Product × Finance × AI: Financial Products in the Age of AIPart One From 0 to 1中文
Chapter 8

Securities must be saleableMarkets, auctions and market making

Shares let many people invest together in a ship, but an investor may urgently need grain at any time. To sell a share, they must first find someone willing to buy, then agree on a price. Asking house by house takes time and effort, and the more urgent the need, the lower the price they must accept. When people agree to gather in the same place at set times, buyers and sellers find each other easily, and the more people come, the easier it gets. Put everyone's quotes together and you can find the price at which the most trades take place. When someone stands ready to buy and sell at any time, sellers need not wait; the cost is the spread between the buying and selling prices. Liquidity thus acquires a price: the harder something is to sell, the higher the return buyers demand.

1. Wanting to sell a share and finding no buyer

A household in the village holds a share in a ship. The ship's prospects are good, but this year someone in the family has fallen ill, and the household urgently needs grain and has to sell its share. It goes from door to door: some households have no spare grain, some do not want a share in a ship, some offer too little. One house after another, several days pass and the share is still unsold. The more urgent the need, the lower the price the household has to accept.

Shares solve the problem of financing large projects, but they bring a new one: whether a share can be sold in time and at a reasonable price.

Today's counterpart. Equity in private companies, unlisted debt and property often take a long time to sell, and a quick sale requires a steep discount.

The more urgent the sale, the lower the price

A ship share is worth 10 portions of grain on its prospects. The seller can ask three households a day; each has a 15% chance of wanting to buy, offering between 6 and 12 portions. Drag the most days the seller can wait and see the average price obtained by selling in the best way.

Illustrative: if the share is still unsold when time runs out, it can only be dumped for 5 portions to anyone willing to take it. The best approach is to compare each day’s offer with the expected gain from waiting longer and sell if the offer is higher (computed by backward induction).

2. A fixed place: the market square

Suppose the village agrees that on the first day of each month, everyone who wants to buy or sell shares comes to the big tree at the edge of the village. Things change. Sellers no longer need to go from door to door, and buyers know where to look. The more people come, the easier it is to find a counterparty willing to trade at a reasonable price; and the more people come, the more reason there is to come. Trading therefore gathers in a few central places.

After the Dutch East India Company issued its shares in 1602, merchants in Amsterdam began trading them within days, and a custom of trading shares at a fixed place and fixed times gradually took shape (Petram, 2014).

Today's counterpart. A stock exchange brings buyers and sellers from across a country, and even across the world, into the same market; trading in any one stock tends to be concentrated on one or two venues.

The more people come, the easier it is to get a good price

A villager brings a ship share to the market square. Each buyer will pay between 6 and 14 portions. Drag the number of buyers who come and see the chance that he sells for at least 10 portions, and the average of the highest bid.

Chance of selling for at least 10
Average highest bid

Illustrative: buyers’ prices are independent and uniformly distributed between 6 and 14 portions; the share goes to the highest bidder. Average highest bid = 6 + 8 × buyers ÷ (buyers + 1).

3. How the price is set: the call auction

Once everyone has arrived, a price still has to be set. Each would-be buyer has a highest price they will pay, and each would-be seller a lowest price they will accept. Rank all buyers' bids from highest to lowest and all sellers' asks from lowest to highest; where the two lines cross is the price at which the most trades take place. Above that price, too few people are willing to buy; below it, too few are willing to sell. Trading at that price also maximizes the combined gains that buyers and sellers get from trade.

Smith (1962) had students play buyers and sellers in the laboratory, each knowing only their own price. Trading prices and volumes soon came close to the levels the theory predicts. Participants did not need to know anyone else's price; bringing the quotes together was enough to find it.

Today's counterpart. Stock exchanges use call auctions at the open and the close: quotes over a period are pooled and matched in one go at the price that maximizes the volume traded.

Call auction: the price at which the most trades take place

Eight buyers each have a highest price they will pay, and eight sellers each a lowest price they will accept. Drag the trading price and see how many trades take place, and the combined gains buyers and sellers get from trade.

Buyers’ bids, high to lowSellers’ asks, low to highGains from trade

Illustrative: at a given price, buyers bidding at least that much will buy and sellers asking no more than that will sell; the number of trades is the smaller of the two. Combined gains are the sum, over the trades made, of each buyer’s bid minus the seller’s ask.

4. Selling at any time: the market maker and the spread

The market square opens only on the first of the month, and those in a hurry cannot wait. A well-off household in the village steps forward: at any time, it will buy a ship share whose prospects are worth 10 portions for 9.6 portions of grain, and sell one for 10.4. Anyone who wants to sell can sell to it at any time, and anyone who wants to buy can buy from it at any time. It earns the 0.8-portion difference between buying and selling, and bears the risk that the price falls while it holds shares in stock.

A seller in a hurry is in fact choosing between two courses. Willing to wait, they can wait for the first of the month and may meet a buyer who offers more. Unwilling to wait, they sell to this household for 9.6 portions and give up the difference to the party standing ready to trade. The spread is therefore the price paid for trading immediately. How much the household charges depends on how long it expects to hold shares and how much the price may move while it does. The more often shares change hands, the shorter it holds them; the steadier the price, the less risk it bears, and the narrower the spread. If other households are also willing to buy and sell at any time and compete with one another, the spread is pushed down to just what covers these costs.

Today's counterpart. Securities are quoted at a bid and an ask, and the difference between them is the spread; the spread is narrow for actively traded large-company stocks and wider for thinly traded small companies.

The market maker: the spread in exchange for immediacy

The market maker is willing to buy and to sell at any time. Drag the volatility of the share price and the number of trades a day, and see how wide a spread he will quote.

BidSellers can sell to him at any time
AskBuyers can buy from him at any time

Illustrative: spread = fixed cost per trade + compensation for inventory risk; inventory risk rises with price volatility and falls as trading becomes more frequent (shares held can soon be passed on). The value on prospects is taken as 10 portions.

5. Liquidity has a price

Since selling costs either time or the spread, buyers deciding what to buy will take this cost into account. Two ships have the same prospects; shares in one can be sold at any time for a small spread, while shares in the other take a long wait and a large discount to sell. Buyers will pay only a lower price for the second, which is to say they demand a higher return.

How much higher depends on who is buying. A household that has to sell once a year, giving up a discount each time, finds hard-to-sell shares very costly; another household plans to hold for twenty years and sells only once in that time, so the same discount spread over each year is small. Hard-to-sell shares therefore flow to those who plan to hold for the long term, and easy-to-sell shares stay with those who often need to buy and sell. Precisely because hard-to-sell shares are held by those who rarely trade, when trading costs rise further, their return need not rise by as much.

Today's counterpart. Illiquid assets, such as private investments locked up for many years, usually have to offer higher returns; investors who plan to hold for the long term can treat liquidity as something they can sell, in exchange for this compensation.

Liquidity has a price

Two ships have the same prospects, but their shares have different spreads. Drag the spread and the number of times a year holders trade, and see how much extra return the hard-to-sell ship must offer before buyers will hold it.

Easy-to-sell ship
Hard-to-sell ship

Illustrative: the easy-to-sell ship’s spread is taken as 0.2%, and the two ships are in balance when their returns after trading costs are equal; the extra return required each year is roughly spread × trades per year. Amihud and Mendelson (1986) also show that the longer an investor’s holding period, the better suited they are to holding hard-to-sell assets.

6. Brokers: finding counterparties for others

There is another kind of person who neither holds shares in stock nor sets prices, but only finds counterparties for others. He knows who wants to sell and who wants to buy, brings the two sides together, and takes a small commission once the trade is done. A broker differs from a market maker: the market maker stands on the other side of the trade itself, while the broker only searches on others' behalf. A broker's value comes from the information he holds and the time he spends, which is exactly what a household lacks when it goes from door to door on its own.

Searching, comparing and bargaining are, at bottom, labour that takes time and thought; the cheaper this labour becomes, the more the form of brokerage will change.

Today's counterpart. Securities brokers accept orders from clients, send them to trading venues for execution and charge a commission; they also choose among venues to get clients a better execution price.

Three ways to sell

You need to sell, in a hurry, a ship share worth 10 portions on its prospects. Select a way to sell and compare how long you wait, how much you end up with, and who is paid the cost.

Illustrative: searching yourself assumes waiting at most five days; the broker finds a buyer within a day and charges a 2% commission; the market maker’s bid is below the value on prospects by half the spread.

7. The market at the edge of the village: Civilization Simulator, version 8

The simulator unlocks the "Market" rule. Forty households in the village hold ship shares; each year some urgently need grain and must sell, and some have grain to spare and want to buy. You can choose to have each household search on its own, hold a regular market day, or hold a market day plus a market maker. Then watch how many of those in a hurry to sell manage to sell in time, and how large a discount they give up on average.

Civilization Simulator · Chapter 8: the market at the edge of the village

Forty households hold ship shares; each year some urgently need grain and must sell, and some have grain to spare and want to buy. The three lines show the average price received by those in a hurry to sell under each household searching on its own, a regular market day, and a market day plus a market maker; select one for details.

CommitmentMoneyInsuranceBankSharesMarketInformation in prices · Ch. 9
Search aloneMarket dayMarket day + market maker

Illustrative model: each ship share is worth 10 portions on its prospects. Each year about 15% of households urgently need grain and must sell; they can wait at most five days, and if no buyer comes they dump the share for 5 portions. Searching alone: the seller asks three households a day; each household met has an even chance of being interested in the ship and offers between 6 and 12 portions. Market day: held every five days, with everyone who wants to sell or buy taking part in a call auction; buyers will pay 8 to 12 portions, and when buyers are too few, the extra sellers must dump their shares. Market maker: buys at any time at the value on prospects minus half the spread, and the more trades, the narrower the spread; when sellers outnumber buyers, the shares he holds are hard to pass on, and he lowers his bid further.

8. What this step leaves open

With markets, shares can be sold at any time and prices are set by many people together, but new problems follow:

  1. Prices contain information. Someone learns first that the ship has docked safely and buys ahead of everyone else; does the price reflect everything everyone knows?
  2. Those who know more take advantage. The market maker does not know whether a buyer has already heard good news; trading with the informed is a sure loss, so the spread has to cover that loss too.
  3. Ordinary people do not have time to watch the market. Deciding when to buy, and which ship to buy, takes time and expertise.
  4. Who guarantees the rules of the market? Someone has to be responsible for quotes being genuine and for trades being settled as agreed.

What this step leaves open

Four new problems that appear once there are markets. Select one to see the assumption it hides.

The village marketAuctions, market making and brokerage

9. Implications for products

Securities trading, brokerage and market making all rest on the mechanisms of this chapter. Three implications follow. First, liquidity has a price, paid in waiting time, the spread and discounts; whether a product is easy to sell matters as much as its expected return, and both should be made clear in advance. Second, trading gathers where it is concentrated, and the quality of execution depends on how many buyers and sellers are there; where an order is sent for execution is itself a service that requires professional judgement. Third, searching, comparing and bargaining are labour; once the cost of this labour falls, the division of work between brokers and market makers will change.

Chapter summary: markets

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

ConcentrationThe more people, the easier the match

Trading gathers in a few central places, and the quality of execution depends on the buyers and sellers there.

AuctionsPooled quotes find the price with the most trades

Each person need only state their own price, and a call auction finds the price that maximizes the gains.

Market making and the spreadThe spread is the price of immediacy

The market maker bears inventory risk; the more frequent the trading and the steadier the price, the narrower the spread.

LiquidityHard-to-sell assets must offer higher returns

Liquidity shows up as waiting, the spread and discounts; searching and bargaining are labour, and their cost shapes the form of brokerage.

References