- Jeff Bacidore

# Trading Cost Models: Uses and Abuses

*Jill Biden has a Ph.D. and insists on being called Dr. Jill Biden. *

*I too have a Ph.D. *

*Therefore, I must also insist on being called Dr. Jill Biden.*

-- Dr. Jeffrey Bacidore, aka Dr. Jill Biden

This joke reminded me of how much abuse – some light-hearted, some not so much – quants used to receive when I first entered the trading world, especially if one had a Ph.D. Ph.Ds were often told to keep the designation off of their business cards. Now, it seems having a Ph.D. is *de rigeur. *(I can now safely expense my “Word of the Day” calendar for tax purposes).

In any case, this further reminded me of my first foray into quantitative trading, which was building a trading cost model for our clients and internal desks. At the time, cost models were not widely available let alone used, and confusion over their application was rampant. Even today, there is a lot of confusion surrounding the benefits and limitations of trading cost models in the investment and trading process.

In this blog, I am going to review some of the common limitations of costs models as well as examples of where cost models can add tremendous value. To be clear, the cost models I will refer to are those that attempt to forecast the expected execution shortfall, i.e., the slippage between the execution price and a pre-trade benchmark. The list below is not meant to be exhaustive. For those wanting to learn more about cost models, especially from a technical perspective, I would refer you to the wealth of excellent work done by the Virtu (formerly ITG) financial engineering team. And for a less technical introduction, cost models are discussed at a higher level along with some related applications in my new book (apologies for the shameless plug).

**Two examples of trading cost model failures**

*Pre-trade cost models are terrible for predicting the cost of individual orders*

Perhaps the most obvious case where t-cost models are of limited use is when forecasting the cost of individual, institutional-sized orders. The issue with a pre-trade cost model lies not in its estimates, per se. Rather, the issue stems from unreasonable user expectations. Simply put, the cost estimate from a model reflects the *expected cost*, or the average cost you’d incur if you did the same trade “eleventy-billion” times. On any given trade, though, there is an entire distribution of possible outcomes around that average. Most cost models only give you that single “point estimate” and not a sense of the variability around that estimate. And unfortunately, the variability tends to dwarf the expected cost estimate for larger orders.

For example, a stock with 30% annualized volatility will have daily volatility of 200 basis points. Most cost estimates are an order of magnitude less than that. This reflects the fact that traders themselves generally cannot impact prices too dramatically if they trade in a reasonable manner. This means that the vast majority of the variability in realized performance relative to the arrival price is *not explainable *or forecastable by a cost model*. *Why not? Because this would require not only predicting the order’s impact on prices, but also forecasting *market prices *over the life of your order*.*

Put differently, the execution price on a given parent order is an average of the individual fills, weighted by the size of the fill. To predict that with accuracy would require predicting the sizing and timing of those fills, the prevailing prices at the times of those fills, and where the fills occur relative to those prevailing prices. A tall order. The timing and possibly even the sizing might be somewhat predictable for a schedule-based algorithm like TWAP and VWAP. Modeling the impact of your own fills at a point in time might be somewhat feasible (e.g., marketable orders pay the spread). But forecasting the last piece requires that you forecast not only the cumulative impact of all your past trades – which itself is a tall order—but also the future price path of the stock! To accurately predict trading costs at a point in time, then, requires you to predict the related market, industry, and other factor returns as well as the stock-specific returns independent of your order. And since these tend to be much more volatile than price impact, market impact models will generally only “explain” a very small fraction of the shortfall cost, meaning realized costs can differ significantly from the cost model estimate.

*T-Cost models Are Less Helpful on Rare or Exceptional Trades*

Perhaps my most terrifying experience on Wall Street was when I heard the head of one of our trading desks screaming “Bacidore!? Where’s Bacidore sit?”. Given the odds were low that the firm had hired another Bacidore, I put my hand up. Apparently, the desk head was using the model to estimate the cost of a large block of stock, many times larger than even the largest order that was used to estimate the model. And when the model spit out gibberish, the trader wanted to give me specific instructions on what I could do with my model. (I cannot repeat the exact words here, but suffice it to say it was not possible to follow his instructions verbatim given that a cost model is not actually a physical object).

Jokes aside, the other major limitation of these models is that they are really most suitable for those orders similar to those used to estimate the model. Putting in an uncharacteristically large order, for example, or for a stock that may not represent those used to estimate the model (e.g., a liquid ETF in a model estimated using only non-ETF common stocks) will often generate unrealistic estimates. The model is simply extrapolating outward, which may or may not be appropriate.

**Examples of Where Trading Cost Models Can Add Value**

*Portfolio Construction*

Investment managers often use trading cost models to help how much of their alpha will be lost due to implementation costs. Trading costs often generate significant drag on performance, especially for funds trading relatively illiquid stocks, relatively large sizes, and/or with relatively high turnover. Understanding whether there is enough “juice” in a trade to overcome implementation costs is a critical part of the investment process. Furthermore, an accurate cost model can help in determining the optimal trade size. Often a trade is viable if sufficiently small, but becomes unprofitable if scaled up too far. A well-specified trading cost model can be useful in determining the optimal size of a given trade.

*Strategy Formulation*

In addition to sizing the trade, a trading cost model can also be useful in formulating an effective trading strategy to implement the trade. While a cost model may not explain much of the variation in performance on any given order, they can provide useful estimates of the *average *performance of given strategy if repeated over and over again. If the model is well-specified, the *mean *realized performance will converge to the cost model estimate. Therefore, the cost model can be used to help develop an optimal trading *strategy,* e.g., one that balances trading cost against alpha and/or risk. In fact, some implementation shortfall algorithms (also called arrival price algorithms) will use these cost models along with an urgency parameter to make this trade-off. So, while the algorithm may do poorly on individual orders– even quite poorly – over time, realized average performance should fall in line with the forecast.

*Portfolio Level Pre-Trade Cost Estimates*

As noted above, the main source of poor accuracy of cost estimates on a single order basis is that it is stymied by the unrelated asset volatility. But this problem is less severe in a two-sided portfolio trade. For example, if a portfolio trade were beta-neutral and/or sector-neutral, a good portion of the variation would be reduced. And if the portfolio were large, with hundreds of orders on each side of the basket, diversification would reduce the per unit risk of the portfolio even further. As the relative importance of the unrelated noise falls, the accuracy of the cost model will increase, making it a more relevant tool for pre-trade pricing of the portfolio trade as a whole.

*Post-trade Analysis*

As with strategy formulation, the averaging of performance across multiple orders helps to reduce the noise caused by unrelated price movements. Over increasingly large samples, the realized average performance should become less noisy. A cost model can then be used as a benchmark in evaluating performance.

Perhaps the most overlooked use of the cost model is that it helps standardize performance across samples of different characteristics. For example, if a buyside trader routes relatively more liquid names to Broker A than to Broker B, Broker A is *expected *to beat Broker B even if the two brokers were identical simply due to differences in sample composition. But if you compared Broker A’s *relative *performance to Broker B’s *relative *performance, this bias can be eliminated.

For example, suppose Broker A’s realized performance is 8 bps, while Broker B’s performance is 9 bps. How do you adjust for differences? One way is to standardize each broker’s performance *relative to the cost model estimates* before comparing to one another. Suppose, based on Broker A’s orders, the cost model forecasts an average cost of 7 bps, while the expected cost for Broker B’s orders is 10 bps (due to its skew toward less liquid orders). Broker A actually performed *worse *than the cost model benchmark while Broker B outperformed the cost model, leading to an entirely different conclusion than one based on absolute or unadjusted performance.[1]

*Takeaway*

Cost models can be extremely effective when used appropriately. Cost models are not crystal balls that can predict future prices. Nor can they be expected to perform well when used to evaluate atypical orders. But they can be quite effective in other uses, especially those applications where the cost model is used to evaluate the *mean* performance, as is the case with a portfolio trade and on post-trade analysis of a sample of trades. The key is not asking the cost model to do things it simply is not equipped to do.

*Footnotes*
[1] For more information including examples, see my new book __Algorithmic Trading: A Practitioner’s Guide____.__

*The author is the Founder and President of The Bacidore Group, LLC and author of the new book ***Algorithmic Trading: A Practitioner's Guide***. For more information on how the Bacidore Group can help improve trading performance as well as measure that performance, please feel free to contact us at **info@bacidore.com** or via our webpage www.bacidore.com. *

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