[MUSIC] Last time we discussed that it is important to account for transaction cost as they reduce the returns investors earn. We divided transaction cost in to explicit and implicit costs. Implicit costs depend on benchmark used. We look at various benchmarks and how to calculate them. In this video, we will illustrate the calculations of these benchmarks and implicit transaction costs with an example. Let's look at an example to understand the five benchmarks method. Here the market opens in 9:30AM at which point, 10,000 shares of XYZ stock trade $45.66 a share. You decide to place an order to buy 1200 shares of XYZ at 10:30AM. The best bid and ask prices at this time are $46.05 and $46.08 respectively. This yields a mid-point of 46.065 at decision time. This is the benchmark for the implementation short-form method, which was denoted as M sub D. Another trader's order executes at 11:08AM at a price of 46.2 for 650 shares. The best bid and ask prices at this time are 46.20 and 46.22 respectively. At 11:46AM 460 shares of your order gets executed at the price of $46.05. Another trader's order for 2,000 shares is executed at 2:16PM at the price of 46.15. At 3:45PM another 530 shares of yours are executed at $46.03. The best bid at ask prices at this time are 45.99 and 46.03 respectively. Finally, the market closes at 4PM and the best bid and ask prices are 45.91 and 45.94 respectively. For simplicity, we'll assume that there are no transactions in XYZ stock during the day. The first benchmark is the TWAP which is a simple average of the transaction prices of the day. Transactions were executed at 45.66, 46.20, 46.05, 46.15, and 46.03. Adding these five numbers and dividing by the total number of transactions for the day, which is 5, yields a TWAP of 46.018. The implicit transaction cost is the summation across all trades of trade size times the trade direction times the difference between the trade price and benchmark. In this case, since you are buying trade direction is plus one in all our calculations. Your transaction cost is 460(46.05- 46.018) + 530(46.03- 46.018) which gives us a transaction cost of $21.08. The second benchmark is the VWAP. It is a trade-size weighted average price for the day. On this day the first transaction was for 10,000 shares at 45.66, the second one for 650 shares at 46.2, the third one for 460 shares at 46.05, the fourth one for 200 shares at 46.15, and the fifth one for 530 shares at 46.03. The VWAP is 10000 x 46.66 + 650 x 46.20 + 460 x 46.05 + 2000 x 46.15 + 530 x 36.03 divided by the total number of shares traded for the day which is 10,000 + 650 + 460 + 2,000 + 530. The VWAP works out to 45.785. Hearing this, we can calculate your transaction costs, that's 460(46.05-45.785) + 530(46.03-45.785), which gives us a transaction cost of $251.64. Since the opening price was a large trade at a very low price, VWAP is far lower than TWAP which leads to a significantly higher implicit transaction cost when we use VWAP as a benchmark. The third benchmark is the bid ask midpoint at decision time. You decide to buy 1,200 shares at 10:30AM when the bid point was was 46.065. The transaction cost, hence, is 460(46.05- 46.065) + 530(46.03- 46.065), which gives us a transaction cost of -$25.45. Interestingly, your transaction cost now is negative as both your transactions are at prices below the decision time midpoint. This method also captures the opportunity cost of not executing the order completely. Out of the 1,200 shares you wanted to buy, you end up buying only 460 plus 530 which is 990 shares. So the opportunity cost is 1,200 minus 990, which is 210 shares. The closing price for the day is a price of the last trade of the day, which is 46.03. So the opportunity cost is 210 times 46.03 minus 46.065, which is a -$7.35. Adding the opportunity cost of -7.35 to the transaction cost of -25.45 use implicit transaction cost of -32.80 through the implementation chart for matter. In this case, prices decreased after you decided to buy shares, and hence the transaction costs are negative. In this case the delayed execution worked in your favor and helped you save money. If prices increased you would have incurred a cost. The fourth benchmark is the closing price. The price of the last transaction is 46.03. So the transaction cost here is 460(46.05-46.03) + 530(46.03-46.03) which gives us a transaction cost of $9.20. Here, prices decrease towards the end of the day, and hence you buy at prices higher than the benchmark. The last benchmark is the bid-ask midpoint at the time of trade. Since you had two transactions we have to determine the benchmark separately for each transaction. The bid-ask midpoint for the first transaction was 46.035 and that for the second transaction was 46.01. Hence the one way effective spread is 460(46.05-46.035) + 530(46.03-46.01), which gives us a one day effective spread of $17.50. The one day effect of spending will usually be positive as traders will buy at prices above the bid-ask midpoint at the time of trade and sell at prices below the midpoint at the time of trade. In our example, the various benchmarks are viewed at very different values of transaction costs. There isn't one correct or wrong value. Since the benchmarks are different, each will need a different value. These will usually be affected by how prices move during the day. On days when prices move favorably, your transaction costs will be negative. That is, you make a profit by trading or not trading as the case may be. On other days when prices move against you, transaction cost will be positive which means that you will incur an implicit cost to trade. Next time, we will take a closer look at the implementation shortfall method of calculating implicit transaction cost. This will further help us understand the cost incurred while trading. [MUSIC]
