“ Why New Issues Are Underpriced”

1. “Why New Issues Are Underpriced” Reference: Rock, Kevin. 1986. “Why new issues are underpriced.” Journal of Financial Economics Vol. 15, pp. 187-212.

2. Discussion & Results: • Explains the “IPO effect” – the phenomenon of the underpricing of initial public offerings. • Information asymmetry between informed and uninformed investors. • “Good issues” are crowded out by informed investors where good (bad) means low (high) offer price. • IPO’s are discounted to entice uninformed investors.

3. Discussion & Results: • IPO’s are not an auction where shares go to the highest bidder. • Shares are allocated by the underwriter to “privileged investors” (informed). • If there is excess demand, underwriter rations shares. • If there is excess supply, underwriter will have unsold shares.

4. Discussion & Results: • However, when demand outstrips supply significantly, then uninformed investors may not be allocated any shares. • As a result, uninformed investors will not buy until price is discounted enough to compensate them. • Rock’s conclusion: • “The analysis shows that the equilibrium offer price includes a finite discount to attract uninformed investors” (p. 188).

5. Discussion & Results: • Rock’s conclusion: • “The analysis shows that the equilibrium offer price includes a finite discount to attract uninformed investors” (p. 188). • However, the underwriter wants to ensure sale of all shares. • “The offering firm must price the shares at a discount in order to guarantee that the uninformed investors purchase the issue” (p. 187).

6. Discussion & Results: • However, the underwriter wants to ensure sale of all shares. • “The offering firm must price the shares at a discount in order to guarantee that the uninformed investors purchase the issue” (p. 187). • This creates a problem… • As price decreases, BOTH informed and uninformed investor demand increases. • But informed investors crowd out allocation of shares from uninformed investors. • Paradox: underpricing leads to increased demand from uninformed investors BUT the probability of receiving an allocation decreases.

7. The Model: • Consider a two asset market: • Risk-free asset (1, 0) • Risky asset with unknown mean and variance denoted as (uncertain value per share) • p = offer price of shares (constant) • Z = quantity of shares offered (constant)* * overallotment option

8. The Model: • Market is segmented into informed and uninformed investors. • Rock considers the issuer uninformed – do you agree with this assumption?

9. The Model: Assumptions (p. 191): • A.1. The informed investors have perfect information about the realized value of the new issue. • A.2. Informed investors cannot borrow securities or short-sell. They cannot sell their private information. • A.3. Informed demand, I, is no greater than the mean value of the shares offered,Z. • A.4. Uninformed investors have homogeneous expectations about the distribution of . • A.5. All investors have the same wealth (equal to 1) and the same utility.

10. The Model: Two states of the market: “Good”  price < value  underpricing “Bad”  price > value  overpricing I if p < (informed demand) 0 if p > (no informed demand) NT* + I if p < (informed and uninformed demand) NT* if p > (where N = # of uninformed investors; T* = optimal fraction of wealth for uninformed)

11. The Model: b = probability of order filled when p < (underpricing) b’ = probability of order filled when p > (overpricing) bias = b / b’  “good” / “bad”  underpriced / overpriced bias < 1 (p. 192)

12. The Model: Expected terminal utility: E[value| underpricing] + E[value | overpricing] + E[value of risk-free asset] T*(b, p) and T*(b/b’, p) T is a function of both price and probability of allocation. T(bias, price) (pp. 192 – 194)

13. The Model: • “…uninformed investment, T(b,p), depends not only upon the price but also upon the probability of receiving an allocation of underpriced shares. The probability of receiving an allocation declines as the price is lowered and, hence, counteracts the usual effect of price on demand” (p. 195). • For uninformed investors, b decreases as p decreases.

14. The Opportunity Set: • When p = , there is no rationing. • Some informed investment but with little interest from uninformed investors. • When p < , order flow from informed investors and greater interest from uninformed investors. • When p << , informed and uninformed compete for allocation. • When p <<< , the IPO reaches “full subscription price” where uninformed could fully absorb issuance. (p. 198) • In the extreme, as p -> 0, uninformed demand explodes.

15. An Example: Table 2, p. 200: • As price (p) decreases, uninformed demand (NT*) increases but probability of allocation of shares (b) decreases. • This result is even more pronounced for larger markets (N). • As market size increases (N -> ∞), b approaches the “zero demand probability.”

16. An Example: Figure 1, p. 201: • As p / decreases (i.e. p = to p < ), b decreases. • As p -> 0 (underpricing occurs), b decreases. Figure 2, p. 202: • From point B to A, bias (b / b’) increases because probability of allocation (b) increases as price increases.

17. Optimal Offer Price: • Assuming ~ uni(0, 2) • E[U(w)] = issuers utility + correction to account for uninformed investor subscription • Maximization problem (p. 203) • Approximation is given by b0(p) = 1 / (2 / p – 1)^2 = p / p + “…price at which uninformed demand is sufficient to subscribe the entire offering…involves a 20% discount from the mean” (p. 200 - 201).

18. Conclusion: • Kevin Rock researches why the equilibrium offer price is underpriced. • Informational asymmetry exists between informed and uninformed investors. • Underpricing occurs because the issuer must guarantee that uninformed investors participate in the offering; otherwise, not all shares will be sold. • However, this underpricing leads to the decreased probability of uninformed investors being allocated shares.