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Alpha Theory Blog - News and Insights

September 23, 2022

The Impact of Large Trades: Helping CenterBook Partner Funds Profit from Transaction Cost Analysis


This article was co-written by Billy Armfield, Data Scientist at Alpha Theory and Director of Partner Fund Services at CenterBook Partners, Aaron Hirsch, Data Scientist at Alpha Theory and Partner Fund Analytics Manager at CenterBook Partners, and Chris White, Head of Risk and Portfolio Implementation at CenterBook Partners. 



“You not only are hunted by others, you unknowingly hunt yourself.” 

― Dejan Stojanovic, The Sun Watches the Sun 


Few things seem more perplexing to the fundamental equity manager than the hidden costs of execution. They appear to be hard to predict, arcane in construction, and yet invariably a frustrating and persistent drag on performance. While managers may follow a heuristic approach for the interplay of trade size, impact, and expected alpha, they are rarely formulated or systematized. Yet, for quantitative managers, Transaction Cost Analysis (TCA) lies at the heart of both the strategy construction and execution process and is a well-accepted and broadly appreciated component. 


At CenterBook Partners LP 1 (“CenterBook”), we have partnered with a select group of Alpha Theory clients (called Partner Funds2) to harvest insights from their Alpha Theory data to build systematic investment strategies. We have been working with our Partner Funds to help bridge the gap between the quantitative and qualitative worlds by providing insights and tools to help our Partner Funds both understand and profit from TCA. 


The Alpha Horizon 


“A stock operator has to fight a lot of expensive enemies within himself.” 

― Edwin Lefèvre, Reminiscences of a Stock Operator 


A concept heavily used in quantitative strategies is that of the “alpha horizon” of a signal and the linked concept of alpha decay. In simple terms, this refers to the tendency of a position to produce positive alpha for a period of time, reach a zenith in terms of performance, and then decay or begin to lose money. 


Applying this to the fundamental world, we refer to the “alpha horizon” of a manager’s trades as being the timeline over which the average position generates positive return before peaking and subsequently flatlining or (more commonly) starting to decline. 


Defining the alpha horizon for a fundamental manager is a complicated exercise. We must decide whether we look only at new positions (and what constitutes “new”3) or only look at the individual trades which make up a position. And how do we measure value creation? For example, do we look at total return,  return relative to a benchmark, idiosyncratic return from a risk model, or something else? The underlying data needs to be meticulously cleaned for outliers, corporate actions, dividend payments, and other potential issues. 


Once this exercise is completed, we can examine the typical value path of a position or a trade for the manager. The shape, steepness, and longevity of this curve are key to assessing the optimum execution strategy, as we will see below. 


Trade Impact 


“Client doesn’t want to move the price, so stay below 30% of volume.” 

  • Overheard (frequently) on the trading desk in the 90s. 


Most fundamental managers understand that there is a cost to executing in the market (over and above the cost of commissions and other fees) and that this cost generally scales with size and speed. The more one wishes to buy or sell, and the greater the urgency, the more likely it is that other market participants will identify your intent and attempt to front-run you, and deeper into the order book you must go to get your fill. This situation has become increasingly acute over the past decade (or more) with the rise of High Frequency Trading (HFT) strategies.  It is generally accepted that a trade greater than 5% of the volume in a security is likely to experience substantial adverse impact from predatory market participants. 


TCA models vary by provider,4 but generally, they incorporate three factors known to correlate to ex-post measures of impact: the volatility of the stock, the bid-ask spread, and the percent of daily volume being executed. As any of these three elements increase, the greater the impact is likely to be5


Given this unavoidable circumstance, how should a manager execute in the most optimal fashion? At one end of the spectrum, executing in minuscule increments will minimize impact but at the expense of potentially missing the alpha. On the other end, maximizing the speed and aggression of the trade will ensure that the position will be present for as much of the alpha as possible, but at the very real risk of uneconomically high impact costs. How should we determine the trade-off? 


Optimal Execution 


“Fast is fine, but accuracy is final. You need to take your time in a hurry.” 

  • Wyatt Earp 


A robust understanding of both the manager’s alpha curve as well as the expected impact costs at different modes of speed and size is key to solving this dilemma. If we define the total dollar size of the position which the manager wishes to achieve as D, then we can use our TCA data in combination with the manager’s alpha curve to determine the optimal number of days over which that position should be implemented. For example: 


  • - Manager A typically generates 2bp of alpha every day for the first 10
  •   days of a new position.
  • - She wishes to achieve a $10MM position in a stock.  
  • - Buying over 1 day will create 25bp of negative trade impact,
  •   resulting in an estimated net loss on the position of 5bp after 10
  •   days.
  • - Buying over 2 days, however, will generate 20bp of negative trade
  •   impact.  
  • - However, we must remember that she will only have a $5MM
  •   position on day 1 and so will only benefit by half the expected alpha
  •   that day, resulting in a net loss of 1bp after 10 days. 
  • - Spreading over 5 days will only generate 10bp of trade impact but at
  •   the expense of missing some of the initial alpha (day 1 will have a
  •   position of $2MM, day 2 $4MM, etc.), resulting in a gain of 6bp after
  •   10 days. 


We can define this quantitatively. If: 

  • - X is the dollar size of the required position 
  • - n is the number of days over which we intend to execute X 
  • - A is the vector of daily expected alphas over some horizon 
  • - and M is the estimated impact for a trade of size X/n 


Then the vector of position sizes each day d is, 

𝑆= {𝑑𝑛 𝑓𝑜𝑟 𝑑<𝑛𝑋 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒S= dn for d<nX otherwise


 Then we are seeking to maximize: 





Typically, our analysis suggests that most managers would benefit from spreading their execution—especially in large percent-of-volume trades—over more days than they currently do. On average, even the highest conviction/size trades have insufficient alpha in the first few days of their lives to overcome the associated impact. 


We reach these insights through our dedicated team of data scientists and execution experts who employ their multi-decadal experience to analyze, enhance, refine, and implement execution strategies. The conclusions that CenterBook Partners reach as they operate their own business are continually reflected back to the Partner Fund team as we collaborate to help refine and enhance all that we do together. We consider ourselves to be an extension of each Partner Funds’ business, helping to bring quantitative and systematic detail to fundamental investment teams. 


We look forward to sharing additional research efforts with our Partner Funds in the near future in order to help them Be Better



1 CenterBook is a multi-manager asset management platform based out of Greenwich, CT. Any communication regarding CenterBook is for information purposes only and should not be regarded as advice, a solicitation of an offer to buy or sell any CenterBook financial product, or as an official statement of CenterBook.  

2 Alpha Theory clients who want to learn more are encouraged to reach out to their CX representative. 

3 For example, if a large position is reduced to a few basis points in size as a “holding position” and then scaled back up, is this a new position? 

4 At CenterBook, we leverage external TCA providers as well as our own internal models. 

5 Our work also suggests that liquidity is a correlate. Ceteris paribus, execution in lower liquidity stocks generates a higher impact than execution in higher liquidity ones. We speculate that this is due to the greater presence of hedgers and other natural flows in more liquid securities. 

August 11, 2022

What does it mean to be a good stock picker? Part 2


BOTTOM LINE UP FRONT: A slugging percentage above 1.65x demonstrates stock picking skill for an active manager.


In the previous post, we explained that comparing an active manager to a randomized version of an active manager was the best way to measure their stock selection skill. We discussed why constructing our random portfolio using absolute return or benchmark adjusted returns was flawed. This resulted in the use of an equal-weighted benchmark (equivalent to a monkey throwing darts in a more normalized time period*). We started with Batting Average and will continue our analysis with Slugging Percentage.


Slugging Percentage


Slugging percentage is a measurement of the average winner divided by the average loser. If I have a batting average of 50% and a slugging of 1.0x, then my fund will generate a 0.0% return (50% of stocks make +20% and 50% make -20%). Anything greater for either of those metrics and the returns turn positive. If you can find winners that go up twice as much as losers, you need only have a batting of 33.3% to result in a return of 0.0%.


To demonstrate skill, a manager needs a slugging percentage* of 1.65x. This may seem high, but we must understand that the market demonstrates persistent positive skew (a straightforward way to think of positive skew is that more stocks go up more than 100% than go down more than 100%). This positive skew is also one of the major reasons that the batting average of the randomized portfolio we calculated in the previous post, 37.8%, seems so low.


If a manager has a 40% batting average (better than 37.8%) and 1.8x slugging percentage (better than 1.65x), they are demonstrating skill in two categories: both in picking winners and picking winners that go up much more than their losers. This is a good start, but how good is 40% and 1.8x?  


The next step would be to Monte Carlo random portfolios and determine the probability of getting a 40% batting and 1.8x slugging portfolio. In fact, the ideal method would be to: 

  •  -  Match manager time period and industry; 
  •  -  Randomly select longs at the ratio of manager long positions; 
  •  -  Randomly select shorts at the ratio of manager short positions; 
  •  -  Randomly assign weights to Monte-Carlo’d portfolios using position
  •     size ranges; 
  •  -  Assess the gross exposure of an individual manager; and 
  •  -  Build a distribution of portfolios with those standardized
  •     characteristics to determine the probability of achieving a
  •     similar portfolio.

With that, you can perform significance tests and take samples from different periods to determine the persistence of skill.


We may explore this concept in the future, but in the interim, the simple approach above is a shortcut method to help elucidate the idea of comparing managers to random as a way of measuring manager skill. 


 *SLUGGING PERCENTAGE FORMULA: (if positive: average (return of stock - return of the average stock in the index) / if negative: average (return of stock – return of the average stock in the index) 


THE RANDOMNESS EQUATION: Equal Weighted Batting Average of ACWI * Slugging Percentage of ACWI + (1-Equal Weighted Batting Average of ACWI * Denominator of Slugging Percentage of ACWI = The Randomness Equation 

37.8% * 165% + 62.2% * -100% = 0.0% Return – The Randomness Equation