The Impact of E-Commerce on Competition in the Retail Brokerage Industry

Transcription

1 undled Incumbent vs. Online Entrant The Imact of E-Commerce on Cometition in the Retail rokerage Industry TECHNICL PPENDIX Proosition : In a duooly setting with an incumbent full service firm selling a ure bundle of R and E and an online entrant selling E, both firms offer their highest feasible quality of execution. Proof: s illustrated in Figure (cross-shaded region), firm sells to investors whose valuation for roduct E is greater than, as well as to investors whose valuation for comonent R is less than ( ). The corresonding rofit functions are ( ( + ) ( ) ) ( ) +, α + +. oth firms choose rices simultaneously in stage-3. Solving for first order conditions we get, ( + ) ( 3 + ) ( ), ( ) 3( + ) (α + ) +. 4 Thus > 0, > 0, < 0 and < 0 (for ( + ) ); i.e., ( + ) < 3 the rofit functions are strictly increasing and concave in their resective rices. In addition, > 0 and > 0, i.e., the incumbent as well as the entrant s rices increase monotonically with their own execution quality (see Figures and ). s its quality of trade execution increases, each firm would rice higher and realize higher rofits. Since we are rimarily interested in the otimal rices and execution quality choices of the two firms, we hold the WTP α constant at.5 for this analysis. Given the rices in stage-3, firm chooses its quality. Substituting the rices from stage-3 back into the rofit function of firm and solving for otimal quality, we find that firm s rofits also increase monotonically with

2 its own execution quality (see Figure ). In other words, irresective of the quality choice of the incumbent, the online entrant always refers to choose the highest ossible quality of execution Figure : Firm s Prices and Profits as a function of and. Substituting the otimal quality choice of firm into firm s rofit function and solving for firm s otimal quality, we find that firm s rofit function also increases monotonically with its own quality (see figure ) Figure : Firm s Prices and Profits as a function of.

3 Without loss of generality, we normalize the maximum execution quality ˆ of firm to, and thus at equilibrium firm chooses ˆ. The corresonding rofit functions for the two firms are then given by ( ( + ) ( ) ) ( ) +, α + +. oth firms choose rices simultaneously in the last stage of the game. Solving for FOCs we get, ( + ) ( 3+ ) ( ), ( ) 3( + ) (α + ) +. 4 In what follows, for simlicity we set α.5. Solving for otimal rices, we have, (7 + 6) , ( ) Substituting these otimal rices back into the rofit functions, we have the exressions for the rofits of firms and. i è H6+7L & H6+5L I H6+7L è H+LH8 +7 LM H36 +H44 +5 LL + k è H6+7L è H+LH8 +7 L & H6+5L I H6+7L è H+LH8 +7 LM H36 +H60+4 LL 6 H6+7L è H+LH8 +7 L H34 +H6 +H557 +H LLLL +48 H3888 +H0736+H4760 +H5878 +H44 +H LLLLLL y {

4 i è H4+ 5LH6+ 5L H6+ 7L è H+LH8 + 7 L & H6+5L I H6+ 7L è H+LH8 + 7 LM + k 4 è H4+ 5LH6+ 5L & H6+ 5L I H6+ 7L è H+LH8+ 7 LM H36 +H LL y 8H6+ 5L H6+ 7L H44 +H37 +H LLL+ 8H6+ 7L è H+LH8+ 7 L H36 +H76 +4 LL H44 +H37 +H LLL { Figures and illustrate how the rofits of firms and change with b b b Figure : Sensitivity of Firm Profits to Execution Quality, b (d) s can be seen from Figure, the entrant s rofits ( ) increases monotonically with its own execution quality, while firm s rofits ( ) decreases with increasing b. In other words, irresective of the quality choice of the incumbent, the online entrant always refers to choose the highest ossible quality of execution, ˆ. If ˆ, then the otimal rices and rofits for both firms are, , 0. 37, , and 0..

5 nalysis of Payments for Order Flow s shown by our analysis, the rofitability of an online entrant roviding just trade execution is significantly lower than that of the full-service incumbent. The ayment for order flow (POF) that some trading venues rovide to brokerages would hel imrove a broker s rofitability and hence would be very attractive to an online entrant. However, as highlighted by the quote below, this deendence on additional revenue streams that enable online brokerages to comete with the full-service offerings of established firms are thought to result in higher hidden execution costs for investors. y oerating as a third market, or having a ayment for order flow arrangement with another dealer firm, brokerage firms can generate additional revenue for their customers orders. Critics say this lessens the chance that customers can get their trades executed between the osted bid-ask sread--the difference between what Wall Street's middlemen are willing to buy and sell a stock for. Most cyberdiscounters oenly acknowledge acceting ayment for order flow, although they argue that it hels subsidize their cut-rate commissions. Without it, everyone would have to raise their commissions says ill Porter, founder of ETrade Securities. However, cyberbrokers have been battling a ercetion that they don't always get customers as good a rice as full-service brokers - Online trading: How to make money the newfangled way, usiness Week, 4/8/96, Foust, Dean. The ractice of ayments for order flow combined with uncertainty about quality of trade execution () makes this an issue of significant concern to investors as well as regulators. We are secifically interested in understanding the imact of POF on the quality choice of the online broker when the incumbent unbundles its offering. s mentioned earlier, online brokerages can route investors trades to a trading venue of their choice. With different trading venues offering differing execution qualities, the choice of the trading venue can be thought of as a choice of the quality of execution by the online broker. Online brokers tyically receive ayments of - cents er share from external third market dealers, alternate trading venues and Electronic Commerce Networks (ECNs) for the order flow generated by their customers. meritrade, for instance, received $5.5 million in ayments for order flow, averaging $.73 er trade in 000, and accounting for 9 ercent of meritrade s revenue for the year (Source: nnual Reort, meritrade, 000). Schwab Caital Markets, Schwab s market making subsidiary, generated $55 million in revenue in 999, or 4 ercent of Schwab s total revenues.

6 Traditional full service brokerages tyically route their orders to the rimary exchanges and offer a high quality of execution. In keeing with this, we assume that the incumbent fullservice firm offers the highest execution quality which is normalized to. In addition to its rice, the online brokerage receives a ayment for order flow F, which is tyically a function of the volume of trades routed to the trading venue by the broker. Following from Proosition 4a, the rofit function for firm receiving a POF is given by, ( F ). We + first comute the rice equilibrium for the given quality choices (b and ) and then comute the F otimal quality choice b. Solving for FOC, we have, ( ). Firm s rofits from E is, ( ˆ) θ ( ). Solving for FOC, we have Firm s E rice ( ) ( + ). y substitution we have, F ( 6 + ), and ( 4 ) 3 + F ( 6 + ), and ( 4 ) the corresonding rofits for firm is ( ( ) + ( ) ) ( 4) ( ) F. Given rices and, we solve for firm s otimal quality b. We have, ( F( ) + ( ) ). (( ) ( 7 4) + F( 8 + ( 8 + ( 9 + )))) 3 ( 4) ( ). is concave in b for F 64 ( 4)( ).5.5 ( ) Figure 3 shows the otimal execution quality for firm for different values of F. s can be seen, b decreases as F increases. In other words, the online entrant chooses a lower execution quality than the full-service incumbent, which further decreases as the ayments for order flow increase.

7 7 6 b F Figure 3: Otimal Execution Quality b with POF s can be seen from the above analysis is roortional to F. Naturally, there is a strong incentive for the online broker to send orders to markets that offer POF. Our analysis shows that ressures to lower costs and increase rofits could lead online brokers to route orders to exchanges that rovide ayment for order flow, resulting in fewer oortunities for rice imrovement.