Lecture 3 Secondary Equity Markets - I

Trading motives Is it a zero-sum game? Building portfolio for a long run. Trading on information. Short-term speculation. Liquidity provision.

Secondary Market Types Immediacy Provision: –Dealers – all receive immediacy; all pay the spread; –Call auction – none receive immediacy – all wait. –Limit order book – patient supply, impatient demand immediacy. The importance of choice. Electronic vs. Trading Floor. Multilateral vs. Bilateral. Price priority and time priority.

Orders Market order – specifies the quantity, but not the price. Demands immediacy. Limit order – specifies the quantity as well as the price. Usually supplies immediacy. Marketable (executable) limit order – demands immediacy, but not at any price. Orders with conditions.

Limit Order Book (Quotations) 200 1, , ,600 3, PRICES QUANTITIES

Market Buy Order for 500 Shares 200 1, , ,600 3, PRICES QUANTITIES 200 1, ,200 1,300 3,

Limit Buy Orders: 1,000 at 20 and 500 at , ,200 1,300 3, PRICES QUANTITIES 200 1, , ,300 3,

Market Sell Order for 3, PRICES QUANTITIES 200 1, , ,300 3, , ,300 3,

Limit Buy Order: 1,500 at PRICES QUANTITIES 200 1, ,300 3, , ,

Dealer markets Previous example – could it have been a dealer market? Some changes: –Quotes instead of limit orders; –Standard size of a quote; –Quotes are updated: one is removed another appears –Other than that – it would look very similar…

INET An example of a limit order book. Formerly Island, owned by Instinet. Recently purchased by NASDAQ. Pure Limit Order Book without intermediaries..

Dealer markets - Overview Inventory model – risk averse dealer provides immediacy to all, but bears the risk. Asymmetric information model – risk- neutral dealer faces better informed traders. Other aspects of competition. Examples.

Inventory model Dealer stands ready to provide immediacy to all clients by quoting prices and supplying the stocks from his inventory: The dealer takes into account: –His risk tolerance (define); –His inventory; –Trade size; –Competition.

Let’s play another game You are a dealer in a particular security. Write down the last 4 digits of your phone number. Your inventory is: After the round of trading each share will pay either $80 or $120 with equal probabilities. Last 4 digits of your phone number Inventory Even and > 5,00 Long 1,000 shares Even and 0 Long 250 shares Odd and 0 Short 250 shares Odd and > 5,000 Short 1,000 shares

Rules (cont.) In a few seconds a market order will arrive; it could be a buy or a sell order for 500 shares. You have to quote a Bid and an Ask price at which you are willing to make these trades. You compete with your classmates for these trades. All of you must set your quotes independently. Go ahead, and quote!

Formal Model Risk averse dealer with inventory Y. Perfectly competitive market (simplification) – derive break-even prices. The value of security, V, is a random variable with Mean  and Variance  . Mean - variance preferences (W – wealth): E(W) – 0.5zVar(W) Trade size is X.

Dealer choice: Perfect competition ensures that the dealer is indifferent between buying (selling) and not trading. The action determines the risk. We derive the Bid and the Ask price separately, then compute the Dealer Spread. Discussion.

Bid Price No action: Y  0.5zY 2  2. Buy at the Bid, B, to increase the inventory by X: Y  + (  - B)X  0.5z(Y + X) 2  2 If indifferent, then the maximal bid price must be: B max  z  2 Y  0.5z  2 X.

Ask Price and Spread No action: Y  0.5zY 2  2. Sell at the Ask, A, to increase the inventory by X: Y  + (A -  )X  0.5z(Y - X) 2  2 If indifferent, then the bid price must be: A min =  z  2 Y  0.5z  2 X.

Dealer Spread The same dealer quotes two different prices: A min =  z  2 Y  0.5z  2 X; B max  z  2 Y  0.5z  2 X. The dealer’s spread is: A min - B max = z  2 X.

Dealer Spread B max  A min. B max  A min. Zero inventory Negative inventory Positive inventory B max  A min.

Is this possible? B max A min  Very large negative inventory Very large positive inventory  B max A min

Market spread B 1 max  A 1 min Dealer 1 - Positive inventory Dealer 2 - Negative inventory B 2 max A 2 min Market Spread

Discussion Why isn’t the spread symmetric around the mean value? When will we ever observe it as a Market Spread? What if the volume depends on the spread? Alternative competition models. The basic intuition remains: if traders demand liquidity, they impose costs on the dealer, and have to pay a premium to cover these costs.

Asymmetric Information Risk neutral dealer is willing to provide liquidity from his inventory: what are his considerations? –Risk aversion? - No –Competition? - Yes. –Inventory size? - No –Trade size? - No –Information? - Yes

Refresher When somebody has private information, they will use it to choose actions. While the others cannot observe the information, they can observe the action, thus should infer the information from the action. This assumes rationality on the part of the informed party.

Formal Model Risk neutral dealer, who has to quote Bid and Ask prices. Perfectly competitive market (simplification). The value of security, V, is a random variable, which can be either V H with probability  or V L, with probability (1-  ): V A = V H *  + V L *(1-  ). The trader that submits a market order knows the realized value of V with probability 

Dealer choice: A trade may signal information, in which case the dealer will lose money on it. Otherwise the trade is profitable. If he is willing to quote prices to all, he must on average break even, thus he has to charge informationless traders for the losses caused by the informed.

Prices A min = V A + (V H - V A )  V A B max = V A - (V A - V L )  V A These prices take into account the information imbedded in the trades. They yield zero profits to the dealer. The spread S = (V H - V L ) is not  symmetric around the V A. Why?

Conclusions Inventory models – spread exists to cover the cost of risk imposed on the dealer by the demanders of immediacy. Information models – the mainstream – the spread protects the dealer from the better informed traders. The spread covers dealer’s “cost of ignorance”. In both cases the spread may impede trading. Insider trading prohibition.