Official statements and the order book

Six statements about the model; the mapping to markets around official statements is a reconstruction R, and none estimates the extent of informed trading before any real statement.

• The spread is the price of leakage, and the uninformed pay it. A dealer who breaks even quotes $\frac{5}{8}$ and $\frac{3}{8}$ around a prior of $\frac{1}{2}$ when a quarter of orders are informed: the spread, $\frac{1}{4}$, equals the informed share. An informed order gains $\frac{3}{8}$ in expectation and an uninformed order loses $\frac{1}{8}$. Unlike Model F5, where the sponsor pays the insider, every unit of the informed gain is a loss of someone who traded at the wider spread D [Proposition 10.15 (p. 422)].

• Credibility and surprise are what leaks. If the market believes the statement only to accuracy $a=\frac{3}{4}$, spread and gain halve ($\frac{1}{8}$ and $\frac{3}{16}$); if a committed policy rule makes the statement predictable (prior $\frac{1}{10}$), the informed gain falls from $\frac{3}{8}$ to $\frac{9}{64}$. This is Chapter 4's commitment read from the side of the market (Proposition 4.7 (p. 171)) D [Proposition 10.15 (p. 422)].

• A small run-up is not evidence of no leakage. When the statement settles the contract ($a=1$), the share of its price move that occurs before it is exactly the share of the outcome's variance that the pre-statement price has resolved: ${\mu }^2=\frac{1}{16}$ with one order, although a quarter of the flow is informed, and $\frac{2}{17}$ with two. An event study that finds a modest pre-announcement drift has measured resolution, not the informed share; the price before the statement is calibrated throughout, and, as in Model F5, only resolution moves D [Proposition 10.16 (p. 423)].

• A sampled audit finds little, and a flag is not a finding. Sampling one order in ten finds an informed order in a two-order window with probability $\frac{79}{1600}$, and over twenty orders with probability $0.3973$. Surveillance that flags informed orders with probability $\frac{4}{5}$ and uninformed ones with probability $\frac{1}{20}$ is right about a flag $\frac{16}{19}$ of the time when a quarter of orders are informed and $\frac{16}{115}$ of the time when one in a hundred is. Turnover concentrated before an announcement is at most a flag in this sense, and what a flag is worth depends on the share of informed orders and on the flag's error rates, which public data do not reveal: hence item 1's “an audit question, not an identification” D [Proposition 10.17 (p. 424)].

• Penalties proportional to gain set a threshold that the market does not move. If an identified informed trader forfeits its gain and pays $k$ times it, trading on any positive gain in the model's single order slot is deterred exactly when the sampling rate is at least $1/(1+k)$: the threshold does not depend on the gain's size, so no spread, prior or credibility behind that gain moves it, and a zero gain is never traded on. A fixed penalty acts through the spread instead: the informed share falls from $\frac{1}{2}$ to zero at $s=\frac{2}{15}$ D [Proposition 10.18 (p. 424); Table 10.3 (p. 409)].

• The enforcement record is not a measure of informed trading. Under the fixed penalty, identifications per order are $\frac{1}{40}$ both at $s=\frac{1}{20}$ and at $s=\frac{1}{10}$, while the informed share is $\frac{1}{2}$ in the first case and $\frac{1}{4}$ in the second. Counting cases cannot tell more informed trading under weak surveillance from less under strong: Chapter 11's deterrence that removes its own evidence (Proposition 11.9 (p. 459)), in the order book D [Proposition 10.18 (p. 424)].

Orders are of one unit; in Kyle's setting an informed trader chooses the size and timing of its orders to hide among uninformed flow (Kyle 1985), a choice Model F6 holds fixed. Allowing it changes the relation between order flow and price discovery, and how the run-up then compares with Model F6's would need a matched comparison — a common horizon, a common volume measure and a parameter map — which the book does not make. Spreads also widen for reasons other than adverse selection, such as inventory risk and volatility after a shock, so a widening cannot be read as an informed share without a model that separates them. The statement is exogenous; a speaker who chooses content or timing makes the price a signal inside a game (Model F5's stake, Chapter 4's commitment). The model's “informed trader” is not the legal notion: a well-informed analyst is informed and breaks no rule, and a legal identification needs a link between an account and information held in breach of a duty. Penalties are stylised, and one contract is priced at a time, while a real statement moves many.