Measurement and Determination of Cost of Trade

Trade Cost Measurement

In its simplest terms, trade cost would just represent the commission paid to place a trade. However, this view is simplistic in that it only represents a portion of the total costs. The vocabulary from Reading 11, Los (11 c) is important to know well before tackling this section. It is recommended that candidates do a quick review before moving on.

Implementation Shortfall

Implementation Shortfall (IS) stands as a crucial post-trade metric in finance, examining past actions. It accounts for all types of costs, both evident (like fees) and hidden (such as opportunity costs). IS can be complex to grasp due to its intricacies, but it’s a highly testable subject, making it worth the effort to study.

IS measures the variance between a hypothetical portfolio’s return (assuming all transactions occur at the manager’s decision price) and the actual return of the portfolio, encompassing all fees and costs. The hypothetical portfolio is like an ideal, theoretical portfolio that doesn’t exist; it’s a “what-if” concept used as a basis for measuring actual returns.

Here’s another crucial formula, simpler than those that follow, which aids in understanding IS.

$$ IS = \text{Execution cost} + \text{Opportunity cost} + \text{Fees} $$

Execution cost: Reduce profits when the impact of the orders in the market moves prices adversely. Execution costs will also occur owing to price drift over the trading period. For example, buying stocks that are increasing in value over the trading period and selling stocks that are decreasing in value over the trading period.

$$ IS = \text{Paper return} – \text{Actual return} $$

Opportunity cost: Refers to orders that did not get filled, a ‘missed’ chance to transact. Opportunity costs may also arise in times of insufficient market liquidity when the fund is not able to find counterparties to complete the trade. The opportunity cost provides managers with insight into missed profit opportunities for their investment idea.

Fixed fees: Includes all explicit fees, such as commissions, exchange fees, and taxes.

Expanded Implementation Shortfall

Expanded IS was later introduced by Wagner (1991) to include a delay component. The delay component refers to a period when the order has not been submitted to the market as promptly as it could have been. Thus, the expanded and most robust version of IS is as follows:

$$ IS = \text{Delay cost} + \text{Execution cost} + \text{Opportunity cost} + \text{Fees} $$

Calculating IS for the Exam – An Example

Up to this point, you've learned about Implementation Shortfall concepts, but now let’s dive into a complete example. Don’t worry if you can’t answer all the questions below just yet; the focus here is to understand which prices to use in each part, a critical aspect of mastering IS. One example won’t suffice; practice with multiple examples to truly grasp IS.

Here’s an example:

A portfolio manager decides to buy 100,000 shares of KAM at 9:00 a.m., priced at $50.00. He sets a limit price of $50.50. The buy-side trader holds off executing the order until 10:30 a.m. when the price is $50.10. The fund incurs a commission of $0.05 per share, with no other fees. By day’s end, 75,000 shares are executed, and KAM closes at $50.65. Here are the order and execution details:

$$ \begin{array}{c|c}
\textbf{Ticker} & \textbf{KAM} \\ \hline
\textbf{Transaction} & \text{Buy} \\ \hline
\textbf{Shares} & {100,000} \\ \hline
\textbf{Limit Price} & \$50.50
\end{array} $$

$$ \textbf{Trade Table:} \\
\begin{array}{c|c|c}
\textbf{Trade} & \textbf{Execution Price} & \textbf{Shares Executed} \\ \hline
1 & \$50.20 & 30,000 \\ \hline
2 & \$50.30 & 20,000 \\ \hline
3 & \$50.40 & 20,000 \\ \hline
4 & \$50.50 & 5,000 \\ \hline
\textbf{Total} & & \bf{75,000}
\end{array} $$

1. Calculate the execution cost: This is the difference between the costs of the real portfolio and the paper portfolio. This is accomplished by taking the figures from the trade table and multiplying the shares executed by the respective execution price for each trade. This means we will have 4 terms in the equation, one for each trade.

   $$
   (30,000 \times \$50.20 + 20,000 \times \$50.30 + 20,000 \times \$50.40 + 5,000 \times \$50.50) \\ = \$3,772,500 $$

   Next subtract the paper portfolio cost. This is comprised of the decision price, and then NOT the total number of desired shares transacted, but the total number of shares transacted, which looks like this:

   $$ 75,000 \times \$50.00 = \$3,7450,000 $$

   Now use:

   $$ \begin{align*} \text{Cost of real portfolio} – \text{cost of paper portfolio} & = \text{execution cost} \\
   \$3,772,500- \$3,7450,000 & = \$22,500 \end{align*} $$

2. Calculate the opportunity cost: This is based on the number of shares left unexecuted and reflects the cost of not being able to execute all shares at the decision price. Opportunity cost can be calculated as follows:

   $$ (100,000 – 75,000) \times (\$50.65 – \$50.00) = \$16,250 $$

   The first term has a value of 25,000. These are shares that the manager wanted to purchase. Also, imagine that over the course of the day, as is stated in the vignette, the price of the shares continues to climb over the day. If we imagine that the entire 100,000 shares had been immediately purchased, the difference in the decision price and the closing price represents a lost profit or an opportunity cost.

3. Calculate the fixed fees: These are the simplest components of trade cost to calculate. They are simply equal to the commission per share, multiplied by the total number of shares actually transacted upon (not desired):

   $$ \$0.05 \times 75,000 = \$3,750 $$

4. Calculate the implementation shortfall in basis points: The IS will be easier to calculate now that some of the intermediate steps have been worked through. The following formula is used in the next step:

   $$ \begin{align*} \text{Execution cost} + \text{opportunity cost} + \text{fees} = \text{Implementation shortfall} \\
   \$22,500 + \$16,250 + \$3,750 = \$42,500 \text{ (represents IS in absolute }\$’\text s) \end{align*} $$

   To convert to basis points, the decision price will again be used, in the following formula:

   $$ \frac {IS (\$) }{ (\text{Total Shares} \times \text{Decision Price}) }= \frac { \$42,500 }{ (100,000 \times $50.00) } = 0.0085 $$

   $$
   0.0085 \times 10,000 \text{ bps} = 85 \text{ bps} $$

5. Calculate delay cost: The delay cost shows us what we lost by waiting to enter an order into the market. This shows up in the vignette as the part where the buy-side trader waits for an hour and a half to enter the order into the market. Use the actual shares transacted and the stock price at the time the order was entered and the decision price:

   $$ (75,000 \times \$50.10) – (75,000 \times \$50.00) = \$7,500 $$

6. Calculate trading cost:

   $$ \begin{align*} & (30,000 \times \$50.20 + 20,000 \times \$50.30 + 20,000 \times \$50.40 + 5,000 \times \$50.50) \\ & – (75,000 \times \$50.10) = \$15,000 \end{align*} $$

   Note that trading cost is very similar to execution cost, the difference lies in the use of the decision price vs the use of the price at the time the order was entered into the market.

7. Show the expanded IS in basis points

   The expanded IS will come out to the same final value as the traditional IS (answer #4). The difference is that execution cost is broken out into delay cost and trading cost, as follows:

   $$ \begin{align*}
   \text{Expanded IS} & = \text{Delay cost} + \text{trading cost} + \text{opportunity cost} + \text{fees} \\
   \$42,500 & = \$7,500 + \$15,000 + \$16,250 + \$3,750 \end{align*} $$

   To convert to basis points, the decision price will again be used, in the following formula:

   $$ \frac {IS (\$) }{ (\text{Total Shares} \times \text{Decision Price}) } = \frac { \$42,500 }{ (100,000 \times \$50.00) } = 0.0085 $$

   $$ 0.0085 \times 10,000 \text{ bps} = 85 \text{ bps} $$

Portfolio Management Pathway Volume 2: Learning Module 8: Trade Strategy and Execution; Los 8(g) Explain how trade costs are measured and determine the cost of a trade