When measuring an algorithm against the Volume Weighted Average Price (VWAP) benchmark, it can be very informative to separate the benchmark into skill and luck.

Luck is an important factor in measuring VWAP performance and it is worth evaluating persistent good or bad luck as part of trading analysis. Ultimately, a trader cares about buying at the lowest price and selling at the highest price and an algorithm’s skill along with a trader’s luck factor into this total trading cost. In the end, an algorithm’s trading skill should be able to help a trader achieve his best execution.

Plotting volume through the trading day reveals a relative decline until about mid-day, but then the trend reverses and volume builds for the remainder of the day. As a result, the volume distribution pattern takes on the shape of a smile and is often called the volume smile.

In regards to trading, the volume smile allows an algorithm to trade proactively in anticipation of expected volume instead of reactively as volume occurs in the market. Because the algorithm is anticipating volume it has to make skillful choices to determine the best price to buy or sell.

Although the volume smile slowly evolves over time, the average smile from day to day remains roughly constant. It can be confidently expected that the volume of trades occurring in the market will follow this general pattern daily across most of the market.

“A stock’s volume generally follows the same pattern daily, high at the open gradually falling to a mid-day low then increasing to high again at the close forming a smile shape,” said Terry Ransford, senior vice president and director of trading and technology at Northern Trust Securities.

The standard benchmark to measure actual volume in the market on a weighted basis is VWAP which does not capture the statistics of a volume smile.

With the VWAP benchmark each trade receives a weight relative to the volume of the trade so larger trades reflect greater meaning in the average price.

“The idea is that a particular algo could over or under perform depending on its volume of shares consumed at various price points,” Ransford said. “A buy order using a VWAP strategy would underperform if it consumed too many shares at a high prices or too few at low. If it consumed shares consistent with market volumes at every price it would exactly match the benchmark.”

The implications of the volume smile for matching and measuring a benchmark like VWAP are important.

In order to measure an algorithm’s ability to trade in this environment, it’s necessary to create a new benchmark that captures the statistics of a volume smile.

The proposed new benchmark is called SWAP, which stands for Smile Weighted Average Price. It is calculated by weighting trade prices against the expected volume for the market.

Instead of using actual volume and price of the trades, SWAP uses actual price but weights it by the expected volume smile instead of actual volume. While the volume distribution ultimately does matter in performance analysis, it does not factor into the value of this benchmark.

Knowing that the market typically follows a volume smile means that an algorithm should be able to trade at least as well as the SWAP benchmark. SWAP is a benchmark that represents zero skill and any deviation from this metric shows the skill behind the trading strategy an algorithm employs.

Trading worse than SWAP demonstrates a sub-optimal strategy which could be called poor trading skill. If an algorithm can consistently outperform SWAP, then it has demonstrated a trading strategy with good skill.

SWAP takes into account the concept of luck in trading. This is where the volume profile of actual executions becomes part of the equation again.

Oftentimes the actual volume profile deviates from the expected volume profile. But brokers, traders and algorithms have little control over volume through the day. For example, a large increase of volume at the low prices of the day will make most buy orders look poor when compared to the VWAP benchmark over that time period when using a VWAP algorithm.

The unanticipated volume was not favorable to the performance of the algorithm, but since the algorithm cannot control when this volume trades, it is referred to as bad luck. Therefore, luck can be calculated as the difference between VWAP and SWAP. A large influence on determining if a strategy will have positive or negative luck is the underlying portfolio strategy. For example, a Mean Revert strategy will have very different luck/skill characteristics than a Momentum strategy.

The SWAP benchmark allows a trader to normalize his assessment of algorithm performance across brokers and times traded. Luck and skill are both important factors in determining this benchmark and in turn helps a trader achieve his best execution.