Product × Finance × AI: Financial Products in the Age of AIPart One From 0 to 1中文
Chapter 9

Prices carry everyone's informationInformation, prices and the zero-sum game

Once the market square opened, someone spotted an opportunity. The man who lived on the hill always saw the ships coming home first, so he bought ship shares before the news spread and sold them once everyone else knew. When he bought, the price moved; others saw the price moving and guessed there might be good news. Prices thus pool information scattered among many people: each person knows only a little, but the price combines what all of them know. Because the price already reflects what people know, how it changes from here depends only on what nobody knows yet, and so it is hard to predict. Market makers pay a cost for trading with the informed, gathering information is costly, and the gains from information are zero-sum among traders.

1. The man on the hill sees the ships first

One family in the village lives on the hill, and whenever a ship returns from far away, he is always the first to see it. Before the news reaches the village gate, he hurries to the market square and buys ship shares: if the ship comes home safely, the shares will rise in value. The more he buys, the more the market maker sells, and the quote rises with it. By the time the ship docks and the whole village knows, the price has already risen all the way; he sells and pockets the difference.

Today's counterpart. Trading securities on material non-public information is defined as insider trading in most markets today and is prohibited by law. Getting ahead by analysing public information faster and more carefully, however, remains a way that many traders compete.

The man on the hill sees the ship first

On day 2 the man on the hill sees the ship return safely, and the shares' value rises from 10 portions to 12; the news reaches the whole village only on day 8. Drag how hard he buys to see how much the price has risen before the news is public, and how much he earns.

True value of the sharesPrice in the market squareThe difference he earns

Illustrative: seeing steady buy orders, the market maker raises his quote, each day moving the price part of the way towards the true value; the share of the gap closed each day rises with how hard he buys.

2. Prices pool scattered information

The man on the hill is only one example. Every villager knows something others do not: the fisherman knows the recent winds, the carpenter knows the state of the ships' repairs, the merchant knows the price of salt on other islands. No one knows everything, but each person buys or sells according to what they know, and the price pulls these scraps of information together. Someone who sees the price rise does not need to know whether the cause is the wind, the repairs or the salt price elsewhere; by adjusting their own buying and selling to the price, they are in effect using what others know. Hayek (1945) called this role of prices a mechanism for communicating information: people need not know why something has become scarce; seeing its price rise, they economize on it.

A well-known example comes from Galton (1907). At a country fair, 787 people entered a contest to guess the weight of an ox after slaughter. Individual guesses were far apart, yet the median of all the guesses was within one per cent of the actual weight. The many individual errors cancelled each other out, and the pooled guess was more accurate than the great majority of the individual ones.

Today's counterpart. A company's share price combines the scattered information held separately by analysts, customers, suppliers and competitors.

Many guesses pooled are more accurate

Each person guesses the weight of an ox from their own experience, and any one guess may be far off. Drag the number of people guessing to see how close the median of all guesses comes to the true weight.

True weightMedian of all guesses

Illustrative: each guess equals the true weight plus a random error of about one tenth of the true weight; the numbers here are simulated, not Galton's (1907) original data. Of the 787 guesses Galton recorded, the median was within one per cent of the actual weight.

3. Why prices are hard to predict

If everyone knew the ship would return tomorrow, people would rush to buy today, the price would rise all the way today, and it would not rise again tomorrow for the same reason. Whatever can be foreseen is already reflected in today's price; tomorrow's change can come only from news that nobody has today, and whether that news will be good or bad cannot be known in advance. So in a market where people anticipate correctly, price changes cannot be predicted.

Once a predictable pattern is discovered, it gets exploited, and the exploitation makes it disappear. Suppose the ships always return after the harvest festival and the shares always rise afterwards. People will then buy before the festival, the rise moves earlier, to before the festival, then earlier still, until the pattern no longer exists.

Today's counterpart. Positive comments about individual stocks on television are typically fully reflected in the price within about a minute (Busse and Green, 2002). McLean and Pontiff (2016) examined 97 stock-selection patterns found in academic research; after the papers were published, the returns of portfolios built on these patterns fell by an average of 58%.

After a pattern is discovered

The ships always return after the harvest festival, and the shares always rise afterwards. Drag how many people discover this pattern and buy early to see how the price path over the year changes.

Illustrative: the value rises by 2 portions in month 9 (after the harvest festival). The more people buy early, the earlier and more gradual the rise; when everyone knows, the rise is spread evenly across the year, and there is no longer a predictable jump after the festival.

4. Market makers and the informed

A market maker quotes prices to buy and sell at any time, but does not know whether the person coming to trade already knows something. Trading with the uninformed, he earns the spread; trading with the informed, he is bound to lose, because the informed buy only when the price is too low and sell only when it is too high. To stay in business, the market maker must use the spread earned from the uninformed to cover his losses to the informed, so the more informed traders there are, the wider the spread. The uninformed therefore pay a little in every trade for the existence of the informed. Glosten and Milgrom (1985) described this mechanism in a model.

Today's counterpart. Bid-ask spreads on stocks often widen before major announcements, or when the market is full of rumours.

More informed traders, wider spreads

A ship share may be worth 8 portions or 12, with equal odds. The informed buy only when it is worth 12 and sell only when it is worth 8; the uninformed buy and sell at random. Drag the share of informed traders among those who come to trade to see the quotes at which the market maker breaks even.

Bid
Ask

Illustrative: the market maker's ask equals the share's average value given that someone comes to buy, and the bid equals its average value given that someone comes to sell; spread = 4 × share of informed traders (a simplified case of Glosten and Milgrom, 1985).

5. Gathering information is costly

The man on the hill must keep watch every day, the fisherman must go to sea, and the merchant must travel between the islands: gathering information costs something. If prices already reflected all information, no one would be willing to pay that cost, because knowing would earn them nothing. But if no one gathered information, prices would reflect none. Neither extreme can hold, so prices cannot fully reflect all information. The market settles where the share of informed traders is just large enough that the benefit of gathering information equals its cost: prices reflect most of the information but leave a little room to compensate those who paid. When more people dig for news, prices carry more information, each person gains less from digging, and some stop; when fewer dig, prices carry less, and digging becomes worthwhile again.

Today's counterpart. Professional investment firms devote substantial resources to research; the cheaper research becomes and the more people do it, the less each of them gains from it.

How many will dig for news

The more people dig for news, the earlier the price reflects it and the less each of them can earn. Drag the cost of digging for news once to see where the market settles: how many people dig, and how much of the news the price reflects in advance.

What each informed trader earns from the newsCost of digging for news once

Illustrative: when the informed make up a share f, the share of the news reflected in the price in advance is f ÷ (f + 0.15), and each informed trader earns 1.5 × (1 − share reflected in advance) ÷ f. Where the two lines cross, digging for news just breaks even, and the market settles there (Grossman and Stiglitz, 1980).

6. Information advantage is zero-sum

What the informed trader earns is exactly what the people trading with him lose. Taking all traders together, before costs, whenever someone earns more, someone else earns less; after the costs of gathering information and trading, the group as a whole loses. By staying out of this guessing game and holding all the ship shares in proportion, one gets the average result of all the ships without paying these costs.

This conclusion uses nothing but arithmetic. Every ship share in the village is held either by people who hold everything in proportion or by people who actively pick. The former get exactly the average of all ship shares. The two groups together must also get the average of all ship shares, so before costs the active pickers as a group can only get the average too. They pay extra for digging up news and for trading; after those costs, as a group they must fall behind.

Today's counterpart. Index funds hold all stocks in proportion to their market shares; they do no research and no picking, and their fees are very low. Their very existence is a response to the zero-sum nature of competition over information.

Information advantage is zero-sum

Add up everyone's gains and losses for a year. Drag the share of uninformed people who trade frequently and the cost of each trade to see each group's gains and losses, and what remains once they are added together.

Illustrative: the informed earn 10 portions from the uninformed who trade frequently; passive holders, who do not trade, get only the fleet's average return and stay out of these gains and losses. Sharpe (1991): before costs, active investors as a group earn the same as passive ones; after costs, active investors as a group must fall behind.

7. Informed and uninformed: Civilization Simulator, version 9

The simulator unlocks the rule "Information in prices". Each year a new piece of news about the fleet's prospects appears. Those who pay to dig for it learn it first; everyone else must wait until it becomes public. You can adjust the share of people who dig for news, the cost of digging, and how many of the uninformed still trade frequently, and see how much of the news the price reflects in advance, along with the cumulative gains and losses of three groups over twenty years.

Civilization Simulator · Chapter 9: informed and uninformed

Each year a new piece of news about the fleet's prospects appears. Those who pay to dig for it learn it first; everyone else must wait until it is public. Adjust the three settings to see the cumulative gains and losses of three groups over twenty years.

MoneyInsuranceBankSharesMarketInformation in pricesDelegation · Ch. 10
People who dig for newsUninformed people who trade frequentlyPassive holders

Illustrative model: forty households. The vertical axis shows each person's cumulative gain or loss, in portions, relative to getting only the fleet's average return. The more people dig for news, the more the price reflects it before it is public (a share of f ÷ (f + 0.15)); those who dig earn the part not yet reflected from the uninformed who trade frequently, and both groups also pay a cost of 0.05 portions per trade. Passive holders do not trade, and their gain or loss stays at zero.

8. What this step leaves open

Prices pool information, and they also make information advantage costly and zero-sum. New questions follow:

  1. Ordinary people have neither the time nor the expertise. Should they dig for news and judge for themselves, or hand the job to people who specialize in it?
  2. People who dig for news and trade on others' behalf may not do their duty. Whether they are really acting for the principal is hard for the principal to know.
  3. Inside information and deception. Some trade on information others cannot possibly have; some deliberately spread false news. Rules and enforcement are needed.
  4. People make their own mistakes. Even knowing that passive holding is better, people still chase rising prices, sell into falls and trade too often.

What this step leaves open

Four questions still unresolved once prices pool information. Select a question to see the assumption it rests on.

Informed and uninformedPrices, spreads and the zero-sum game

9. Implications for products

Market data, research, trading and index products are all tied to the mechanisms in this chapter. Three implications follow. First, predicting prices should not be the promise. Most information that is already public is already reflected in prices; if a product claims it can predict prices consistently, ask where its information comes from and why others do not have it. Second, competition over information is zero-sum and, after costs, negative for the group as a whole; lowering users' trading and research costs and helping them avoid unnecessary trades is value that can last. Third, the cheaper research becomes and the more people do it, the smaller the advantage research brings; this is especially worth remembering as analysis tools become widespread.

Chapter summary: information in prices

Four conclusions, each corresponding to one mechanism in this chapter.

PoolingPrices pool scattered information

Each person knows only a little, but the price combines everyone; many people's errors cancel out.

Hard to predictWhat can be foreseen is already in the price

Price changes come only from new news; once a pattern is exploited, the exploitation makes it disappear.

CostThe informed make everyone pay a spread

What the market maker loses to the informed, he must recover from the uninformed.

Zero-sumAfter costs, information advantage is negative overall

What the informed earn is what frequent traders lose; holding everything passively stays out of the guessing game.

References