Evaluating Trade Execution

Trade execution, a quantitative process assesses the performance of traders, algorithms, and brokers. Trade cost assessment, known as Trade Cost Analysis (TCA) or post-trade analysis, aids portfolio managers in selecting optimal trading methods and identifying and rectifying process issues. This reading provides an overview of common TCA techniques.

The formulas presented here are structured to treat positive values as unfavorable, indicating underperformance. Conversely, negative values indicate cost savings. These formulas can be adjusted as needed to suit different benchmarks.

Formulas:

Cost in total dollars:

$$
\text{Cost } (\$) = \text{Side} \times (E_p – R_p) \times \text{Shares} $$

Cost in dollars per share:

$$ \text{Cost } (\$/\text{share}) = \text{Side} \times (E_p – R_p) $$

Cost in basis points:

$$ \text{Side} \times \left[\frac {(E_p – R_p)}{R_p} \right] \times 10,000 $$

Where:

Side = +1 if buy; -1 if sell

\(E_p\) = Average execution price

\(R_p\) = Reference price

Shares = Shares executed

The reference price can take on many forms, as will be discussed next in the following sections. It can be tailored to the situation at hand and is meant to represent the most appropriate comparison point for the given trade.

Arrival Price

Arrival price is synonymous with the market price at the time the order was released to the market and the actual transaction price for the fund. Consider the following example, which uses the formula from the section above along with the arrival price to calculate trade cost.

Consider the following facts. A portfolio manager executes a buy order at an average price of = $75.03. The arrival price at the time the order was submitted to the market was $74.99. The arrival cost expressed in basis points is as follows:

Cost in basis points:

$$ \text{Side} \times \left[\frac {(E_p – R_p)}{R_p} \right] \times 10,000 $$

Where:

Side = +1 if buy; -1 if sell

\(E_p\) = Average execution price

\(R_p\) = Reference price

$$ +1 \times \left[\frac {(75.03 – 74.99)}{74.99} \right] \times 10,000 = 5.33 \text{ bps} $$

Therefore, the fund incurred an arrival cost of 5.33 bps, underperforming the arrival price benchmark by this amount.

Volume-weighted Average Price

Volume-weighted average price is a metric that takes into account all of the trading activity of a particular security over the course of a day. This makes it an excellent reference point for comparing the cost of a portfolio's trading with that of overall market's cost of trading.

A hypothetical portfolio manager executes a buy order at an average price of = $99.44. The VWAP over the trading horizon is $100. The VWAP cost benchmark is computed as follows:

$$
+1 \times \left[ \frac { (99.44 – 100)}{100} \right] \times 10,000 = -56 \text{ bps} $$

Therefore, the fund outperformed the VWAP by 56 bps. Although not the case here, the order will typically underperform the VWAP due to bid–ask spreads and the order pressure.

Time-weighted Average Price

The TWAP benchmark is yet another measure to determine whether the portfolio achieved fair and reasonable prices over the trading period. It is used when managers wish to exclude potential trade price outliers.

Market on Close

The closing benchmark (MOC) is often used by index managers and mutual funds that wish to achieve the closing price on the day and compare their actual transaction prices with the closing price. This is important since these funds do not trade intra-day like typical stocks and ETFs but rather are valued at the end of the trading day. Using MOC ensures that the benchmark cost measure will be consistent with the valuation of the fund (usually denoted in NAV). The closing price benchmark is also the benchmark that is consistent with tracking error calculation. MOC benchmarks are often used in fixed-income trading.

Market-adjusted Cost

A market-adjusted cost benchmark is designed to isolate any price movement due to the general market direction from the cost due to the impact of the order.

Said another way, buying stock when the market is rising market and selling stock when the market is falling will cause a portfolio to incur higher costs than expected. Conversely, selling stock in a rising market and buying stock in a falling market will cause the fund to incur lower costs than expected.

In order to calculate the market-adjusted cost, subtract the market movement cost (adjusted for the order side) from the total arrival cost of the trade. The market cost is computed on the basis of the movement in an index and the stock's beta to that index, as follows:

$$
\text{Index cost (bps)} = \text{Side} \times \left[\frac {(\text{Index VWAP} – \text{Index Arrival Price}) }{ \text{Index Arrival Price}} \right] \times 10,000 $$

After calculating the index cost, mark-adjusted cost may be calculated using the following formula:

$$ \text{Market-adjusted cost (bps)} = \text{Arrival cost (bps)} – \beta \times \text{Index cost (bps)} $$

Buying in a Rising Market – Example

Consider the following example from the curriculum of a portfolio manager who executes a buy order at an average price of $30.50. The arrival price at the time the order was entered into the market was $30.00. The selected index price at the time of order entry was $500, and the market index VWAP over the trade horizon was $505. If the stock has a beta to the index of \(\beta\) = 1.25, the market-adjusted cost can be calculated as follows:

1. Calculate Index Cost:

   $$ \begin{align*} & \text{Index cost (bps)} \\ & = \text{Side} \times \left[ \frac {(\text{Index VWAP} – \text{Index Arrival Price}) }{ \text{Index Arrival Price}} \right] \times 10,000 \\
   & +1 \times \left[\frac {(505 – 500)}{500} \right] \times 10,000 = 100 \text{ bps} \end{align*} $$

2. Calculate Arrival Cost:

   $$
   \frac {(30.50 – 30)}{ 30} \times 10,000 = 166.67 \text{ bps} $$

3. Calculate Market-adjusted Cost (bps)

   $$ \text{Market-adjusted cost (bps)} = \text{Arrival cost (bps)} – \beta \times \text{Index cost (bps)} $$

   $$
   166.67 – 1.25 \times 100 = 41.67 \text{ bps} $$

Added Value

Added value is similar to market-adjusted cost in that it compares arrival cost to another metric, but rather than using an index cost, managers use an estimated pre-trade cost.

$$ \text{Added value (bps)} =\text{ Arrival cost (bps)} – \text{Est. pre-trade cost (bps)} $$

The expected trading cost is calculated using a pre-trade model and incorporates such factors as:

• Order size.
• Volatility.
• Market liquidity.
• Investor risk aversion.
• Level of urgency.
• The underlying market conditions at the time of the trade.

If a fund executes at a cost lower than the pre-trade estimate, it is typically considered superior trade performance. If the order is executed at a cost higher than the pre-trade cost benchmark, then the trade is considered to have underperformed expectations. The expected cost is somewhat subjective and uses the expertise of the managers to decide an appropriate estimated cost. On the exam, it may possibly be given rather than something a candidate must calculate.

Consider a manager who executes a buy order at an average price of $20.35. The arrival price at the time the order was entered into the market was $20.00. Prior to trading, the buy-side trader performs a pre-trade analysis of the order and finds that the expected cost of the trade is 60 bps, based on information available prior to trading. The pre-trade adjustment is calculated as follows:

$$ \frac { (20.35-20)}{20} \times 10,000 = 175 \text{ bps} $$

$$ \begin{align*}
\text{Added value (bps)} &= \text{Arrival cost (bps)} – \text{Est. pre-trade cost (bps)} \\
\text{Added Value} & = 175 \text{ bps} – 60 \text{ bps} = 115 \text{ bps} \end{align*} $$

The pre-trade adjusted cost in this example is 115 bps, indicating that the fund underperformed pre-trade expectations by 115 bps.

Hint: thinking of the added value, which is denominated in bps as a cost, may help candidates keep the under vs. overperformed question straight. If your costs are positive, you disappointed or underperformed. On the other hand, if costs are negative, you did well and earned money on the trade, outperforming expectations.

Question

A portfolio manager executes a sell order at an average price of $49.50. The arrival price at the time the order was entered into the market was $50.00.

The arrival cost is closest to:

1. 98 bps.
2. 101 bps.
3. -100 bps.

Solution

The correct answer is C.

Cost in basis points:

$$
\text{Side} \times \left[\frac {(E_p – R_p)}{R_p} \right] \times 10,000 $$

Where:

Side = +1 if buy; -1 if sell

\(E_p\) = Average execution price

\(R_p\) = Reference price

$$ -1 \times \left[\frac { (49.50 – 50)}{50} \right] \times 10,000 = -100 \text{ bps} $$

A is incorrect. From the workings, the correct answer is -100bps.

B is incorrect. It reverses the order of the arrival price and execution price:

$$ \frac {50 – 49.50 }{ 49.50} \times 10,000 = 101 \text{ bps} $$

Portfolio Management Pathway Volume 2: Learning Module 8: Trade Strategy and Execution; Los 8(h) Evaluate the execution of a trade