Ignorance is not bliss - Signal Risk and Machine Learning in portfolio execution

Ignorance is (not) bliss

Market impact and timing risk in execution is often considerably more costly than commission, but often ignored. Just because transaction costs may not be measured, doesn’t mean they don’t exist.

At its simplest, the stock market is characterised by multiple buyers and sellers placing bids and offers, swapping economic interest in companies that are publicly listed. For a purchase to occur, a buyer can “aggress” by crossing the spread and paying the price of the offer, often called the cost of “immediacy”. This price effectively compensates the passive seller for their liquidity and for the risk that the buyer is in the possession of some information that would indicate the stock is mispriced and will continue to increase in value. The opposite is of course true for sales.

The total costs of these buys and sells can be decomposed into “explicit”, being the cost of commissions, and “implicit” which is the, often hard to measure, price impact of the trade made up of market impact and timing risk discussed later in the paper.

Bid/ask spreads have narrowed over time as short-term traders, who may trade only to earn the spread through posting both bids and offers, or to arbitrage fleeting price differences between stocks or execution venues, compete for priority and have increased in presence.

Algorithms now dominate stock market volumes including for both short-term traders and for the execution of longer term fundamental based orders. As algorithms tend to place smaller orders in the market to avoid signalling, a downward spiral of displayed volume has occurred.

The Australian Securities and Investment Commission (ASIC) reports in its quarterly statements that effective spreads have fallen from around 12.5bps in Q1 2012 for the market cap weighted ASX200 to around 9bps in Q1 2018. (0) This ~30% fall in spreads seems to have been accompanied by a significantly larger 50% fall in order book volume, indicating lower spreads are traded off against volume with no obvious benefit.

The plots above demonstrate the volume collapse when selecting two days almost six years apart. The Y axis represents the Cumulative Median Daily Volume (MDV) available at each level in the order book with the X axis, being the trading day. The MDV’s are index weighted with bids sitting below the central line and offers above.

By 2018, there were two obvious changes. Firstly, instead of being consistent through the day, volume builds up towards the market close which is a probable outcome of the shift towards passive investing. Secondly, available volumes on the lit order book have collapsed. This effect is amplified in Japan. (0)

This change in the order book dynamic has necessitated a change in how orders are executed.

An order can either be placed in its entirety on the order book, or be cut up into “child orders” and released slowly to hide among the volume and appear to be uncorrelated “uninformed” orders in an attempt reduce the immediate price impact on the stock.

Placing a large order in the market can create an immediate adverse price move as the market responds to the explicit and sudden excess demand/supply and the expectation the order carries some information about the direction of the stock. As seen above, the signalling risk of posting bids or offers of the same size could have a larger immediate price impact today than 6 years ago. “Market impact” is the excess price move caused by additional demand or supply from a new order entering the market and creating an adverse price move as the order is executed.

The subtle but sustained demand and supply imbalance caused by the “cutting and spreading” of an order can result in adverse price moves before the order is completed as the market becomes aware of the order. The risk of an adverse price move (up for a buy, down for a sell) due to information or research being disseminated into the market before the order can be completed is referred to as “timing risk” or the cost of non-execution.

Low cost execution requires balancing the timing risk (the cost of non-execution) and market impact (the cost of immediacy).

Chasing the wrong signal

In the day-to-day execution of orders, company fundamentals and valuations are rarely a meaningful driver of short-term price moves. While analysis of a company’s fundamentals is vital for modelling longer-term price moves, the trading horizon for most orders is measured in the minutes, days or weeks where company earnings rarely change enough (or are disseminated efficiently) to move the price.

Of more importance to short-term price moves are supply/demand imbalances often caused by herding,  the aggregation of orders traded in batches or simply overly aggressive trading by market participants. Each of these can create multi-horizon price dislocations that bear no resemblance to the underlying fundamentals of the business.

QTRMASTER

For every order, traders are faced with the dilemma of two main decisions being “when to trade” (order timing) and “how to trade” (strategy selection), the outcome of which is the main driver of the order.

To handle this problem, Schroders have developed a trading model named  “Quantitative Trading Research Model for Automated Strategy & Timing Execution Routing” (QTRMASTER) which is primarily designed to forecast alpha decay in an attempt to optimise order timing and select the most appropriate trading strategy for each individual order.

QTRMASTER - Order timing impact on returns

Alpha decay can be defined as the horizon where the expected returns from a new order decay to 0 if trading is delayed.

Conceptually, a model that can capture the general alpha decay of an Investor is the first level of defence in alpha preservation and is designed to act as the translator between the medium/long-term view on a company’s value and the expected speed of the realisation of that valuation.

The figure below represents a typical “trader’s dilemma” where understanding the alpha decay of the trade can help to solve. The X axis represents time (usually represented in volume, not wall clock) with Y representing Cost.

Timing risk relates to the risk of the associated losses from non-execution where a stock price moves before an order can complete, as a result of information being disseminated in the market or where there has been an active decision to trade passively. Market impact represents the excess price deviation of the order caused by either aggressive execution forcing a price move, or signal leakage where the order intentions are leaked or the price reacts.

An order with fast alpha decay expectations should be aggressively executed to compress the time horizon of the trade and minimise timing risk, as long as the associated market impact is lower than the timing risk. Block liquidity can be favoured to reduce market impact, however it is dependent on another investor having the exact opposite view at exactly the same time, which is a low probability event.

Conversely, an order with a slow alpha decay profile (longer horizon) should be executed using a relatively passive strategy, characterised by attempting to capture the spread through liquidity provision without needing to incur the cost of immediacy. For slow alpha decay trades, timing risk is low and the goal is simply to reduce market impact. (See Appendix) (3)

The Alpha Decay Model is part of an ensemble of models with varying levels of upside and accuracy embedded in QTRMASTER. The difference between getting it right and getting is wrong is greater than 30 basis points on average, with some strategies being many multiples of that. While the model can have very large payoffs when correct, it also contains a high level of statistical noise. Where the signals display weak probabilities of success, the alpha decay signal is effectively de-weighted and the speed of execution is left to the downstream models (algorithms). These tend to be more accurate in determining shorter-term price moves but with lower payoffs.

Markets shift from momentum through to mean reverting over time and the behaviours of the person generating the order may change considerably to react. Given the human behavioural element and that history repeats itself until it doesn’t, the risk of non-stationarity in this data implies the Alpha Decay Model is designed to only prime the order with an initial expectation of the immediate price move and there are many other factors that determine the ultimate cost of the order.

Tactical intra-day order timing – How algorithms differ.  

Fixed Schedule Algorithms rely on a fixed start and end time, with a pre-calculated schedule applied for cutting up and distributing individual orders over the period, generally naïve to price and actual market conditions. This class of algorithm (which includes VWAP, POV and TWAP) tend to be the dominant execution strategy for traders across the industry, which is disappointing.

While traders may try and hide in “over the day” fixed schedule strategies, excess market impact can be incurred as a result of predictable timing of orders into the market such as the following which leaves an easily identifiable signal:

“Post liquidity….. -> …..Wait ->….. Cross the spread -> …..Reload…”

This naïve method of participation can cause prices to dislocate on excess volume, an indicator of short-term momentum. The chart below uses real data from fixed schedule algorithms on varying alpha profile portfolios, where each order is broken up into deciles of completion and the deviation from the arrival price is calculated for each decile. The averages are taken and plotted below.

The surface plot represents the average deviation from the arrival price of the order by participation rate (-‘ve = worse outcome) and also by decile of order completion. Performance decreases across time as participation rates increase for fixed schedule algorithms.

A likely cause for this excess cost is the combination of a predefined pattern revealing a probable future price move for the stock combined with naïve aggression creating a price dislocation.

The excess market impact from these types of orders is the profit to short-term trading firms not limited to HFT, from detecting and trading ahead of these orders or betting on a price reversal when the order completes and the signal dissipates.

In this dataset, orders with a participation rate above ~5% of passing volume tend to suffer from deterioration in performance across time as the order completes. This pattern of performance deterioration is not as obvious across strategies that respect an anchor price and where participation appears less predictable.

As a house, Schroders rarely deploys fixed schedule algorithms, preferring instead to route to Cost Objective (price aware) strategies including arrival price strategies… but with a twist.

The cost of portfolio implementation is normally calculated as the deviation in returns from the theoretical portfolio to the realised portfolio.  To solve this, the industry created a popular alternative to the fixed schedule algorithms being those that anchor to the “arrival price” of the order to the desk. These algorithms simply vary aggression levels as the price deviates usually by slowing down trading during adverse price movements, and vice versa. The underlying premise of this strategy is mean reversion and the assumption the algorithm is mostly responsible for the observed price moves.  

While theoretically using a fixed price anchor seems logical to minimise cost, in reality it can result in adverse outcomes as the strategy can cut winners early and extend the trading horizon of losing trades, typically where mean reversion is expected in what is actually a momentum period.  These issues compound when the alpha decay is ignored.

Markets are incredibly dynamic with many participants trading multiple strategies in any given stock at any time of the day. Market “regimes” shift dramatically intra-day, which can have an impact on the initial expectation set by the Alpha Decay Model. Naïve algorithms or those with fixed anchors tend to ignore important signals through the life of the trade.

In general, The best performing strategies as measured by QTRMASTER are those that ignore the fixed “arrival price” of the order in favour of dynamic price forecasts. Calculating a quantitative based intra-day forecast price can improve the probability of recognising legitimate shifts in momentum from short-term anomalous price moves, triggering very different behaviours in the strategy and avoiding the aforementioned issues.

An example of such an algorithm designed by Schroders is below, where a dynamic short term price forecast is employed as an anchor to accelerate or decelerate executions.

Beta can be defined as the measure of variance of a security in comparison to the market as a whole. Normally Beta is measured using long-term daily returns; however can be  adapted at an intra-day level to proxy for short-term changes in trader behaviour or for new orders entering the market.

In the example above (HVN.ASX), the intra-day Beta of the stock to the index in one day moved between

• β=0 (independent of the market) to…
• β= -2 (An extreme inverse relationship to the market) to…
• β= +1 (A positive relationship to the market).

An inference is that there were dominant players in this stock at different points in the day (such as the beta deviation at 11:30) with various objectives resulting in swings in the how the stock behaved.

Intra-day Beta is one input into a multi-horizon price forecast model which includes a model for multi-day price forecasts, shorter-term intra-day price forecasts and microstructure forecasts where  servers co-located with the exchange matching engine are utilised to reduce latency and react to higher frequency order book events.

New orders in a market can inadvertently create intra-day momentum that can be detected through proxies such as simultaneous volume and idiosyncratic price spikes. No human trader can calculate this in the time necessary to react and quite often the cause is an overestimation of the speed of the alpha decay of the order, or individual orders such as those from segregated accounts that are batched and sent to the market in waves.

Tracking this metric, among others, allows for subtle intra-day adjustments to the timing of the order by accelerating or decelerating the order based on inferences of how other participants are executing.

The plot above of a BUY HVN order highlights the benefits of intra-day order timing. The forecast price (light blue) is compared to the actual price (orange) with the realised price of the stock in black. The blue bars represent 5-minute bins of the suggested volume from a Fixed Schedule (VWAP) strategy showing a constant distribution of prices through the day, against the red bars being actual trades.

Participation was constrained where prices represented a significant premium to the forecast between 11:00 and 14:00 and aggressive during the closing period where prices were cheap. The traders see this data in real time through the day however often the decisions are best left to the algorithm.

The order received an initial alpha signal however the overlay can enhance the original alpha decay expectation of the order by dynamically adjusting the trade horizon based on new information. Any savings represent real dollars saved to the end investor.

As data and quantitative analysis of the order book is made more accessible through friendly environments for development, the resource dedicated to short-term trading strategies (not limited to HFT) based on order anticipation is greater than it’s ever been. Protection of our investment signal has never been more important and tracking our own signal can increase self-awareness if the order in the market is suffering from adverse impact.

Forecasting prices and regime shifts allows our orders to gain an advantage where we can recognise poor execution by others. In effect, we are attempting to turn our orders to the hunter instead of being the hunted.

QTRMASTER – The idea behind algorithm strategy selection

QTRMASTER is designed to select the best algorithm for the trade based on the behaviour of each strategy given a range of information.  

The ability to calculate complex problems at high speed and to not suffer from overconfidence means there is little question that algorithms are better suited than humans to handle noisy data such as stock prices and orders involving higher frequency interactions with the fragmented liquidity available in the market.

A data set of sales trader daily “market predictions” were collected over a year to capture whether there was any forecasting ability. Unfortunately, the predictions offered a -1.7% correlation to the actual index return whilst in comparison a random number generator using historic mean and standard deviation offered a +1.4% correlation.

There is no doubt that there are some sales traders that would have a far better hit rate and like humans, algorithms, even those with the same objective, are not equal.

Algorithmic strategies are usually constructed to optimise on a specific benchmark such as arrival price as discussed previously, or simply are coded as per the experience of the developer leaving a behavioural footprint.

It seems to be standard industry practice to measure algorithm performance by grouping orders by a single variable. The percent of average/median daily volume (ADV/MDV) or market capitalisation are the most common where average costs compared between brokers over an arbitrary period of time are used as a very crude forecasting measure.

The outcome (cost) of an order is dependent on many variables. While ADV is often the largest driver, factors such as spread, stock volatility, embedded alpha, and time of day amongst others also contribute.

Discretising continuous variables at arbitrary intervals ignores a significant amount of information that could improve the forecasts. Industry standard reports tend to bucket all orders between 1-5% of average daily volume (ADV) in the same bin. Depending on the strategy, this may include orders that include only a handful of individual transactions for an order of 1.1% of ADV, and larger orders up to 4.99% of ADV that transact over the full day.

Trying to forecast execution cost with only 1 dimension severely limits how useful that measurement can be deployed as a forecast for a given order.

QTRMASTER is an attempt to re-shape the all too common question from “what is the best algorithm” to “what is the best predicted outcome for each algorithm for an order with a specific set of variables?” Unless this question can be answered, trading becomes guesswork, and often worse than random.

QTRMASTER - Machine Learning in algorithm selection

Supervised Machine learning, the type deployed in QTRMASTER, utilises a large amount of trading data to train a model to understand the non-linear cost responses to individual variables within the dataset and construct a generalised model with minimal error. By building hundreds of individual models, each with low bias but high variance, averaging them to reduce variance and sub-setting the data and variables to reduce the correlation between the models, we end up with a model that has a reduced error.

Machine learning in QTRMASTER was only introduced after testing more traditional statistical models to ensure that complexity wasn’t being added to the process for no gain. The underlying technique adopted in QTRMASTER has allowed for the creation of a proprietary market impact model that captures the complex non-linear relationships of each order variable and the interactions between them. The improvements justify the complexity. It remains that the most important step in any research is to understand the data and domain and construct a robust process that questions the outcomes. Complexity should not be added for complexity’s sake. Cross-validation is deployed to address overfitting.

Often there are specific situations where there is simply not enough data to create inferences or where one variable dominates the price reaction (such as a profit up/down-grade). These events are not frequent and the orders can benefit from human intuition where humans may be better at interpreting single variable reactions.

To forecast successfully, the order needs to be viewed through the prism of variables that are most likely to drive cost, not a collection of variables selected on gut feel that have little bearing on the outcome. For example, an order in a mining company should be observed through the dimension of attributes such as order size, spread, volatility, expected return etc.…not long-term commodity prices and shipping rates.

For QTRMASTER to route orders accurately, it is required to understand the behaviours of each strategy relative to the range of variables. When the model is trained, it understands the underlying cost responses to a wide variety of orders (tens of thousands of orders) that it can then apply to the next order that the trader receives. These models require large amounts of data to train.

QTRMASTER subsequently decomposes each order into the variables that will contribute most to the cost with the strategy selected being the one that can improve returns across the variables of each order.

One common complaint of machine learning models is the “black box” nature of what happens within them. In the case of linear regression, considerable insight can be gained into the structure of the model by simply viewing the coefficients. There is no such neat output for machine learning so alternative techniques have been designed to observe how the underlying model is likely to route orders and how each algorithm responds to each variable in isolation.

The Partial Dependence Plot below represents a simple cost response of each algorithm (Y axis) to intra-day volatility (X axis) for five anonymised algorithmic strategies. There are multiple variables in the model that ultimately drive outcomes, however being able to isolate the response to a single variable allows for a window into the algorithms behaviour.

For a given set of data, algorithm #3 (purple) tends to produce the worst outcomes where volatility is low, yet should be the best performer in volatile periods. QTRMASTER is more likely route to algo #3 in higher volatility periods than in periods of low volatility when other variables are factored in.

Observing the behavioural differences per variable between each execution strategy is the key to strategy selection, however the interactions between various variables are important. Interactions exist between variables when their effect on the forecast is not entirely independent and the impact of one variable on the outcome is modified by another variable.

In the surface plot below, an interaction between spread and market cap is present. Order outcomes (z) tend to realise higher costs as both the spread of the stock is widens and the market cap falls. The interaction is demonstrated by a observing a larger effect on outcome (z) between market caps on smaller spread stocks than larger ones.

It is these subtle differences in discovering how specific algorithms behave in specific environments that can add significant value to a client portfolio. These strategy behaviours across multiple variables and the interactions between them are such that a human would be generally unable to recognise and therefore exploit them.

Conclusion 

Anybody that has a dollar in the equity market is forced to execute at some point, yet not everyone is armed with the proper suite of tools to properly minimise transaction costs. Available volumes at the immediate bid/offer are falling with signal detection of live orders becoming more sophisticated and costly to investors as implicit costs. Reducing transaction costs should involve a combination of alpha decay analysis, intra-day price modelling and forecasting the implicit costs of various strategies culminating in proper algorithm selection.

The internalisation of electronic trading research within Schroders as a service to the trading desk has allowed for considerable improvements in execution through improved order timing and strategy selection which will ultimately feed into client returns, our primary objective. The development of QTRMASTER has formalised the understanding of algorithm behaviour and allows for a more systematic approach to estimating the short-term behaviour of an order where there are many variables at play dynamically altering the price of the stock. This can free up capacity for the human trader to focus on events that are dominated by a single variable such as upgrades/downgrades, or takeovers, that may require intuition to achieve a better result and where payoffs are larger.

Appendix

1. The above plots from the ASIC 2018 1Q equity market report show the decline in effective spreads on the left hand chart and the corresponding decline in available liquidity for the top 5 order book levels for the Australian Market across the ASX 200. Conversely, displayed volumes in all stocks (including small and microcap outside the ASX200) have increased as more FUM is focussed in this market cap band where intra-day traders aren’t usually dominant. 

2. The above plots illustrate the extreme decline in liquidity available at the top 5 levels of the order book for Japan. This period includes various initiatives by the exchange such as latency initiatives and reducing tick sizes which altered the underlying mechanics of the order book and the economics of participants. Please note the scale differences. Plotted on the same scale, the differences are far more dramatic.

3. The density plots represent outcomes (x axis basis points) for two different order timing methods across a given set of orders. The pink density plot represents a more passive trading method outcomes characterised by high variance given the additional timing risk but with a better average expected outcome. The Blue density plot represents a more aggressive order timing method leading to higher market impact by a worse average but a tighter variance given the shorter trading horizon. For this data, an estimated ~70% probability exists that an order executed via the passive method will have a better outcome than an order executed by aggressive method indicating a slow alpha decay profile.