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Chapter 13 &14
Dealers and Bid-Ask
Spreads
What defines a dealer?
A broker acts as an agent for a customer,
representing customer orders in the market
(e.g., a real estate broker).
A dealer takes the other side of customer
trades (e.g., a used-car dealer).
Much of US securities regulation applies to
both brokers and dealers. The US Securities
and Exchange Commission (SEC) refers to
such people as “broker-dealers”. In fact,
broker and dealer functions are quite distinct.
Dealer quotes
Dealer spread vs. inside spread
 One-sided vs. two-sided market
 Firm vs. soft quotes
 Quoted vs. realized spread
 Best execution rule
 Order preferencing

The bid-ask spread
The bid-ask spread is the difference
between the ask price and the bid price
(quoted spread).
 The quoted spread gives an estimation of
the remuneration of the service provided by
dealers to traders. The remuneration
increases with the spread.
 Dealers make money by buying low and
selling high. They lose money when
market conditions lead them to buy at high
prices and sell at low prices.

The realized spread
The realized spread (difference between
the price at which dealers effectively buy
and sell their securities) is the true
remuneration of providing liquidity.
Dealer inventories

Inventories are positions that dealers have
on the security they trade. They may hold a
long position or a short position.

Target Inventories are positions that
dealers want to hold.

Dealers’ inventories are in balance when
they are near the dealers’ target levels and
out of balance otherwise.
Inventory risk
For risk averse dealers any difference
between inventories is costly.
 They then require compensation for
absorbing transitory mismatches in supply
and demand over time (transitory risk
premium).
 The larger the mismatch, the greater the risk
the dealer must assume and the greater the
compensation required by dealers.

Dealer inventory control
Dealers may act to control their inventories.
 As dealers’ prices affect other traders’
trading decisions, the placement of the
dealers’ bid-ask spread may be used to
control their inventories.
 When dealers’ inventories are below (above)
their target inventories, they must buy (sell)
the security.


Dealers increase their prices (bid and ask)
when they want to increase their inventory.
•

Higher bid prices encourage traders from selling
to them and higher ask prices discourage
traders from buying from them.
Dealers decrease their prices when they
want to decrease their inventory.
•
Lower bid prices discourage traders from selling
to dealers and lower ask prices encourage
traders from buying from the dealers.
Depth (size) control
Inventory risk

Diversifiable inventory risk
•
When future price changes are independent of
inventory imbalances
• Can be minimized by dealing in many
instruments

Adverse selection risk
•
When future price changes are inversely related
to inventory imbalances
• Arises when dealers trade with informed traders
Adverse selection losses
Informed traders buy when they think that
prices will rise and sell otherwise.
When dealers trade with informed traders,
• prices tend to fall after the dealers buy and
rise after the dealers sell (i.e., future price
changes are inversely related to inventory
imbalances)
• their realized spreads are often negative.
Dealer optimization problem

Dealers always gain from liquiditymotivated traders.

Dealers can balance the losses made on
informed trading with the profits made on
uninformed trading.
Dealer optimal responses when
sold to an informed trader
Raise ask price and lower ask size
 Raise bid price and increase bid size
 Buy from another trader at his ask price
 Buy a correlated instrument

Dealer optimal responses when
bought from an informed trader
Lower ask price and raise ask size
 Lower bid price and reduce bid size
 Sell to another trader at his bid price
 Sell a correlated instrument

Dealer optimal responses when the
next trader is an informed traders
Ask price = the best estimate of
fundamental value, conditional on the next
trader being a buyer. (regret-free price)
 Bid price = the best estimate of
fundamental value, conditional on the next
trader being a seller.
 Because dealers generally do not know
whether the next trader is well informed,
they use the probability that the next trader
is well informed.

Bid/ask spreads – Chapter 14
The spread is the compensation dealers
and limit order traders receive for offering
immediacy.
 The most important factor in order
placement decision (market vs. limit orders)
 The most important factor in dealer’s
liquidity provision decision
 The most important chapter of the book.

Dealer spreads
Monopoly dealers
 Low barriers to entry in most markets
 In many markets, dealers face competition
from public limit order traders
 Normal vs. economic profits – Dealers
earn only normal profits in competitive
dealer markets

Components of the spread


Transaction cost component
• Transitory spread component
• Covers the normal costs of doing business,
monopoly profits, risk premium
• Responsible for bid-ask bounce
Adverse selection component
• Compensate dealers for losses to informed
traders
• Permanent spread component
Two explanations for adverse
selection component

Information perspective
•

The difference in the value estimates that
dealers make conditional on the next trader
being a buyer or a seller
Accounting perspective
•
The portion of the spread that dealers must
quote to recover from uninformed traders
what they lose to informed traders
Definition and assumption
V = the unconditional value of a security
P = the probability that the next trader is an
informed trader
V+E = the value of the security when an
informed trader wants to buy
V-E = the value of the security when an
informed trader wants to sell
The next trader is equally likely to be a buyer
or a seller.
Information model
Conditional expectation of the security value given
that the next trader is a buyer
= (1-P)V + P(V+E) = V + PE
Conditional expectation of the security value given
that the next trader is a seller
= (1-P)V + P(V-E) = V - PE
Adverse selection component of the spread
= (V + PE) – (V - PE) = 2PE
Accounting model
Let B = the dealer’s bid price and A = the dealer’s ask price.
Conditional expectation of dealer profit given that the next
trader is a seller
= (1-P)(V-B) + P[(V-E) - B] = V - B – PE.
Conditional expectation of dealer profit given that the next
trader is a buyer
= (1-P)(A-V) + P[A - (V+E)] = A - V – PE.
Since the next trader is equally likely to be a buyer or a seller,
the expected dealer profit is
= ½(V – B – PE) + ½(A – V – PE) = ½(A – B) – PE.
Finally, setting ½(A – B) – PE = 0, we obtain A – B = 2PE.
Uninformed traders lose to
informed traders


When uninformed traders use limit orders
• Informed traders trade on either the other side
or the same side, depending on their private
information.
• Uninformed traders either regret trading or
regret not trading.
When uninformed traders use market orders
• Pay large spreads (due to informed trading)
Determinants of equilibrium spreads
in continuous order-driven markets




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

Information asymmetry among traders (+++)
Time to cancel limit orders (++)
Volatility (++)
Limit order management costs (+)
Value of trader time (+)
Differential commission between limit and
market orders
Trader risk aversion (+)
Cross-sectional determinants of
equilibrium spreads – Primary
Information asymmetry
 Volatility

•
•
•

Limit order option values increase with volatility
Inventory risks increase with volatility
Asymmetry problem increases with volatility
Utilitarian trading interest
•
•
Utilitarian traders are uninformed - lower adverse selection
High volume stocks have lower order processing costs, smaller
inventory risks, more limit order trading, smaller timing option
value, and more dealer competition
Cross-sectional determinants of
equilibrium spreads – Secondary

Information asymmetry proxies
Information disclosure rule, market condition reports,
analyst following, information vendors, diversified portfolios,
diversified companies, value vs. growth stocks, company age,
Insider trading rules, when material information is expected

Volatility proxies
Financial leverage, operating leverage, growth options

Utilitarian trading interest proxies
Trading activity, firm size, debt issue size, risk replication, volatility
Illustrative examples
(See also Chapter 21:
Liquidity and Transaction Cost
Measurement)
Issues



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Interplay of trading objectives and costs
Measuring trading costs in the overall framework:
the implementation shortfall
Explicit and implicit trading cost
Simple strategies (see Chapter 18 also)
Evaluating market orders
Quoted, effective, and realized spreads.
SEC Rule 11ac1-5
Evaluating limit orders
Costs/benefits of delay and nonexecution

Objective: what are we trying to accomplish?
e.g., Buy 1,000 shares of INTL by today’s close. (This
is a relatively clear objective.)

Strategies: what are the possible ways of meeting this
objective?
e.g., We could put in a market buy order right now.

Costs: What measure (metric) do we use for
evaluating strategies?
If I pursue strategy x, will I buy more cheaply on
average (than if I’d used a market order)?
How risky is strategy x? What are the best/worst
possible outcomes?

Among the set of strategies I’m considering, which
one has the best (for me) risk and return?
The implementation shortfall framework

Suppose that we observe a portfolio’s returns over time.

Can we decompose this “investment gains/losses” and “trading
gains/losses”?

Portfolio and trading decisions are (in practice) linked.
A responsible portfolio manager will take into account
trading costs in planning her strategies.
Trading objectives are often fuzzy. The trader needs to
know how badly the portfolio manager needs the trade
done (the cost of non-execution).

The implementation shortfall approach is a framework for the separation.

We assume a separation between investment and trading decisions.
“Long term” investment strategies are made by “portfolio
managers”. They make clear decisions about what to buy, sell
and hold.
These decisions are implemented by a trading desk.

We compare the performance of an actual portfolio (gain, loss or
return) to the performance of a hypothetical paper portfolio in which
all trades are made at notional (“benchmark”) prices. The cost is the
difference.
e.g., If the return on the paper portfolio is 10% and the return on
the actual portfolio is 9%, the implementation shortfall is 1%.

Interpretation: If we had a perfect trading desk, our trades could be
executed at the notional prices. Any divergence must be attributed to
trading (implementation) costs.

The framework tells us about costs at the portfolio level, but not about
the costs of individual trades.
Often, the framework leads to an obvious cost measurement.

A common benchmark price for trades is the midpoint of the bid and ask
quotes prevailing at the time the decision was made to invest.
bid-ask midpoint = “BAM”

Other candidate benchmarks (to be discussed later)
BAM subsequent to the trade
Average price for the day
Previous day’s closing price
The implementation shortfall: an example:

I buy 100 shares of ABC. When I decide to buy the shares, the market is
50 bid, 51 offered. I actually buy at 51.20, paying a $29 commission.
Cash outflow = 5,120 + 29 = 5,149

When I make the decision to sell, the market is 54 bid, 54.50 offered. I
actually sell at 54, paying a $29 commission.
Cash inflow = 5,400 – 29 = 5,371

My net cash flow is 5,371 – 5,149 = 222. [A return of 4.31%(= 222/5,149)]

In my paper portfolio, I buy and sell at the midpoint of the bid and ask
quotes at the time I decide to trade.

I buy 100 shares at 50.50 and sell at 54.25 = 375 (a 7.43% return)

The implementation shortfall is 375 – 222 = 153 (ignoring interest)

Alternatively, the implementation shortfall is 7.43% – 4.31% = 3.12%
Further analysis

The cost of a trade is explicit cost + implicit cost
Explicit cost: commission (net of any rebates of goods or services,
“soft dollars”)
Implicit cost: the cost of interacting with the market.
The initial purchase was made $0.70/sh above the BAM,
so the implicit cost = $70
The final sale was made $0.25/sh below the BAM,
so the implicit cost = $25

The implicit cost computed with respect to the BAM is the effective cost.

The effective cost is a useful measure for market orders.
Effective cost
The effective spread

Effective spread = 2 x effective cost
For the initial purchase, the effective spread
= 2 x $0.70 = $1.40 / share.
Intuition
The quoted (posted) spread is 51 – 50 = 1. If a
buyer pays $0.70 above the BAM and sells $0.70
below the BAM, they are effectively facing a bidask spread of $1.40.
Realized cost and realized spread
For executed trades, the realized cost is
the transaction price relative to the BAM at
some time subsequent to the trade.
 This impounds price movements after the
trade (including the price impact due to the
information in the trade).

Realized cost and realized spread
An interpretation of the realized cost

This cost can be interpreted as the profit realized
by the other (contra) side (e.g., dealer) of the
trade, assuming the contra side could lay off the
position at the new BAM.
Example
•
•
•
•
The dealer sells to the customer at 100.09.
Five minutes later, the market is bid 100.02, 100.12
offered (BAM = (100.02+100.12)/2 = 100.07.)
The realized cost is 0.02.
This would be the dealer’s profit if he could reverse
the trade (purchase the stock) at the subsequent BAM.
Summary
Quoted Spread = (Ask – Bid)
= [(Ask – M) + (M – Bid)],
where
M = (1/2)(Ask + Bid)
= the midpoint of the bid and ask.
Effective Spread = 2Abs(T – M) = 2D(T – M)
= 2 x Effective Cost,
where
T = the transaction price,
D = +1 for customer buy order and
-1 for customer sell order.
Price Impact = D(M+ – M).
Price Impact measures decreases in M following
customer sells and increases in asset value
following customer buys, which reflect the
market’s assessment of the private information the
trades convey. Such price moves constitutes a
cost to market makers, who buy prior to price
decreases and sell prior to price increases.
Realized Spread = Effective Spread - Price Impact
= 2D(T – M) - 2D(M+ – M) = 2D(T - M+)
= 2 x Realized Cost
= Market making revenue, net of losses to
better-informed traders
The effective cost of a sequence of
market orders




Oftentimes traders break up large orders into smaller ones,
and feed them to the market over time.
In a sequence of orders, the cumulative price impact
means that later orders will trade at worse prices than
early ones.
For a buy sequence, the effective cost is:
(volume weighted average purchase price) –
(BAM prevailing at time of trading decision)
Suppose the BAM is 10.00. We buy 100 shares at 10.10,
500 shares at 10.25 and 400 shares at 10.50.
•
•
The vol wtd average purchase price is 10.335/share.
The effective cost is $0.335 per share.
Inferring impact costs from effective
and realized spreads




Suppose the BAM = $10.00. We want to buy 1,000
shares.
The effective cost of one 1,000 share order is $0.30/sh.
If we split the order into two 500 share trades, we pay
500 x ($10.00 + $0.20) + 500 x ($10.00 + $0.35)
= $10,275
Relative to the initial midpoint, the trading cost is 275
($0.275/sh)
Measuring market impact


Statistical tools from time series analysis attempt
to correlate orders with subsequent price
movements. See Chung et al. (2004)
General considerations.
•
•
•
•
Market impact is not the same for all orders in all
markets.
Large orders have higher impact than smaller orders.
Orders perceived as originating from “smart” traders
will have high impact.
Orders that execute in markets that cater to retail
investors will have low impact.
Measuring the cost of limit orders



For a single limit order there are no summary
measures comparable to effective and realized
spreads.
Market orders always execute. The only issue is
price.
Limit orders often don’t execute.
•
•

How should we account for an order that wasn’t filled?
What is the cost of a delayed execution?
It is possible to measure the effective cost of
strategies that use limit orders if the strategy
ensures an (eventual) execution.
The cost of a first-limit-then-market
strategy


Situation: the trader must fill an order by some pre-set time (like the
close of trading).
Strategy
•
•
First use limit orders at (or away from) the market.
If a limit order doesn’t execute within some pre-set time, replace it with a
more aggressively priced order.
• Repeat.
• If no limit orders have been filled by the end of the day, switch to a market
order.

Example: It’s 10am. I have to buy 100 shares by today’s close. The
market is 20.50 bid 20.60 offered.
•
•
•
I put in a buy limit order at 20.50.
If the order hasn’t executed in 30 minutes, I’ll cancel and replace with a
buy limit order priced at 20.51, etc.
If no fill by the close, I’ll cancel the limit order and submit a market order.
Adverse selection models I
and II
&
Components of bid-ask
spreads
(see lecture notes)