Complex mathematics behind online trading systems

NASDAQ Exchange
How online trading system works? Here I am going to explain how online brokers and trading system works and how they make profit irrespective of order market movements:
Online brokers provide you a very good service, that a customer can trade anywhere using the computer. Nowadays it is easy to trade stocks online, but it is also complicated means how transactions take place and how brokers and other market makers make money out of placing customers' orders.

Let's consider an example of a customer, who has chosen Scottrade as an online broker for trading. He puts an order in computer to buy a hundred shares of IBM at market price and 2 second after he receives conformation that you have successfully bought 100 shares of IBM at $ 125.15 current price. 

If we think how did the order place?, where did it go and who is the seller of 100 shares of IBM? Here are some Math starts.

How It All Happens 

Scottrade is a discount broker means he is not directly selling or buying
the shares. It is using service of market makers like Knight Capital, UBS, Citadel and Citigroup and route the electronic orders to them and it receives payments for those orders. Where to route the order is decided based on criteria like speed, price, and quality of the service.

Let;s say Scottrade routing that order to UBS as it has selected it based on above criteria. UBS sells Scottrade 100 shares immediately and order was filled and customer owns the IBM shares at $125.15.

Now, how UBS deal with that order as it has already sells those shares of IBM to Scottrade. UBS and other market makers have two options as they can look up their order inventory and try to find a same order of buying 100 shares of IBM and match off its 100 shares of sell order with it. If they can't find the order than they sent an order out to an exchange or in dark pool ( But they have to pay for that ) to buy those shares or most of the times they stay short sell side and wait for a buy order to be in the system. To remain short sell side means they have sold the shares and waiting to price drop a little to buy shares again and turn it in to their profit.

If UBS finds a buy order a penny less means at $ 125.14 and it executes the order then UBS has earned 1 cent profit per share means 1$ for 100 shares order and it pays Scottrade a tenth of a dollar means 10 cents per dollar profit, so it is earning 90 cents. Although figure looks very small, but when you apply this for so many trades and a huge volumes then it turns out to be a huge profit.

Indeed, these types of trades do happen millions of times a day: retail customers interact with online brokers (AmeriTrade, Schwab, ETrade, Scottrade, etc.) who route orders to market makers, who in turn match orders against their own supply or interact with exchanges (NYSE, Arca, NASDAQ, BATS, Direct Edge).
Pump Up the Volume: Connecting Buyers and Sellers

Now let's see how this order might interact with other players. Vanguard is one of the largest mutual fund company in the US and it trades more than 10 million shares of a stock a day, including many shares of IBM. Sauter is Vanguard's Chief Investment Officer 

The goal of Sauter and his trading desk is to get the lowest execution cost, and he has several choices when he has to buy or sell stocks like IBM. He can execute a particularly large order manually by directing all or parts of it to specific trading venues. Or, he can bundle orders to buy and sell many different stocks into a "basket" that will be executed as a single computer program.

He can also choose to use an an algorithm and a smart order routing system, which will likely chop up an order to buy or sell a specific stock (like IBM) into small pieces (100 orders of 100 shares each, for example), and will then direct those orders to whatever venue offers the best combination of speed and price.

So it's likely that part of any order to buy or sell IBM will end up in different locations: at a market maker like Knight Capital or UBS, exchanges like the NYSE, NASDAQ, or BATS, or dark pools like Liquidnet. 

Clearly, Sauter's trade is considerably more complicated than a customer's buying IBM at Scottrade.

Sauter may include specific instructions on how the order is to be executed. For example, some mutual fund and pension fund managers want to make sure their trades are executed at the Volume Weighted Average Price (VWAP), which is the dollar value of all the shares traded in that stock divided by the volume. This is a measure to ensure that price execution is at least as good as the average.

Sauter says he has an even higher standard for his orders. He wants to make sure that the stock is bought or sold at the price he or his fund managers want to buy or sell it at, not the market price. If a Vanguard fund manager wants to sell IBM at $128.60, for example, he may want his broker to make sure he sells at that price, and not, say, at $128.58 (this is called "implementation shortfall").

Other factors beside speed and price may also influence the decision of asset managers. Some may want to send order flow to a specific firm in exchange for services—analyst research, trader commentary, access to conferences and meetings. In exchange, the firm may provide execution to an asset manager at very low cost.

Tradeworx, a high frequency trading company located in New Jersey. Company trades using statistical arbitrage, where traders are short one security and long another, based on historical performance.

For example, IBM historically trades in a certain relationship with the S&P 500. When it trades above that relationship, Tradeworx system may put in large orders to sell IBM and buy the S&P (all in a fraction of a second) assuming the relationship may revert to its historic mean.

Company trades 50 to 100 million shares of stock a day, including many trades in IBM, Sometimes firm has traded 21 million shares, for a net profit of $7,000.

Tradeworx and other high-frequency traders execute their trades through direct access. The computers are linked to servers very close to those of the major exchanges. Why? Because the pricing inefficiencies last for only a fraction of a second, so speed is paramount.

Bottom Line: Technology, Liquidity, Complexity

So what is happening here? Three customers—Retail Investor, who wants to buy 100 shares of IBM, Sauter, a mutual fund manager who will be buying or selling tens of thousands of shares or more of IBM, and Tradeworx, a high frequency trader who will also be buying and selling thousands (perhaps millions) of shares of IBM—are all interacting in different spaces: in the computers of market makers who match off the orders, on exchanges, and in alternative trading systems like dark pools.

All three of these orders could interact with each other. All three of these customers, in their own way, are adding liquidity—but there are a lot more places for them to trade.

How did things get so complicated? You can blame it on the relentless march of technology and a decision by the SEC to encourage competition among exchanges.

( Source: CNBC )
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