Cost of price support is: ������É� ���� � � ������ � � � � �� �� �� ��� �� � � ����� �� � ���� �� ��� �� � � � � ; � � underwriters maximize earnings by pricing the IPO offer price at: ���� ��� ������ (obtained � by solving ������ � � �� � ��� ��� �����). The numerator for first-day returns is: ����� �� �� � � ���� ��� ����� ��� ���� � ��� � ������� ����������; as f is generally fixed at 0.07, investor sentiment should predict first-day returns (if δ > z0, Pfdr is strictly increasing with increasing δ). 8 Formally, the predicted price equals the actual price plus an uncorrelated disturbance term: � �� ��� ���. As ε is by definition uncorrelated with P * , the variance of predicted prices must equal the sum of the variances for observed prices and the disturbance term: � � �� � � � ���� ����; as variances cannot be lower than zero, the variance of predicted prices cannot be lower than the variance of observed prices: � � �� � � ����. Conversely, if the variance of predicted prices is lower � than that for observed prices, then �� ��� must be predictable. Since EMH asserts that predicted prices are the DPV of future dividends, the volatility of dividends should be greater than or equal to that of observed prices. Shiller demonstrates that is not the case (equivalently by showing that log dividend-price ratios are more variable than present value models), and that the excess volatility of stock prices directly implies predictability of long-run returns (LeRoy and Porter 1981; Shiller 1981, 1984; Campbell and Shiller 1987, 1988). 9 Formally, prospect theory hypothesizes that people assign gambles the value � �������, where ��� � if x ≥ 0 and � ������� � if x < 0; � � ���� �� ���� � � �; ���� � � �� 45 ����������� �� � ; and p* is the probability that the gamble will yield outcomes at least as good as x. A wide range of studies supports λ ≈ 2 (coefficient of loss aversion, a measure of relative sensitivity to gains and losses), violating SEU preference axioms since the sensitivity to gains and losses should be uniform. 10 One could justifiably ask why an investment bank must underwrite IPOs and price them in a two-stage bookbuilding process. While non-Bayesian investor models generally assert that underwriters are soliciting private price information from rational investors, IPOs have been priced by auction methods or sold directly to public investors in the United States and other countries, with a specialized investment bank, WR Hambrecht + Co, championing Dutch auction

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