Trading costs - Spread measures

Transcription

1 Trading costs - Spread measures Bernt Arne Ødegaard 20 September 2018 Introduction In this lecture we discuss various definitions of spreads, all of which are used to estimate the transaction costs of trading. 1 The Bid/Ask Spread The Bid/ask spread: Intuitively difference prices at which somebody is willing to buy (bid), and price at which somebody is willing to sell (ask). The spread is viewed as an estimate of transaction costs because: Suppose you are the active trader, first buy a stock and immediately sell it again to current quotes. The price you buy it for (the ask) is higher than what you sell it for (the bid). The difference is a loss to this trader, and therefore an estimate of the transaction costs. But treating the observed bid/ask spread as the transaction costs one faces as a trader is not sufficient. One need to also bring quantities into the picture. This is easiest to see in the context of a limit order book. Let us look at an example from trading at the Oslo Stock Exchange, the company DAK Figure 1 Order book Volume Buy Sell Volume If you treat these possibilities as given: If you are doing a round trip on shares, your spread is =

2 But if you were doing it for shares, your spread would be 4 000( ) ( ) 5000 = 0.28 So, as this example indicates, the spread one reads off the closing bid and ask prices in the newspaper is not necessarily all that relevant. At best it is an estimate of the trading cost of a small order. 1.1 Why are spreads positive? Always the case that ask bid, but is ask > bid? If so, what causes it? Here one brings in economics. What are the reasons transaction costs for trading equities and other financial assets are nonzero? Typically decompose spread into Order processing costs. Inventory effects. Information effects (adverse selection) The Quoted Spread The quoted spread (or typically just the spread, is a measure of transaction costs, and measures the cost of a small round-trip transaction In a limit order book, one observe the best bid (P B ) and best ask (P A ) prices. The quoted spread is the difference of these two. Quoted Spread = P A P B The quoted spread is in units of currency. It is usually easier to think of the spread as a relative number, and we introduce the relative, or percentage spread, as the quoted spread relative to an estimate of the current true price P. Relative Spread = spread = P A P B P P The true price can be calculated in various ways. Two common cases: Use the last trade price P = P last Use the average of the bid and the ask P = (P A P B )/2 1.2 Example: Oslo Stock Exchange Median (closing) relative spread across listed stocks at the Oslo Stock Exchange. Monthly observations. 2

3 Exercise 1. You want to look at the evolution of the bid/ask spread for the company Odfjell. You have access to data for the period Calculate the average daily closing spread for each year Similarly calculate the average daily relative (closing) spread for each of the same years. Solution to Exercise 1. Reading the data DataOD <- read.zoo("../data/odfjell.csv", header=true,sep=";",format="%d.%m.%y") The data has the following structure, (showing first few lines) head(dataod) Siste Kjøper Selger Høy Lav Totalt.omsatt..NOK NA NA Totalt.antall.aksjer.omsatt Antall.off..handler NA NA NA NA Antall.handler.totalt NA NA To calculate the spread simply Spread <- DataOD$Selger - DataOD$Kjøper > RSpread <- Spread / DataOD$Siste Let us plot the spread and relative spread 3

4 > s08 <-na.omit( window(spread,start=as.date(" "),end=as.date(" "))) > sumstat <- c(mean(s08),min(s08),median(s08),max(s08)) > smstattable <- sumstat mean min median max mean min median max Spreads - intraday When one has access to the full orderbook, one can also observe the buy and sell quotes in the order book at any point of time during the trading day, and calculate the spread as difference between the two The Effective Spread The effective spread is an attempt to measure the transaction cost involved in a trade by asking how much did I have to change the price to achieve a trade? What is the price concession given by the active trader (the one accepting the current bid or ask). If the active party is selling, the trader accepts a lower price. Contrary, if the active trader is buying, this trader accepts a higher price. The effective spread is measured from the sequency of actual prices observed in a market. To measure it, we need to specify which side of the trade is active, by an order direction indicator d: { -1 if buyer-initiated d = +1 if seller-initiated The effective spread compares the transaction price p with an estimate of the price (m) just before the trade: S t = d(p m) 4

5 m is typically estimated as the midpoint price at the time of order submission. To do this estimation, the ideal case is to know the timing when an order is submitted. One then measures the effective spread by calculating the actual price achieved (which can be a weighted average if the order is split), which is compared to the the midpoint price at order submission. This spread figure then explicitly accounts for the order size. But this is an ideal. In practice estimation of effective spread done from sequences of transactions in limit order book. A number of problems occur when Only see one trade, not the total sequence of trades, which implies that one only see effect of small trade. Do not see which is the active party in the order (ie whether the buyer or seller crossed the spread There is a large literature on the problem of signing the order from the typical market data available (classifying trades into buy and sell orders). Will typically have sequences of limit order books, trades Trade is signed by it distance from the current mid price. Let m t be the midprice, and p t the trade price. A typical classification is buyer-initiated if p t > m t buyer-initiated if p t = m t and p t < p t 1 (downtick) seller-initiated if p t < m t seller-initiated if p t = m t and p t > p t 1 (uptick) This algorithm is called the Lee-Ready trade classification. Note that it is imperfect, there is no guarantee that the classification is correct. In fact, comparing the Lee-Ready algorithm with the true directions from observing the actual active party (whether a buyer or seller sent the last order), Odders-White (2000) find it is only correct 85% of the time. The effective spread is a measure from the point of view of a liquidity demander: If I send a market order, what is the price I expect to pay? The Realized Spread A different measure is the realized spread, which is more of an ex-post measure. It is an attempt to estimate: By how much did prices move as a result of a transaction? The realized spread is esimated by comparing The executed price The market price after a while To show the calculation of the realized spread, define d t as a trade direction indicator, equal to 1 if this is a buyer-initiated trade, and +1 if it is seller-initiated. Further, let p t be the transaction price, m t the mid price when transaction is submitted, and m t+ mid price later (typically five or ten minutes). Realized Spread = d t (p t m t+ ) To see how the realized spread is linked to the effective spread, add and subtract the current mid price, and rewrite the above as Realized Spread = d t (p t m t ) (m t+ m t ) Recoginizing the first term on the right as the definition of the effective spread, we have Realized Spread = Effective Spread (m t+ m t ). This expression link the difference between realized spread and effective spread to change in reference price. By the way, the second expression on the right is often called the price impact, or adverse selection associated with a trade. From that expression we see that Price Impact = (m t+ m t ) = Effective Spread Realized Spread 5

6 2 More Technical papers, how to estimate and decompose the spread? 2.1 Measuring the bid ask spread. This part looks at estimation of the bid ask spread. Using serial covariances to infer spread. Using a trade direction measure. Want to decompose spread into Order processing costs. Inventory effects. Information effects (adverse selection) An early effort was the paper by Roll (1984). 2.2 Decomposing the spread. Alternative, not working throught the serial covarinces, but rather using regressions, was Glosten and Harris (1988). See also Glosten (1987). 2.3 Continuing on this groundwork. George, Kaul, and Nimalendran (1991) extends the papers above, adds a AR part to returns, by adjusting for this get a better estimate of components of spread. (improving on Roll (1984)). Does the same thing in the regression framework of Glosten and Harris (1988) Apply to NYSE, NASDAQ daily data. Huang and Stoll (1997) is a recent contribution. Tries to reconcile the serial covariance and trade indicator approach within same framework. Can not distinguish adverse selection and inventory. Apply to trade NYSE data. Estimates of spread. Madhavan, Richardson, and Roomans (1997) methodological, develop general model similar to Huang and Stoll (1997), get a decomposition of spread, measurement of spread. Structural model of price formation. 6

7 References Thomas J George, Gautam Kaul, and M Nimalendran. Estimation of the bid ask spread and its components: A new approach. Review of Financial Studies, 4: , Lawrence R Glosten. Components of the bid ask spread and the statistical properties of transaction prices. Journal of Finance, 48(5): , December Lawrence R Glosten and Lawrence E Harris. Estimating the components of the bid/ask spread. Journal of Financial Economics, 21:123 42, Roger D Huang and Hans R Stoll. The components of the bid-ask spread: A general approach. Review of Financial Studies, 10(4): , Ananth Madhavan, Matthew Richardson, and Mark Roomans. Why do security prices change? A transaction-level analysis of NYSE stocks. Review of Financial Studies, 10(4): , Elizabeth J Odders-White. On the occurrence and consequences of inaccurate trade classification. Journal of Financial Markets, Richard Roll. A simple implicit measure of the effective bid ask spread in an efficient market. Journal of Finance, 39(4): , September