Aggressiveness measures and ordered probit model

Orders submitted during normal trading are classified into six categories according to their aggressiveness using the scheme developed by Griffiths et al. (2000). Order aggressiveness is measured by the order price relative to the best bid and ask price on the schedule. Table 6.2 summarises the categories used for grouping the orders.

Table 6.2 Classification of new orders submitted to the market

PO represents the price of the order, PA represents the price of the best ask order, PB represents the

price of the best bid order, QA represents the quantity (number of shares) at the best ask price, QB

represents the quantity (number of shares) at the best bid price.

Order Type Price Criteria Quantity Order

Category _{Bid Ask Bid Ask}

1 PO>PA PO<PB

2 PO=PA PO=PB QO>QA QO>QB

3 Market orders PO=PA PO=PB QO≤QA QO≤QB

4 In the market PA<PO<PB PA<PO<PB

5 At the market PO=PB PO=PA

6 Behind the market PO<PB PO>PA

Category 1 orders are the most aggressive. Orders in this category include buy (sell) orders with order price greater (less) than the best ask (bid) price. The best ask and bid are the ask and bid orders with the highest order priority.31 Category 1 buy (sell) orders are executed against the limit orders at the best ask (bid) and at least in part against the depth available higher (lower) in the book up (down) to the order price.

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Category 2 and 3 buy (sell) orders have order prices equal to the best ask (bid) price. Category 2 and 3 orders are differentiated by the order size with reference to the depth at the best price on the opposite side. Category 2 orders are larger than the depth at the best price on the opposite side of the book whereas Category 3 orders are less than or equal to the depth at the best price on the opposite side. Consequently, Category 3 orders are executed immediately in full while Category 2 orders are executed immediately in part, with the unfilled part entering as a limit order. Orders in Category 1 to 3 are collectively known as market orders. Due to the dataset used, it is not possible to distinguish market from marketable limit orders.32

Category 4 orders have order prices that lie between the best bid and ask prices and are known as orders placed “in the market”. Category 5 buy (sell) orders have prices equal to the best bid (ask). These orders are referred to as being placed “at the market”. The most passive orders are in Category 6. These buy (sell) orders have their prices less (greater) than the best bid (ask) and are referred to as being placed “behind the market”. Orders in Categories 4, 5 and 6 do not result in immediate execution. They are standing limit orders and provide liquidity to traders who require immediacy, i.e., traders who subsequently submit market orders.

Using the criteria described above, each order is placed into one of the six groups. Before examining the differences in the order usage by different trader types, the market conditions at the time of the order placement and the order type are analysed to verify the relationship documented in Al-Suhaibani and Kryzanowski (2001) and Verhoeven et al. (2004). Subsequently, univariate analysis is conducted to examine the differences in the use of order types by the three types of trader. Time of day differences are also examined to add to the prior research on the intraday patterns of the order types. For example, Biais et al. (1995) observe large trades at the end of the day. They hypothesise that the large trades are, among other reasons, due to fund managers being evaluated at the closing price and strategic traders unwinding their trading positions at the end of the day.

32 _{Marketable limit orders are limit orders with a price equal to or better than the best existing price on}

Ordered probit analysis similar to that described in Griffith et al. (2000) is used to isolate the effect of trader type on the order type selection. Let *

t

G be the unobservable continuous variable denoting the aggressiveness of the order placed at time t. *

t

G is assumed to depend linearly on the explanatory variables x_{i t,} where i = 1, 2, …, l. * , 1 l t i i t t i G x = =

∑

The observed value of G_t is determined from G_t* using the rule:

* * * 5 if , 1 if for = 2, 3, 4 and 5 6 if t t m t m t G G m G m G 1 −1 ⎧ − ∞ < ≤ γ ⎪ =_⎨ γ < ≤ γ ⎪ _{γ < ≤ ∞} ⎩

The probabilities of observing each value of G_t are given by:

l l l l 1 1 1 1 1 5 1 Pr[ 1| ] ( ), Pr[ | ] ( ) ( ) for = 2, 3, 4 and 5, Pr[ 6 | ] 1 ( ) l i t i i l l i i t i m i m i l i t i i G x x G m x x x m G x x − = = Φ γ − α = = Φ γ − α − Φ γ − α = = − Φ γ − α

∑

∑

∑

∑

where Φ(.) is the cumulative normal distribution.

The explanatory variables, xi t, , are defined as follows:

t

DumRet is a dummy variable for orders from retail traders, taking on the value of one if a retail trader submits the order (and zero otherwise).

t

DumIns is a dummy variable for orders from institutional traders, taking on the value of one if a institutional trader submits the order.

120 t

DepthSame is the depth at the best price on the same side of the market as the order submitted.

t

DepthOpp is the depth at the best price on the opposing side of the market as the order submitted.

t DepthSame

Δ is the change in the depth at the best price on the same side of the market as the order submitted as a result of the previous market ord limit order.

t DepthOpp

Δ is the change in the depth at the best price on the opposing side of the market as the order submitted as a result of the previous market or limit order.

t

Relspd is the relative bid-ask spread, which is calculated by dividing the bid-ask spread by the midpoint of the spread.

t

Volume is the number of shares in the order submitted. t

LastAggressive is a dummy variable that takes on the value of one if the previous order is classified in Categories 1, 2 or 3 in terms of order aggressiveness.

t

DumAsk is a dummy variable that takes on the value of one if the order is on the sell side.

The depth on both sides of the market has been shown by Griffith et al. (2000) to influence the order placement strategies of traders on the Toronto Stock Exchange. A larger depth on the same side (DepthSame_t) of the market encourages traders to be more aggressive, whereas a larger depth on the other side of the order book (DepthOppt) encourages more passive orders. Two variables capturing the change in the order are included: (1)ΔDepthSamet, and (2)ΔDepthOppt. These variables measure the change in the depth on the same and opposing side of the market as the order submitted. An increase on the same side of the market would encourage more aggressive orders while a decrease on the opposing side would have the same effect.

Verhoeven et al. (2004) and Al-Suhaibani and Kryzanowski (2001) find a greater proportion of limit orders when the market spread is large. In the probit analysis, larger spread, Relspd_t, is expected to be associated with more passive orders. Biais

et al. (1995) find positive serial correlation in order aggressiveness. It is predicted that an order is likely to be more aggressive if the previous order is also aggressive (LastAggressive

t).

Harris and Hasbrouck (1996) propose order placement strategy should be a joint decision in terms of the size and aggressiveness of the order. As there are costs involved in placing aggressive orders, the larger the order placed (i.e., Volume_t), the more passive the order is expected to be. The last explanatory variable, DumAsk_t, is included to allow for any differences between the aggressiveness of sell and buy orders. Keim and Madhavan (1995) find traders are more passive with buy orders, to hide their information, but more aggressive with sell orders, implying a greater urgency when they decide to sell.