Introducing IS to our Algo Suite

7 min readApr 12, 2024

(IS Algo Article — Part 1/2)

By Suren Markosov, head of Quantitative Research, Anboto Labs

Summary

Implementation Shortfall (IS) can be defined as the difference between the order’s execution price and arrival price.
The IS algo seeks a balance between urgency of execution and minimizing market impact. Longer the execution time horizon, lower the expected market impact but higher the execution risk.
IS is suitable to use when capturing the best possible price is more important than fully executing the entire order immediately.

Introduction

In the fast-paced world of cryptocurrency trading, controlling transaction costs and slippage is a critical priority for professional traders. In our previous article, “Slippage, Benchmarks and Beyond,” we introduced the topic of Implementation Shortfall (IS), also known as “Arrival Price Slippage,” a very important benchmark for most traders.

In this article, we explain the definition, use cases and key dynamics of the IS algo. We have also released another article that digs deeper into the Almgren-Chriss (AC) framework and how Anboto leverages this framework in its IS algo.

IS (Implementation Shortfall) definition

IS has generally been defined as the difference between the order’s execution price to the so-called “arrival price” i.e. the mid price of the asset at the time the order arrives at the broker’s algo. The IS algo seeks a balance between urgency of execution and minimizing market impact. Longer the execution time horizon, lower the expected market impact but higher the execution risk.

In other contexts, the IS definition may use other benchmark prices, e.g. the “decision price” (the price at the time of the portfolio manager’s decision to buy or sell that coin). In TradFi markets, which have breaks in trading, today’s Open price, or the previous day’s Close may be treated as the “arrival price” benchmark for IS calculations. This is less relevant in Crypto markets but highlights that the “shortfall” to be minimized by the algo can be against many different benchmarks.

Another interpretation of IS as a Transaction Cost Analysis (TCA) benchmark defines IS as the difference between paper trading P&L, e.g., in a backtest of a quant trading model, and the actual trading P&L of that same trading model.

Use Cases

Suitable when capturing the best possible price is more important than fully executing the entire order immediately.
Can be used as an alternative to POV (Percentage of Volume) with the trader’s Urgency in IS instead of the Target Participation Rate in POV.

The Trader’s Dilemma: Two Drivers of Slippage

Our previous article also highlighted the so-called “Trader’s Dilemma”, i.e. the idea that minimizing the arrival price slippage (a.k.a. IS) involves the trade-off between IS’s two drivers:

the price impact, which comes from trading rapidly/aggressively
the “execution risk”, i.e. the risk of the price running “away” (i.e. higher for buy orders, lower for sell orders) from us, forcing us to complete the order at worse prices.

IS’s first component, price impact, is easier for traders to conceptualize, though not necessarily easy to measure accurately, especially in the context of a single order. Technically speaking, the price impact of the order is the difference between the asset’s price trajectory with the order in the market versus without the order in the market, and since the latter is obviously unobservable, we can never really tell for sure what the impact of that order was. For this reason, it is difficult to accurately forecast the price impact of a given single order. However, over a large number of orders, these forecast errors “average out” and become small. Thus, trading algos relying on forecasts of price impact can be very effective in managing the client’s aggregate slippage. The price impact component is thus provided by average (a.k.a. “expected”) IS value.

Execution risk, The second component of IS, is also known as the “opportunity cost” , because by trading too slow we’re missing out on the opportunity of transacting at prices which may, in retrospect (in the scenarios where the price “runs away”), turn out to be the best prices for us to execute at, over our order’s time horizon. Typically this component is measured as the volatility (or its square, variance) of the arrival price slippage since higher volatility also increases the probability (and the expected cost) of the prices “running away”.

Technically, using an asymmetric measure of risk like semi-variance or Value At Risk (VaR), rather than a “symmetric” risk measure like volatility or variance since clients only care about minimizing the adverse outcomes (price “running away”).
While trading models using asymmetric risk measures do exist, they come at the cost of significant increases in model complexity (and therefore — reduced transparency and tractability) without necessarily materially changing the algo’s trading behavior.

To help traders strike the optimal balance between impact and risk, we need to introduce a “trade-off coefficient” or a “relative price” between these two drivers of IS. This coefficient is typically described as the “risk-aversion” or “risk intolerance” or “urgency” parameter. This parameter aims to answer this question: “how many additional units of price impact are you willing to accept, in order to reduce the execution risk by one unit?”

This parameter has many other names, including “Lagrange multiplier” (a term from the optimization literature), which is why the Greek letter Lambda (λ) is typically used in the formulas to denote it
As discussed in our previous article, while in theory it is meant to be a measure of the trader’s intolerance to execution risk, in practice, traders decide on the value of this parameter based on many criteria, including the price momentum expected by the trader on the given asset at the time of the trade, or the expected time horizon of their strategy’s alpha (the more short-term their alpha, the higher the Lambda (λ) value should be).

The Figure 1 below reproduces the chart from our previous article, of the “risk-adjusted cost”, at two different risk-aversion (λ) settings for a hypothetical coin — as discussed in our previous article, the higher λ values results in faster execution (shorter expected execution horizon):

The Risk Adjusted Cost in the chart above is calculated as follows:

Risk adjusted cost = Average impact cost + Urgency * risk
= Expected(IS) + λ * Volatility(IS)

where Expected(IS) stands for the expected value of IS, and Volatility is the one standard deviation (i.e. square root of Variance) of IS, for a given trading strategy (i.e. trade schedule) for a given order quantity in a given asset.

Since the IS of an order is always a random variable subject to uncertainty, it is appropriate to speak of Expected IS and Volatility of IS, even if for a single order, in the context of forming our strategy optimization problem.
As can be seen in the Figure 1 above, for the higher urgency value of 0.01 (the solid green curve), the risk-adjusted cost reaches its optimal (minimum) level of 35bps at a time horizon of 0.32 days. For the lower urgency setting of 0.13 (the dashed red curve), the minimum risk adjusted cost of 30bps is reached at a longer execution time value of 0.52 days. of 0.32 days. As we can see, the higher the urgency setting, the shorter the time horizon of the optimal — cost-risk efficient — trading strategy.
Please note that in this example we used Volatility as a measure of execution risk, for ease of illustration, but in many optimal strategy analyses (including the Almgren-Chriss framework which we’ll discuss in the next section) Variance (volatility squared) is used instead, to help simplify the calculations involved.
When using Variance as a risk measure, the values of the Risk Aversion Parameter (λ) need to be re-scaled accordingly.

The execution cost-risk relationship described above is also often represented via the “optimal” (a.k.a. “efficient”) trading frontier, shown in Figure 2 below. The hypothetical trade scenario from the Figure 1 is represented by the blue curve called “Frontier # 1”. All cost-risk optimal strategies for that hypothetical coin will lie on that blue curve, including the two optimal strategies shown on Figure 1, for urgency settings 0.08 (green point) and 0.13 (red point). Just like in Figure 1, the higher Urgency (λ=0.13) point has a higher Market Impact (average or expected IS) but a lower execution risk, while the lower Urgency (λ=0.08 ) point has a lower market impact, but a higher execution risk.

Also note that Figure 2 shows another efficient frontier, represented by a red dashed curve, for a different hypothetical coin. Note that this “Frontier # 2” has a worse profile: this coin is more difficult/expensive to trade, since the expected slippage is higher for this same level of execution risk, compared to our original (blue curve) frontier. Other things being equal (i.e. for the same expected alpha on a trade), a rational risk-averse trader would prefer an asset with an efficient frontier as far to the ‘south-west’ as possible, i.e., as close as possible to the {zero risk, zero impact} origin. If a coin’s frontier is to the ‘north-east’ relative to another coin (as shown by the dashed line), such a coin is fundamentally more difficult to trade.

Conclusion

Anboto’s implementation of the Almgren-Chriss framework in the newly released IS algo represents a significant addition to our algo suite. It will help our clients strike a balance between price impact and execution risk, by adapting the algo’s trading behavior to the specific characteristics of the individual digital assets, and to the clients urgency/risk-aversion levels.

As the crypto trading landscape continues to evolve, the importance of effective execution algorithms will only grow. Anboto’s pioneering work in this area sets a strong foundation for further innovation and development.

For a deep dive into the Almgren-Chriss Framework and and how Anboto leverages this framework in its IS algo, read part 2 of the article here.

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If you have any questions about our IS algo or any other aspects of our product offering, please feel free to reach out to us at info@anboto.xyz