Regression analysis of the permanent price effect on trader

The relationship between price effect and order size has been documented in earlier research (Walsh, 1997). I examine the impact of adding the identity of the trader to

, i t t Q TQ , 1 1 i t n t t Q TQ n = ⎛ ⎞ ⎜ ⎟ ⎝

∑

the price effect and order size relationship. A simple model is used to analyse the permanent effect on price (PPEt) of order size (Sizet) and the identity of the trader:

(

)

PPE Size Size DumIns Size DumRet DumAggr

Depth Depth α α α α α α ε + + = = + × + × + + + Δ +

∑

Size = a dummy variable equal to one if order size is in quintile j and zero otherwise (ranges from j=1, smallest, to j=5, largest order),

t

DumIns = a dummy variable equal to one for orders placed through institutional brokers,

DumRett = a dummy variable equal to one for orders placed through retail brokers,

DumAggrt = a dummy variable equal to one for orders that have buy (ask) order price greater (less) than the best sell (buy) order price (i.e., market buy (sell) orders that walk up (down) the book) ,

Opp t

Depth = the standardised depth on the opposing side of the order prior to the order being placed,24

Opp t Depth

Δ = the difference between the depth on the opposite side at transaction time, t-5, and transaction time, t-1.

The above model does not contain an intercept term because there are five size dummy variables (one for each size quintile). It is important to note that the placement of orders by rational traders is likely to be conditioned on their anticipation of any impact on price (Griffiths et al., 2000). Where the price impact is expected to be large, rational traders are likely to reduce the size of their order or avoid placing orders altogether. Thus the findings here are conditional on the orders being placed.

24 _{Depth is standardised using the stock’s depth on the same side over the period examined (Chan et}

al., 1995). For example, we standardised bid depth by firstly calculating the mean and standard deviation of the depth on the bid side for the period examined. Each depth measure is standardised by subtracting the mean and dividing the result by the standard deviation.

90

Wagner and Edwards (1993) suggest order size, market depth, trade urgency and broker skill all affect the price impact of an order. A number of explanatory variables are included in the model to isolate the information effect of trader identity. The first set of variables is the order size. As the relationship between size and price effect may not be linear, the specification above allows us to compare the information content of orders of different size directly from the regression coefficients (Chan and Fong, 2000). Suppose orders in a medium size category (e.g., j=3) are more likely to be information motivated; then the coefficient α3 is expected to be the highest among the coefficients α1 to α5.

Studies that have examined trade or order size have typically used three (Barclay and Warner, 1993) or five (Chan and Fong, 2000) groupings. For this thesis, the choice of the number of groups for classifying order size is affected by the distribution of order size by trader type. While choosing a larger number of groups allows a finer analysis of the relation between order size and price effect, the number of groups is constrained by retail traders placing relatively few larger orders. For instance, initial analysis using ten groups revealed no retail orders in the largest order size decile. I settled on five.

The interaction variables Size_{j t,} ×DumIns_t and Size_{j t,} ×DumRet_t are included to allow the sensitivity of price to order size to vary by trader type. Traders are likely to vary their order size conditional on the information they have. While the relationship between size and price impact is expected to vary in a similar direction across different trader type, the magnitude of the coefficient may not be the same. Keloharju and Torstila (2002) suggest that when an individual investor and an institutional investor place orders of similar size, the individual investor is likely to be risking a much large proportion of his wealth. Thus, the individual investor can be expected to be more informed when placing a similarly large order compared to an institutional trader.

Another explanatory variable is the aggressiveness of the order, DumAggrt. The orders examined here comprise market and marketable limit orders. While they are all more aggressive compared to limit orders, they are, within the group, differentiable from each other. Buy (sell) orders that have a nominated price greater

(less) than the sell (buy) side are more aggressive than the buy (sell) orders that have a price equal to the opposing side. More aggressive orders are likely to have a greater price impact as they convey more information and are likely to cause a change in the best opposing price. For example, buy orders with price greater than the best sell can “walk up” the order book if there is insufficient depth at the best sell to complete the order. Depth on the opposing side to the order, Opp

t

Depth , will affect the price impact of the order. The lack of depth on the opposing side will result in a larger price impact. As the stock variable can incorporate stale orders, the change in

depth, Opp

t Depth

Δ , is also included. It provides a more current indication of how the market is moving.

The model is analysed for both bid and ask orders and also for stocks in the first and last deciles. Griffiths et al. (2000) suggest aggressive buys are more likely to be motivated by information than aggressive sells. Purchases and sales are examined separately due to the possible asymmetry in the relationship between order size, trader identity and price effect. To obtain the same signed coefficients for the independent variables, -PEt is used for the ask orders. Two measures of the permanent (total) price effect are used in the regressions: PPE1t and PPE2t(TPE1t and TPE2t). These provide evidence on the effect of the durations examined, j and k. The computation of PPE1t and TPE1t uses one lead (j=1) and one lag (k=1) while the computation of PPE2t and TPE2t uses five leads (j=5) and five lags (k=5).