maximize portfolio performance

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28 A FRAMEWORK FOR PORTFOLIO MANAGERS AND TRADERS TO MAXIMIZE PORTFOLIO PERFORMANCE WINTER 2013

Trader Alpha Frontier: A Framework for Portfolio Managers and Traders to Maximize Portfolio PerformanceVLAD RASHKOVICH

VLAD RASHKOVICH

is the global busi-ness manager for Trade Analytics at Bloomberg in New York, [email protected]

Portfolio managers have tools to mea-sure the return and the risk of their performance. They also have the benefit of using performance attri-

bution techniques to see where their returns come from. Traders have only the tools to measure their costs, which at best can be used as a proxy for return. They don’t have tech-niques that would enable them to attribute their performance or measure how much risk they are taking.

We suggest a benchmark that we believe correctly delineates the trader’s contribution to overall portfolio return. We then introduce trader alpha frontier (TAF), which seeks to provide a complete picture of trader perfor-mance. In addition to looking at trader return against a certain benchmark, we introduce a new dimension, risk, which we measure as the volatility of trader returns. We then attribute trader return to momentum management and liquidity-sourcing components using existing industry benchmarks. Then we point out the missing third component, which we call exe-cution maneuvering, and which requires a new benchmark that we have named execution-weighted price (EWP).

Finally, we bring together all alpha components and their underlying risks from both the portfolio manager and trader into an overall portfolio performance attribution.

We introduce the concepts in this article as a holistic framework, but practitioners can

choose to adopt its underlying concepts sepa-rately. For instance, some will find the risk concept to be the most valuable, and some might be interested in trader performance attribution.

MEASURING TRADER PERFORMANCE

Currently, measuring trader perfor-mance is about choosing the right benchmark. However, each trader executes numerous trades over time and the performance of those trades relative to any benchmark f luctuates substantially. If we compare one trader with a trading performance of 20 basis points (bps) and high volatility of results to another trader with 10bp performance and low volatility of results, how can we tell whose trading results are better? Today, the answer is 20bp since the trading-results volatility is not taken into account.

Hundreds of benchmarks exist in trans-action cost analysis (TCA) to measure trading returns. Some of them, such as day open price or day VWAP, use static figures that don’t take into account the start and the end time of the trade. Others, like arrival price or interval VWAP, use dynamic trade-specific figures.

Exhibit 1 shows a number of popular benchmarks juxtaposed against a timeline. Each of those benchmarks has its strengths and weaknesses. For instance, implementation

Article Abstract

Trader Alpha Frontier: A Framework for Portfolio Managersand Traders to Maximize Portfolio Performance

Vlad Rashkovich

Trader performance is currently measured against various benchmarks without consideration forthe volatility of trading results. The author introduces trader alpha frontier (TAF) as a way to meas-ure trader performance against the risks taken by the trader. This article formulates how to carveout trader alpha from overall portfolio returns. It also explores trader performance attribution bydelineating between the main components of trader alpha and suggesting benchmarks to measureeach component. As a result, the author unveils a new benchmark, called execution-weighted price(EWP). It is tough to reach TAF, but it is worth the effort since it aligns the mutual objective of aportfolio manager and a trader to maximize overall portfolio performance.

A FrAmework For PortFolio mAnAgers And trAders to mAximize PortFolio PerFormAnce winter 2013

Trader Alpha Frontier: A Framework for Portfolio Managers and Traders to Maximize Portfolio PerformanceVlad RashkoVich

Vlad RashkoVich

is the global busi-ness manager for Trade Analytics at Bloomberg in New York, [email protected]

Portfolio managers have tools to mea-sure the return and the risk of their performance. They also have the benefit of using performance attri-

bution techniques to see where their returns come from. Traders have only the tools to measure their costs, which at best can be used as a proxy for return. They don’t have tech-niques that would enable them to attribute their performance or measure how much risk they are taking.

We suggest a benchmark that we believe correctly delineates the trader’s contribution to overall portfolio return. We then introduce trader alpha frontier (TAF), which seeks to provide a complete picture of trader perfor-mance. In addition to looking at trader return against a certain benchmark, we introduce a new dimension, risk, which we measure as the volatility of trader returns. We then attribute trader return to momentum management and liquidity-sourcing components using existing industry benchmarks. Then we point out the missing third component, which we call exe-cution maneuvering, and which requires a new benchmark that we have named execution-weighted price (EWP).

Finally, we bring together all alpha components and their underlying risks from both the portfolio manager and trader into an overall portfolio performance attribution.

We introduce the concepts in this article as a holistic framework, but practitioners can

choose to adopt its underlying concepts sepa-rately. For instance, some will find the risk concept to be the most valuable, and some might be interested in trader performance attribution.

MEASURING TRADER PERFORMANCE

Currently, measuring trader perfor-mance is about choosing the right benchmark. However, each trader executes numerous trades over time and the performance of those trades relative to any benchmark f luctuates substantially. If we compare one trader with a trading performance of 20 basis points (bps) and high volatility of results to another trader with 10bp performance and low volatility of results, how can we tell whose trading results are better? Today, the answer is 20bp since the trading-results volatility is not taken into account.

Hundreds of benchmarks exist in trans-action cost analysis (TCA) to measure trading returns. Some of them, such as day open price or day VWAP, use static figures that don’t take into account the start and the end time of the trade. Others, like arrival price or interval VWAP, use dynamic trade-specific figures.

Exhibit 1 shows a number of popular benchmarks juxtaposed against a timeline. Each of those benchmarks has its strengths and weaknesses. For instance, implementation

the JournAl oF trAding winter 2013

shortfall (IS), introduced by Perold [1988], measures performance from the time the trade arrives from the portfolio manager to the trader versus average execution price. IS, a benchmark that is difficult to game, ref lects the timing of a trade’s arrival from portfolio manager to trader. For momentum trades, illiquid names, or large orders, however, this method often results in an average execution price that is worse than the arrival price, cre-ating the appearance of negative performance for the trader.

Another benchmark, interval VWAP, is a good ref lection of all prices available to the trader from the start to the end of the trade and can result in positive or nega-tive trader performance. Interval VWAP can be gamed, however, since the trader defines the interval’s end.

Numerous attempts have been made to correct the deficiencies of those benchmarks. One popular method is to use quantitative models to calculate a trade cost estimate, as an adjustment to arrival price. However, the accuracy of those quantitative models is low, even though the latest model introduced by Rashkovich and Verma [2012] shows much higher R2. Later in this article, we explain the reason for generally low accuracy of the trade cost models.

Another method, peer universe, compares trades that have similar characteristics, such as country, sector, order size to ADV, intra-day momentum, and so on. While that approach brings some level of objectivity, it generates noisy results because each trade is different.

For example, two trades for the same country, sector, order size to ADV, and intra-day momentum can have different instructions for urgency and timing and, thus, will be executed differently by the trader, causing very different perfor-mance results.

The aforementioned challenges in measuring trader alpha led to the intro-duction of the participation rate bench-mark, or PWP (participation-weighted price). The idea behind this benchmark is that the trader is given a certain target participation rate, for example, 20%, and that participation rate is used to generate an interval to measure the performance of the trader. The benchmark to assess trader alpha is then based on the weighted

average of all trades that happened in the market during that interval. For instance, if the trader is asked to buy 200,000 shares of a stock and the requested participa-tion rate is 20%, then the performance is measured as the weighted-average price of all trades from the order arrival until 1,000,000 shares (200,000 shares/20%) of the stock are traded. If the portfolio manager’s urgency level is lower, for example, 10%, we would calculate PWP benchmark based on 2,000,000 shares (200,000 shares/10%).

The PWP benchmark is similar to interval VWAP, but because the duration is implied by the portfolio manager’s requested participation rate, PWP cannot be easily gamed. PWP allows us to measure the trader’s judgment and skill, which is why we use it as a bench-mark of choice. For a high target PWP, the benchmark will be inf luenced by the trader, since the trade becomes a substantial percentage of the market volume. There-fore, we recommend capping the target PWP at a rate of 30%–35%.

Exhibit 2 demonstrates how urgency levels, set by the portfolio manager, could be translated into target participation rates.

Exhibit 2 can be more granular and allow target participation rates to be set by portfolio managers and traders in smaller increments, such as 5%.

We find target PWP to be the best benchmark, but, as we explain below, any benchmark can be used with the TAF framework. Ultimately, no matter which

E x h i b i t 1Trader Performance Benchmarks


benchmark is used to measure trader performance, none of them capture the risk the trader takes.

TRADER RISK

If we ask an investor or a portfolio manager whether 20% expected return is better than 10%, the answer will depend on the underlying risks of each investment. When we ask traders whether outperforming VWAP by 20bp is better than by 10bp, the answer will be that 20bp is better.

We believe that trader performance should be put in the context of the risk the trader takes. For the pur-pose of this article, we define risk as the volatility of trading results.

We introduce trader alpha frontier (TAF) somewhat similarly to the Markowitz [1952] efficiency frontier for portfolio managers. TAF juxtaposes trader performance vis-à-vis the volatility of trading results. As we explain later, TAF answers a different question than the effi-cient trading frontier (ETF) introduced by Almgren and Chriss [2000].

In Exhibit 3, the Y-axis shows trader performance in basis points compared to the target PWP benchmark. The X-axis shows the volatility of results for all the underlying trades versus the target PWP. The frontier line in Exhibit 3 represents the best traders in terms of their benchmark out-performance compared to the volatility of the underlying trades. As we mentioned in the previous section, target PWP can be substituted with another benchmark of choice.

When we look at the results of various traders over time (for example, monthly or quarterly), we have enough points of reference to build TAF. The resulting chart in Exhibit 3 looks very similar to what portfolio managers

are used to seeing with Markowitz’s efficiency frontier. One important difference to note is that each point in Exhibit 3, including those on the frontier, is an actual result of a trader’s performance over a certain time.

For those who would rather look at one figure instead of the efficiency frontier, we introduce Sharpe ratio for traders (Sharpe [1994]). It is similar to the Sharpe ratio for portfolio return, but instead of the excess return over the risk-free rate, we use excess return over the target PWP benchmark. To measure trader risk, we use the stan-dard deviation of the underlying trading results (σ). We can define trader alpha (TA) as follows in Equation (1).

TA = (PBM

– PEXE

)/PBM

(1)

PBM

is the price of the benchmark—in our case, PWP with a target participation rate. P

EXE is the average exe-

cution price for every order.Note that Equation (1) is correct for buy orders.

For sell orders, it will be the execution price minus the benchmark price. The Sharpe Ratio formula for Traders can be defined as follows in Equation (2).

Sharpe ratio for traders = TA/σ (2)

TAF is different from the efficient trading frontier (ETF) introduced by Almgren and Chriss for a number of reasons. The main difference is that TAF and ETF are trying to answer different questions. TAF measures de-facto trader alpha versus the volatility of trading results. ETF solves the question of finding an optimal trading strategy by balancing estimated cost and timing risk.

E x h i b i t 2Example of How Urgency Levels Can Be Translated into Target Participation Rates

E x h i b i t 3Trader Alpha Frontier (TAF)


Another important difference is that TAF measures trader performance vis-à-vis target PWP and not IS. Target PWP allows trader performance to be positive or negative depending on the alpha the trader gener-ates. ETF uses the IS and, thus, solves for minimizing negative returns for traders. There is also a psychological aspect to this difference in approaches. We believe that it is very important for traders to wake up every morning with a mindset that their performance can be positive, instead of just hoping to minimize negative returns, which is not very healthy or a fair way to start the day.

Another difference is that TAF defines trader risk as the volatility of trading results and not as timing risk defined by ETF. Finally, TAF looks at actual results for multiple traders over time rather than the theoretical optimal results used by ETF. In that regard, ETF is closer to the Markowitz efficiency frontier.

DECOMPOSING TRADER ALPHA

Now that we have carved out trader alpha, we pro-pose a method to decompose a trader’s return into its main attributes. According to Rob Shapiro and George Sofianos (Mehta [2009]), a trader’s job can be defined as performing two main tasks: momentum man-agement and liquidity sourcing.

Momentum management requires reading the market and correctly expecting the price of the stock to go up or down in the short term. If a portfolio manager requests a trade at a certain participation rate, the trader can increase the rate when the momentum is unfavorable and decrease it when the momentum is favorable.

Liquidity sourcing requires f inding the other side(s) of the trade for the best available prices. While momentum management depends on the market condi-tions, liquidity sourcing ref lects the order complexity, which depends on order size versus ADV, bid/ask spread, volatility, and so on.

We can decompose TA into the two aforemen-tioned tasks as follows in Equation (3).

TA = TAMOM

+ TALIQ

(3)

TAMOM

stands for trader alpha earned from momentum management, and TA

LIQ stands for trader alpha earned

from liquidity sourcing.Rashkovich and Verma [2012] show that intratrade

stock momentum explains (R2) approximately 83% of

TA. The remaining some 17% can be attributed to the liquidity-sourcing component. The trade cost models, which we have mentioned in an earlier section of this article, estimate the complexity of liquidity sourcing because trade momentum is unknown prior to the trade. Therefore, those models can estimate only up to 17% of trader performance, which explains the very low R2 of these models.

Because of the shortcomings of trade cost models and peer universe approaches, both of which we have reviewed here, our goal is to find a more objective and precise method to measure each component of trader alpha.

MEASURING TRADER ALPHA WITH EXISTING BENCHMARKS

We would like to take a closer look at each trader alpha component, described previously, in order to for-mulate a correct method to measure each one.

1. Liquidity SourcingWhen a trader is asked to buy shares of a stock at

20% participation rate and the trade is executed at 20% participation rate, the momentum management com-ponent is equal to zero, because the trader did not take a stance on the stock’s momentum. In this case, we can measure only the liquidity-sourcing component. The PWP benchmark will be equal to the interval VWAP, since the trader used the duration implied by the port-folio manager. Thus, the interval VWAP benchmark measures the liquidity-sourcing component.

TALIQ

= (PIntVWAP

– PEXE

)/PPWP Target

(4)

Equation (4) is correct for buy orders. For sell orders, it will be the execution price minus the interval VWAP.

The denominator for TALIQ

and TAMOM

has to be the same, so the two components can be added together to form TA. We use P

PWP Target as the denominator for

both TA components since this is our point of reference in measuring trader alpha.

2. Momentum ManagementWhen a trader takes a stance on stock momentum,

the participation rate will deviate from the rate suggested by the portfolio manager. In this case, the PWP and the interval VWAP will be different. The difference results


in the momentum management component of TA as depicted in Equation (5).

TAMOM

= (PPWP Target

– PIntVWAP

)/PPWP Target

(5)

Equation (5) is correct for buy orders. For sell orders, it will be the interval VWAP minus the PWP target.

It is worth noting that momentum management and liquidity sourcing are not two independent attributes. For example, if traders face very negative momentum, they can significantly increase the participation rate and be willing to compromise on crossing deeper into the spread and aggressively taking liquidity. In this case, the trader will have positive performance for momentum manage-ment and negative performance for liquidity sourcing. This is a good example of when one attribute has to be negative in order to improve the other and, thus, improve the overall performance.

However, if the participation rate is low or medium, let’s say up to 15%, either because of the portfolio man-ager’s target rate or the trader’s decision, then liquidity sourcing does not have to be affected.

The bottom line is that total trader performance (TA) versus the target PWP is the metric that matters. Decomposing TA provides additional insights into where the trade performance comes from.

INTRODUCING A NEW BENCHMARK FOR TRADER ALPHA ATTRIBUTION

In the previous section we have used existing industry benchmarks to provide the formulaic decompo-sition of TA. One scenario is missing though. When the trader front- or back-loads the trade or otherwise varies participation throughout the trade, the two trader alpha components will not measure this type of maneuver.

Let us take a sell order with a target participation rate of 20%. The trader sees the stock going up and, thus, decides to start trading with 10%, gradually increasing the participation rate as the stock is climbing up and finishing the trade with a participation rate of 30%. On average, the participation rate of this trade might be 20% and, thus, TA

MOM = 0, as if the trader did not take a

stance on momentum. In this case, the alpha generated from this back-loading maneuver would be hidden in TA

LIQ. Another example is when the trader decides to

trade with 15% participation and increase participation on the price spikes. Again, average participation could

be 20%, but it’s a very different strategy versus trading 20% throughout the entire trade.

Therefore, we introduce a third component of TA, which we call execution maneuvering. By doing this, we will effectively subdivide TA

LIQ into two components—

maneuvering and true liquidity sourcing.To measure the execution maneuvering compo-

nent we will need to introduce a new benchmark, which we call execution-weighted price (EWP).

Let us take a sell order of 200,000 shares executed over 30 minutes. To calculate the EWP benchmark, we will divide the trading interval into a certain number of buckets. Let us use deciles as an example. Each decile will be driven by volume, not time. If the trade was executed over 30 minutes, while one million shares traded in the market, each bucket would have 100,000 shares. One bucket (100,000 shares) might have traded for one minute and another one for five minutes—trade execution time depends on the market volume.

Then we look at the filled shares for this order in each bucket versus the total number of shares filled in this order. In the first bucket 10,000 shares might be filled, which is 10% of the total order, again 10,000 shares in the second bucket, no shares in the third bucket, 20,000 shares in the fourth one, and so on.

For each 100,000 shares we would calculate interval VWAP and then apply the weightings of shares filled in each bucket versus the total executed shares in the order, thus ref lecting the relevance of each VWAP bucket. That’s how we get to EWP, which is a weighted average of 10 interval VWAPs, where weightings ref lect the relevance of each decile for completion of a given order. To demon-strate the concept numerically, let us look at Exhibit 4.

This 200,000 share order (cell F13) started at 10:30 (C3) and ended at 11:00 (E12). The total number of shares traded (market volume) during the duration of this order was 1 million (B13).

To create deciles, we have divided this order into 10 buckets with an equal number of shares of 1,000,000/10 = 100,000. Rows 3 through 12 represent those deciles. Note that the duration of each bucket can be different (column E).

In each bucket, we calculate the number of shares filled (column F). To calculate a weight for each bucket (column G), we divide shares filled (column F) by the total shares filled (F13).

For each bucket, we calculate an interval VWAP (column H) based on all market prices during that decile.


An industry standard interval VWAP assumes that each bucket contributes equally into the interval VWAP of the entire order since each bucket has the same number of shares. Thus, we calculate interval VWAP by applying 10% weight to each decile (column I). As a result, we have the industry standard interval VWAP, which is equal to 30.43 (I13).

The EWP calculation does not assume equal weight-ings for each bucket since the order was not filled equally in each bucket. We multiply the weight (column G) by interval VWAP for each bucket (column H) to calculate EWP (column J). As a result, we have an EWP equal to 30.58 (J13).

So, in this example, the interval VWAP = 30.43 versus EWP = 30.58. Those 15 cents per share (cps) can be attributed to trader maneuvering, in this case, back-loading the order. So if an average execution price P

EXE

= 30.70, for example, then for this sell order the trader outperformed interval VWAP by 30.70 – 30.43 = 0.27, where 30.70 – 30.58 = 0.12 is attributed to the true liquidity sourcing and 30.58 – 30.43 = 0.15 is attributed to execution maneuvering.

To generalize the EWP calculation, we suggest using a number of buckets depending on size/ADV, instead of using deciles or any other arbitrary number of buckets. The larger an order is, the longer on average it will take to trade, thus, creating more buckets. A linear relationship between the size/ADV and the number of buckets would create an unnecessarily large number of

buckets for bigger trades. We have found that the coef-ficient of 0.7 provides an adequate number of buckets for the formula in Equation (6).

Number of buckets = round (Size/ADV%)0.7 (6)

To ensure we have enough buckets for small sizes, we introduced a f loor of 5 buckets. For large trades, we Winsorize the number of buckets to 50. Our adjusted number of buckets is calculated in Equation (7).

Adjusted number of buckets = max [5, (min (50, round (Size/ADV%)0.7] (7)

Exhibit 5 demonstrates how Equations (6) and (7) translate into the number of EWP buckets.

The algorithm to calculate the number of buckets can be summarized in the following four steps:

1. Round size/ADV to the closest positive integer.2. Set number of buckets as size/ADV% in a power

of 0.7, for example, if size/ADV = 20%, then the number of buckets is 200.7 = 8.

3. If the result from step 2 is less than 5, then set the number of buckets to 5.

4. If the result in step 2 is more than 50 then set the number of buckets to 50.

Each bucket represents an equal number of shares traded in the market. The number of shares in the bucket

E x h i b i t 4Numeric Example of an EWP Computation


is calculated as the total shares traded in the market during order execution, and then divided by the number of buckets.

We realize that some practitioners might prefer to use a different algorithm to decide on the number of buckets for the EWP calculation. In order to zoom into a trader’s actions even further, some might create buckets that have an equal number of shares filled, instead of an equal number of shares traded in the market. Our goal is to introduce execution maneuvering as an important component of a trader’s performance, while leaving the practitioner room to maneuver how it is calculated.

Now that we have introduced a measurement for execution maneuvering, our former TA

LIQ, which was

calculated as PIntVWAP

versus PEXE

, is divided into maneu-vering and true liquidity sourcing.

Below are the formulae to calculate each component.

TAMANEUVERING

= (PIntVWAP

– PEWP

)/PPWP Target

(8)

Note that Equation (8) is correct for buy orders. For sell orders, it will be EWP minus the interval VWAP.

TALIQUIDITY

= (PEWP

– PEXE

)/PPWP Target

(9)

Note that Equation (9) is correct for buy orders. For sell orders, it will be the execution price minus the EWP.

The calculation TAMOM

from Equation (5) has not changed, but we would like to rename it to average speed (TA

AVG SPEED) since, as we have seen in the back-

loading example, the maneuvering component can be part of momentum management.

Thus, the average-speed component formula is shown in Equation (10).

TAAVG SPEED

= (PPWP Target

– PIntVWAP

)/PPWP Target

(10)

Note that Equation (10) is correct for buy orders. For sell orders, it will be the interval VWAP minus the PWP target.

Our total calculation of TA will be as follows in Equation (11).

TA = TAAVG SPEED

+ TAMANEUVERING

+ TALIQUIDITY

(11)

As we have mentioned before, the three TA com-ponents are not independent. Traders, who decide to trade slowly while significantly intensifying buying on the dips, will have a positive TA

MANEUVERING and most

likely a negative TALIQUIDITY

due to aggressive execu-tions on the dips. Traders will always have to watch their overall TA, but seeing where performance is coming from can be very useful.

To complete our numeric example above, let us assume that target PWP was 30% resulting in P

PWP Target =

30.22. The trader read the favorable momentum cor-rectly and executed the trade slower, with a participation rate of 20%, which translated into the interval VWAP = 30.43. Thus, our average-speed attribution is 30.43 – 30.22 = 0.21.

To summarize that example we have a sell order with P

EXE = 30.70, P

EWP = 30.58, P

IntVWAP = 30.43 and

PPWP Target

= 30.22.A trader’s performance by attribute in both abso-

lute and relative terms is shown in Exhibit 6.At the end, we can calculate a Sharpe ratio for each

component. To do that, we divide performance in each component by the volatility of the underlying results of each component.

SharpeAVG SPEED

= TASPEED

/σSPEED

(12)

SharpeMANEUVERING

= TAMANEUVERING

/σMANEUVERING

(13)

SharpeLIQUIDITY

= TALIQUIDITY

/σLIQUIDITY

(14)

Our goal is to take a close look at the TA and σ of each component to see whether the trader’s performance and risks are aligned. It may well be that the majority of the trader’s performance comes from TA

AVG SPEED, while

the majority of the trader’s risk comes from σLIQUIDITY

. In

E x h i b i t 5Numeric Example of an EWP Buckets Calculation


that case, the trader can focus on taking fewer liquidity risks while keeping the alpha from the average execution speed, thus, improving the overall Sharpe ratio.

INVESTMENT TIMELINE AND PERFORMANCE ATTRIBUTION

After taking a close look at trader alpha, we would like to see how it fits into the overall portfolio perfor-mance. In Exhibit 7, we are depicting a trade where

the portfolio manager sends an order to a trader to buy a stock when the price was below $100 (Arr

B). The

trader sees negative momentum and executes this buy order right away with an average price of $100 (Exe

B),

while the PWP equals $101 (PWPB). After holding

the stock for a while, the portfolio manager decides to sell it (Arr

S). The trader correctly reads the favorable

momentum, slows down, and executes the sell order with an average price of $120 (Exe

S), while the PWP

for the sell is $119 (PWPS). The overall performance of

E x h i b i t 6Numeric Example of TA Attribution

E x h i b i t 7Trade Timeline and Performance Attribution


Coppejans and Ananth [2007] showed that trading costs could, indeed, halve investors’ excess return. Domowitz, Glen, and Madhavan [2001] found that the execution costs, which include both implicit and explicit ones, can dramatically reduce the notional return.

TRADITIONAL PERFORMANCE ATTRIBUTION AND TRADER ALPHA

The portfolio performance attribution suggested by Brinson and Fachler [1985] divided the portfolio’s value-added into three components:

• asset allocation;• stock selection;• interaction between the first two components.

One can add FX, and perhaps other components, but we focus our analysis on the performance attribu-tion of the trader versus portfolio manager. Exploring additional potential components of portfolio manager performance is beyond the scope of this article.

If we visualize performance attribution simply, we can draw it as a rectangular shape where the whole rep-resents 100% of portfolio alpha and then the rectangle is divided by the 3 aforementioned components (see Exhibit 8).

When we look at overall portfolio performance, trader performance should be carved out before attribu-tion for asset allocation, stock selection, and so on, since traders’ performance attributes are different. Exhibit 9 visualizes that concept.

Now that we have delineated the portfolio man-ager’s and the trader’s contribution, we can dissect the trader alpha into underlying attributes based on Equa-

this investment is ExeS – Exe

B or $120 – $100 = $20 or

in percentages: (ExeS/Exe

B – 1) * 100 or ($120/$100 –

1) * 100 = 20%.

Let’s try to attribute overall performance.

• Trader performance for the buy order was PWPB

– ExeB:

$101 – $100 = $1

• Portfolio manager performance is measured from the PWP

B until the PWP

S:

$119 – $101 = $18

• Trader performance for the sell order was from the PWP

S – Exe

S:

$120 – $119 = $1

Overall, the portfolio manager’s contribution was $18 out of total $20 performance, while the trader’s con-tribution was $2 out of $20. In percentages, the portfolio manager contributed $18/$20 = 90% and the trader con-tributed $2/$20 = 10%. It seems that 10% contribution by the trader is fairly small and, perhaps, it is not worth spending much time focusing on that figure.

However, let us look at the portfolio return (r) as a combination of market return (r

m) and excess return

(re) shown in Equation (15).

r = rm + r

e (15)

Let us assume for a moment that the underlying benchmark (r

m) for this portfolio, such as the S&P 500,

grew 16% during the holding period for the stock. Each $100 invested in the S&P 500 would return $16. Our stock returned 20% and, thus, outperformed the S&P 500 (r

e) by 4%, which is $4. If we look at the trader’s

contribution (rt) of $2, suddenly it is 50% of the overall

$4 outperformance. The other 50% came from the port-folio manager’s contribution (r

pm).

It might be worth noting that re can be negative

or zero. Therefore, we look at re as a combination of the

portfolio manager return (rpm

) and the trader return (rt).

re = r

pm + r

t (16)

In Equation (16), while the overall portfolio excess return can be zero, the trader’s contribution can be posi-tive, for instance 2%, while the portfolio manager’s con-tribution can be negative (2%), or vice-versa.

E x h i b i t 8Visualization of Portfolio Performance Components


tion (11) from the earlier section. The resulting approach is shown in Exhibit 10.

CONCLUSION

We believe that this framework can help port-folio managers and traders work together to generate additional alpha for investors. TAF is tough to reach because it requires great trading skills, but discovering the efficiency frontier for traders can ultimately benefit the investors.

ENDNOTES

I am grateful to Bill Stephenson (Franklin Templeton) for being an advocate of the target PWP approach, for asking questions on measuring trader risk, and for quickly trying out

E x h i b i t 1 0Dissecting Components of PM and Trader Performance

my answers. Rob Shapiro’s (Bloomberg Tradebook) delinea-tion of trader performance components was instrumental in creating the framework around trader alpha. My thanks go to George Mylnikov (Charter Atlantic) for the detailed review of the first draft and his encouragement. I appreciate Alper Atam-turk’s (University of California–Berkeley) review of the later draft with his comments and corrections. It was key to have Arun Verma’s (Bloomberg) sharp intellect on my side while discussing alternative ways of calculating the EWP bench-mark. Todd Levinson’s (Bloomberg) and Danielle Amedeo’s (Bloomberg) editorial efforts greatly benefited this article.

REFERENCES

Almgren, R., and C. Neil. “Optimal Execution of Portfolio Transactions.” JournalofRisk, Vol. 3, No. 2, pp. 5-39.

Brinson, G.P., and N. Fachler. “Measuring Non-U.S. Equity Portfolio Performance.” TheJournalofPortfolioManagement (Spring 1985), pp. 73-76.

Coppejans, M.T., and M. Ananth. “The Value of Transaction Cost Forecasts: Another Source of Alpha.” JournalofInvestmentManagement, First Quarter 2007, Vol. 5, No. 1.

Domowitz, I., J. Glen, and A. Madhavan. “Liquidity, Vola-tility, and Equity Trading Costs across Countries and over Time.” JournalofInternationalFinance, Vol. 4, No. 2 (2001), pp. 221-255.

Markowitz, H.M. “Portfolio Selection.” JournalofFinance, Vol. 7, No. 1 (1952), pp. 77-91.

Perold, A.F. “The Implementation Shortfall: Paper vs. Reality.” TheJournalofPortfolioManagement, 14 (1988), pp. 4-9.

Rashkovich, V., and V. Arun. “Trade Cost: Handicapping on PAR.” TheJournalofTrading (Fall 2012), pp. 47-54.

Mehta, N. “A New Way to Judge the Buyside.” Traders Mag-azine, Vol. 22, No. 292 (March 2009), p. 48.

Sharpe, W.F. “The Sharpe Ratio.” TheJournalofPortfolioMan-agement (Fall 1994), pp. 49-58.

Toorderreprintsofthisarticle,pleasecontactDeweyPalmieriatdpalmieri@iijournals.comor212-224-3675.

E x h i b i t 9Portfolio Performance Components including Trading

maximize portfolio performance

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