[MUSIC] Last time we discussed the idea of liquidity and its various dimensions. Even in the most liquid of markets investors still have to bear transaction costs. This can't be avoided. These costs reduce the returns a person earns from their investments. To increase returns net of transaction costs it is critical to understand what the transaction costs are, how to measure them, and then attempt to trade in a matter that reduces these costs. In this video, we will focus on discussing what the transaction costs are and how to measure them. In the next video, we will enlisted these calculations with an example. Transaction costs help investors evaluate how well they and their brokers have executed their trading strategies. It is also used by exchangers, brokers and regulators. Exchangers are interested in calculating transaction cost to determine how liquid their market is and use this as part of their marketing strategies. They also help brokers evaluate their execution performance. It helps them identify better execution strategies and minimize transaction costs. Regulators too are interested in calculating transaction cost as they help to monitor the performance of exchanges and change policies accordingly to further reduce transaction cost on exchanges. How do we measure transaction costs? It is the difference between the value of a paper portfolio and the value of a real portfolio. Say that you decide to put together a portfolio of stocks worth $100,000. The paper portfolio will assume that you paid the decision time midpoint of the best bid and ask prices. However, in reality you have to pay the bid ask spread, brokerage commissions, price impact, fees, taxes, etc. All of these will effect the actual return you realize from your investment portfolio. There are two components to transaction costs. One is the explicit costs and the other is the implicit costs. Explicit costs are actual out of the pocket expenses incurred. They include brokerage commissions and any taxes and fees paid for every transaction. These are easy to identify and measure and need to be simply added up. Implicit costs are those that are not obvious but still impost on traders. These includes spreads market impact cost, opportunity cost, delay cost etc. Implicit costs are more difficult to identify and quantify. For example, if you want to measure the price impact of a trade, we must have some estimate of what the price would have been, had the trade not taken place. Unfortunately, we can't observe that. There are a number of ways to measure these implicit costs. The only difference among these different ways is the benchmark use. One-way implicit transaction costs have the following general form. It is the summation over all trades executed by a trader of the product, of the size of each trade, denoted by x sub j times the direction of trade denoted by d sub j times the difference between the trade price p sub j and the benchmark at the time of trade denoted by b sub j. Trade direction takes a value of plus one if it is a buy order and a value of negative one if it is a sell order. Essentially these implicit costs measure how large a premium over the benchmark a trader is willing to pay while buying and how large a discount relative to the benchmark a trader is willing to accept while selling. The benchmark is assumed to represent the true value of the stock. A round-trip implicit transaction cost is two times the one-way implicit transaction cost. There are five common benchmarks used to compute implicit transaction costs. They are time-weighted average price, TWAP, volume-weighted average price, VWAP, decision-time bid and ask price midpoint, closing price, and a one-way effective spread. For a stock with N trades in a given day, TWAP is the average transaction price across the N trades. VWAP is the trade-size weighted average transaction price. The price of each transaction is multiplied by it's size and then divided by the total volume traded for the day, this is summed up across all trades of the day to give us the VWAP for the day. The third benchmark is the midpoint of the bid and ask prices and the time they invested decides to trade. In other words, the decision time. In this case, in addition to the difference between the trade price and the benchmark, the transaction cost also captures an opportunity cost for the part of the order that is not executed. This method is called the implementation shortfall method. For each trade we have the trade size x sub j times the trade direction, d sub j. Times the difference between the trade price, P sub j and the decision time bidask price mid point denoted by m sub d. This is added across all trades for the day. The opportunity cost is computed as the difference between the total outer size capital X and total number of shares bought or sold the summation x of j across all trades times the order direction d times the difference between the last price of the day p-sub-N and the decision time bidask mid point m-sub-d. The difference between x and the summation of all x-sub-js represent the part of the order that isn't executed by the end of the day. this non-execution results in a opportunity cost due to potentially lost profits. This is captured by the difference between P sub N and M sub D. For a buy order is assumes that you could have bought the share at M sub D and sold them at P sub N at the end of the day. As prices increase during the day, this is lost profit on the other hand, if prices decrease during the day, this difference is losses avoided. The implementation short form method adds this opportunity cost to the implicit transaction cost calculated using the decision time bidask price mid point as the benchmark. A fourth benchmark is the closing price of the day, which is typically the price of the last transaction of the day. A fifth benchmark is the midpoint of the bid and ask prices a the time of trade. There are a few other benchmarks that traders use which we won't focus on. Nevertheless I will list them here. These are the previous day's closing price, the current day's opening price, the next day's closing price, the bid-ask price midpoint at the time the order arrives in the market, and the average of the day's open, high, low, and closing prices. Next time we will look at a detailed example that will illustrate how to compute these benchmarks and then calculate implicit transaction costs. [MUSIC]
