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**Dealers and Bid-Ask Spreads**

Chapter 13 &14 Dealers and Bid-Ask Spreads

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**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.

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**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

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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.

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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.

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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.

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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.

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**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.

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**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.

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Depth (size) control

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**Inventory risk Diversifiable inventory risk Adverse selection 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

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**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.

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**Dealer optimization problem**

Dealers always gain from liquidity-motivated traders. Dealers can balance the losses made on informed trading with the profits made on uninformed trading.

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**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

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**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

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**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.

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**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.

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**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

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**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

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**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

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**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.

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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

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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.

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**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) d

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**Determinants of equilibrium spreads in continuous order-driven markets**

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 (+)

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**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

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**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

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**Illustrative examples**

(See also Chapter 21: Liquidity and Transaction Cost Measurement)

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**Issues 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 non- execution

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**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?

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**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.

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**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.

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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

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**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, = 5,149 When I make the decision to sell, the market is 54 bid, 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 and sell at = 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%

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**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.

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Effective cost

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**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 bid-ask spread of $1.40.

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**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).

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**Realized cost and realized spread**

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**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 Five minutes later, the market is bid , offered (BAM = ( )/2 = ) 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.

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**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.

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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

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**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 We buy 100 shares at 10.10, 500 shares at and 400 shares at The vol wtd average purchase price is /share. The effective cost is $0.335 per share.

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**Inferring impact costs from effective and realized spreads**

Suppose the BAM = $ We want to buy 1,000 shares. The effective cost of one 1,000 share order is $0.30/sh. If we split the order into two 500 share trades, we pay 500 x ($ $0.20) x ($ $0.35) = $10,275 Relative to the initial midpoint, the trading cost is 275 ($0.275/sh)

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**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.

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**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.

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**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 bid offered. I put in a buy limit order at 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.

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**Adverse selection models I and II & Components of bid-ask spreads (see lecture notes)**

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