Algorithm Design And Evaluation Further Reveal Connection Between Investment And Trading Processes

IntroductionThe design of effective algorithms for trading may sometimes seem an “art on its own”, full of rules of thumb and very disconnected from the investment process within which algos exist.

We show, via clear and practical examples, that such notion is misleading, in sometimes surprising ways. We then connect those examples with approaches that appropriately fix the algorithmic flaws presented. Those approaches fix those flaws mostly by keeping the initial investment decision in mind and knowing how to manage transaction costs.

Part I: Love And HateLearning How To Love By Knowing

What To Look For (In An Algorithm)...

A Novel Idea:A Tale Of Love And Hate (really novel!)

• Loved Algo FILLS MORE AT BETTER PRICES• Loved has traded those 5 orders better than Hated… Right?• Remark: 1-Day Stock Pr Chg = from order placement to 24h later.

# Stock Side Order Arrival Pr Traded Sh Traded Pr Fill Slipp (BP) 1-Day Stock Pr Chg (BP)

1 XYZ B 1,000,000 102.08$ 850,000 102.31$ 85% -8 11

2 XYZ B 1,000,000 102.30$ 1,000,000 102.60$ 100% -14 21

3 XYZ B 1,000,000 102.11$ 636,000 102.24$ 64% 2 184 XYZ B 1,000,000 102.09$ 1,000,000 102.34$ 100% -9 65 XYZ B 1,000,000 102.06$ 514,326 102.07$ 51% 14 19

Avg 1,000,000 102.13$ 800,000 102.31$ 80% -3 15

Loved Algo

# Stock Side Order Arrival Pr Traded Sh Traded Pr Fill Slipp (BP) 1-Day Stock Pr Chg (BP)

1 XYZ B 1,000,000 102.08$ 885,011 102.28$ 89% -5 17

2 XYZ B 1,000,000 102.30$ 859,882 102.60$ 86% -14 23

3 XYZ B 1,000,000 102.11$ 823,525 102.30$ 82% -4 19

4 XYZ B 1,000,000 102.09$ 561,434 102.21$ 56% 3 10

5 XYZ B 1,000,000 102.06$ 370,148 102.26$ 37% -5 6

Avg 1,000,000 102.13$ 700,000 102.33$ 70% -5 15

Hated Algo

(Profit From Flipping)

Algo's Ordered Traded Fill Slipp Slipp 1-Day 1-Day 1-Day Chg Flipping Flipping Flipping

Avg # Shares Shares (BP) ($/sh) Pr Chg Pr Chg Net of Slipp Proceeds ($) Proceeds Proceeds

Trade (BP) ($/sh) ($/sh) (Net X Shares) ($/sh) (BP)

Loved Algo 5 1,000,000 800,000 80% -3 (0.031)$ 15 0.153$ 0.12$ 98,043$ 0.10$ 9.6

Hated Algo 5 1,000,000 700,000 70% -5 (0.051)$ 15 0.153$ 0.10$ 71,490$ 0.07$ 7.0

Loved Algo Does Seem To Deserve Love

• “Flipping” Exercise: Buy at arrival plus slippage (that is, traded price), sell at 24h later price, keep net.

• Average trade conditions same.• From table, “Fill The Most At Best Prices” works:

Loved lets the fund pocket 9.6 BP ($98k) per order on average, while Hated lets fund pocket only 7.0 BP ($72k) per order, on average.

• Loved Algo Is Better… RIGHT?

# Stock Side Ordered Shares Arrival Pr Traded Sh Traded Pr 1-Day Stock Pr Chg Fill Slipp Flipped $/sh $ Flipped1 XYZ B 1,000,000 102.08$ 885,011 102.28$ 0.17$ 89% (0.05)$ 0.12$ 108,410$ 2 XYZ B 1,000,000 102.30$ 859,882 102.60$ 0.24$ 86% (0.14)$ 0.09$ 79,169$ 3 XYZ B 1,000,000 102.11$ 823,525 102.30$ 0.19$ 82% (0.04)$ 0.15$ 126,135$ 4 XYZ B 1,000,000 102.09$ 561,434 102.21$ 0.10$ 56% 0.03$ 0.13$ 74,512$ 5 XYZ B 1,000,000 102.06$ 370,148 102.26$ 0.06$ 37% (0.05)$ 0.01$ 3,778$

Avg 1,000,000 102.13$ 700,000 102.33$ 0.15$ 70% (0.05)$ 0.10$ 78,401$ Total 5,000,000 3,500,000 392,004$

Hated Algo

# Stock Side Ordered Shares Arrival Pr Traded Sh Traded Pr 1-Day Stock Pr Chg Fill Slipp Flipped $/sh $ Flipped

1 XYZ B 1,000,000 102.08$ 850,000 102.31$ 0.11$ 85% (0.08)$ 0.03$ 26,030$

2 XYZ B 1,000,000 102.30$ 1,000,000 102.60$ 0.21$ 100% (0.14)$ 0.07$ 71,610$

3 XYZ B 1,000,000 102.11$ 636,000 102.24$ 0.18$ 64% 0.02$ 0.20$ 129,884$ 4 XYZ B 1,000,000 102.09$ 1,000,000 102.34$ 0.06$ 100% (0.09)$ (0.03)$ (30,627)$ 5 XYZ B 1,000,000 102.06$ 514,326 102.07$ 0.19$ 51% 0.14$ 0.34$ 173,224$

Avg 1,000,000 102.13$ 800,065 102.31$ 0.153$ 80% (0.03)$ 0.12$ 74,024$ Total 5,000,000 4,000,326 370,121$

Loved Algo

Looking More Closely: Potential Profit If Flipped Shares Next Day* Loved fills

more, at lower prices than Hated...

... But ??

7.2 BP =

370k/ 500MM

7.7 BP =

390k/ 500MM

• Now fund seems to keep more money using Hated.• Perhaps it is time to give more love to the Hated –

and vice versa?* For simplicity – and without compromising results – transaction costs not shown in flipped sells (included only when fund really sells, not in potential profit exercise). If included when sale happens, transaction cost is appropriately taken into account, and no double count happens.

Confusion: Loved Algo Better Before, Worse Now ?????

• Now, with Loved Algo, fund nets ONLY 7.2 BP per order.• With Hated Algo, fund nets 7.7 BP per order.• Which one is correct, once and for all?

Potential Gross

Given To Algosum of StockChgi * TargetShi

for i=1, ..., 5 trades

Both Algos Loved Algo Hated Algo Loved Algo Hated Algo

Total $ 766,100$ 370,121$ 392,004$ 370,121$ 392,004$ For # Shares 5,000,000 4,000,000 3,500,000 5,000,000 5,000,000 Per Share 0.15$ 0.09$ 0.11$ 0.074$ 0.078$ BP 15 9 11 7.2 7.7

Algo Receives

Fund's Research

Quality And Tries To Make The Best Out

Of It

Algo's Potential Proceeds Fund's Proceeds

From Flipping From Algosum of (StockChgi - Slippi) * TRADEDShi Over Planned Shares

for i=1, ..., 5 trades (5,000,000 shares)

Algos' Fill Rates X (24h Pr Chg - Slipp): Capitalizing on Fill Rate, Slipp Effort

0%20%40%60%80%

100%120%

-10 0 10 20 30 40

Trade's Return - Slippage (BP)

Trad

e's

Fill

Rat

e

LovedHated

Loved's High Fill + Low Slipp Efforts Are Lost In

NEGATIVE (Fill, PrChg-Slipp) Correlation (-93%)

Hated's Lower Fill + Higher Slipp Are Made Up In

POSITIVE (Fill, Ret-Slipp) Correlation

(+65%)

Answer: ”Hated” Did Perform Better Than “Loved” –

We Have To Add Each Trade’s $. “Loved”’s AIM Strategy, When Under Bad TC

Mgmt, Leads To A Self-Imposed Adverse Selection

“Hated Algo” Returns More Money Back To Fund’s Research Alpha

• Loved algo jumps too hard at cheaper opportunities.

• Because initially lower prices tend to yield not as good medium term returns, the additional mkt impact from those “rushes to cheap” cancels the benefits from better prices.

• Loved algo needs better TC management.

Potential Gross

Given To Algosum of StockChgi * TargetShi

for i=1, ..., 5 trades

Both Algos Loved Algo Hated Algo Loved Algo Hated Algo

Total $ 766,100$ 370,121$ 392,004$ 370,121$ 392,004$ For # Shares 5,000,000 4,000,000 3,500,000 5,000,000 5,000,000 Per Share 0.15$ 0.09$ 0.11$ 0.074$ 0.078$ BP 15 9 11 7.2 7.7

Algo Receives

Fund's Research

Quality And Tries To Make The Best Out

Of It

Algo's Potential Proceeds Fund's Proceeds

From Flipping From Algosum of (StockChgi - Slippi) * TRADEDShi Over Planned Shares

for i=1, ..., 5 trades (5,000,000 shares)

Why We Should Start Really Loving The “Hated Algo”:

The Power of 1 BP• Reinvest net x

BP proceeds from each 24-hour investment horizon.

• 200 days/year.• Compounding

yields (1.000x)200-1 annual returns.

• Simple setup, but illustrates power of 1 BP saved.

Annual Fund Return(Calculated based on an avg of 1 trade per day)

Formula = (1.000x )200-1, based on 200 days per year

6%8%

11%13%

15%17%

20%22%

25%27%

0%

5%

10%

15%

20%

25%

30%

3 4 5 6 7 8 9 10 11 12 13

Net Return (BP) (= 24-hour pr chg - slippage) Per 24-Hour Investment Period

Ann

ual F

und

Ret

urn

Potential Savings May Increase Annal Returns By A

Lot

The Conclusion From Love X Hate: Algorithms Depend Enormously On Appropriate

TC Mgmt – Investment/Trading Together:The Trading X Alpha Orthogonality Principle

•

Fund’s alpha

Optimal Net (orthogonal with fill)

Hated Slipp

Loved Slipp

Optimal Slipp

• Graphic Interpretation: 5-point slippage and alpha numbers can be represented as vectors.• Correlations fill, net angle• Conclusions: • Loved: traded more when alpha smaller neg correl should not jump so hard at better prices; be less afraid of unfavorable prices.• Hated: traded more at good alphas pos correl could trade some slippage for higher net even when forecasting well.

• Vectors: slippage, alpha and fill rate’s numbers can be represented as R5 vectors. Correlations and angles between those vectors can be shown to be equivalent quantities.• Since cannot see in R5, show above in plane.

Another Conclusion From Love X Hate: Opportunity Cost And Risk, Not Only Slippage, A Major Component In Evaluating Algorithmic

Performance

• Tendency is to select a benchmark (say, arrival), and calculate average cost (slippage) with respect to it. Misleading, as gaming may make benchmark average look better for algos but yielding worse for fund’s returns.

•Different situations: appropriate transaction cost measurements should correct for different trading conditions (momentum, liquidity, etc).

Part II: Algorithms Cannot Avoid TC Management And Investment

IdeaWhen Adapting To Market

Movement, Keep Impact X Risk At Sight + Remember Initial

Preferences

TC Management: Cannot Avoid The Trade-Off Between Risk (And Alpha) And Market Impact

Efficient Trading Frontier(Almgren & Chriss)

Timing Risk

Trad

ing

Cos

t

X*

30

20

Trading Cost Distribution

Trading Cost20

30 30

•Strategy X can be represented by a percentage of volume rate (“POV”) or by a trade schedule.

• Adaptation: Should adapt the initial scheduled plan as trading evolves, without drifting away from initial cost/risk preferences.

Algorithm’s Adaptive Strategies: AIM – Has To Follow TC Management As Well

• Very Important: Reference price has to shift as achieved cost and prices change in order to reflect original preferences.

AIM Adaptation Tactic

Good Risk Bad RiskC3 < C1

Constant Trade Rate

AIM Tactic

Trad

e Ra

te

Comparison of Adaptation Tactics Trading Rates

Pb Pb+frefPb-fref

AIM

Target

PIM

• Loved Algo’s flaw was that, even though it reacted to favorable prices, it lost sight of TC management and initial price X risk trade-off.

Algo Example: Investing & Trading Decisions Tied

Efficient Trading Frontier

Timing Risk

Cos

t

x1

x2x3

c1

c3

c2

r1 r2 r3

*2'..

'

Cwwts

rwMaxw

*'..

'

rrwts

CwwMinw

CwwrwMaxw

'' *

xxMIMinx

Efficient Frontier

Risk

Retu

rn

U2

U3 Frontier

U1

Investment & Trading Frontiers Connected: Losing Sight Of Alpha

May Ruin Trade TC MgmtInvestment Frontier

Risk

Retu

rn

**-c3

*-c1

*-c2

* *+r2 *+r3

x3

x1

x2

*+r1

• Case in point: Loved Algo’s careless attack into cheaper prices.

• By seeing current price levels compared to arrival (or implementation) price, Loved Algo could have managed better its “greed”.

Ensuring Consistency between Investment & Trading Frontiers

Investment Frontier

Risk

Retu

rn

U1

U2

X

Frontier

U3

Z

(VWAP = Ineff icient)

(Very Aggressive = Ineff icient)

Y

(Optimal = Eff icient)

LOVED ALGO: forgets planned alpha and values instant gratification without remembering its exact risk aversion...

HATED ALGO: not VWAP, since it could save slippage even at good alpha forecasts. But, like VWAP, could be more aggressive at cheaper prices (has some room for slippage).

Risk Aversion Should be Consistent Across Investing & Trading

Determining Appropriate Level of Risk Aversion

Risk

Ret

urn

Investment Frontier Cost-Adjusted Frontier

A

ETF-A

X

Slope of Tangent

Part III: Love And Hate AgainBeing Fair Is The Hardest Part (We

All Knew That One)…

Introductory Example:Who Performed Better?

• Avg Cost:• Hated Algo:

-36 BP• Loved Algo:

-11 BP

• Conclusion:• Loved Better

Than Hated.• Obvious,

right?

Hated Algo gets the “curve ball” (9 COG 400k, 1 MSFT 10k)...

Loved Algo gets the “beach breeze” (1 COG 400k, 9 MSFT 10k)...

ALGO Trade# Symbol StockNick Side Order ADV Slippage OppCost CostHated 1 COG "Apple" BUY 400,000 535,000 (30) (10) (40) Hated 2 COG "Apple" BUY 400,000 535,000 (30) (10) (40) Hated 3 COG "Apple" BUY 400,000 535,000 (30) (10) (40) Hated 4 COG "Apple" BUY 400,000 535,000 (30) (10) (40) Hated 5 COG "Apple" BUY 400,000 535,000 (30) (10) (40) Hated 6 COG "Apple" BUY 400,000 535,000 (30) (10) (40) Hated 7 COG "Apple" BUY 400,000 535,000 (30) (10) (40) Hated 8 COG "Apple" BUY 400,000 535,000 (30) (10) (40) Hated 9 COG "Apple" BUY 400,000 535,000 (30) (10) (40) Hated 10 MSFT "Orange" BUY 10,000 63,000,000 (1) 0 (1)Avg 361,000 6,781,500 (27) (9) (36)

ALGO Trade# Symbol StockNick Side Order ADV Slippage OppCost CostLoved 1 MSFT "Orange" BUY 10,000 535,000 (4) (1) (5) Loved 2 MSFT "Orange" BUY 10,000 535,000 (4) (1) (5) Loved 3 MSFT "Orange" BUY 10,000 535,000 (4) (1) (5) Loved 4 MSFT "Orange" BUY 10,000 535,000 (4) (1) (5) Loved 5 MSFT "Orange" BUY 10,000 535,000 (4) (1) (5) Loved 6 MSFT "Orange" BUY 10,000 535,000 (4) (1) (5) Loved 7 MSFT "Orange" BUY 10,000 535,000 (4) (1) (5) Loved 8 MSFT "Orange" BUY 10,000 535,000 (4) (1) (5) Loved 9 MSFT "Orange" BUY 10,000 535,000 (4) (1) (5) Loved 10 COG "Apple" BUY 400,000 63,000,000 (40) (20) (60) Avg 49,000 6,781,500 (8) (3) (11)

CostAlgo COG, 400,000 MSFT, 10,000Hated (40) (1)Loved (60) (5)

Looking More Closely...• Indeed, Loved’s Average of -11 BP Better Than Hated’s -36 BP.• But, strangely... • Hated “beats” Loved in direct “face-offs”:• Hated trades MSFT better than Loved.• Hated trades COG better than Loved.• SO: IS Loved STILL BETTER THAN Hated? IS -11 BP ABOVE

REALLY BETTER THAN -36 BP ABOVE? WHAT GIVES?...

Hated trades COG better than Loved

Hated trades MSFT better than Loved

In the table above, B’s average’s superiority comes into question.

CostAlgo COG, 400,000 MSFT, 10,000Hated (40) (1)Loved (60) (5)

Paradox Resolved• Avg Cost:• Hated: -36 BP• Loved: -11 BP• But Hated better

for each stock. How come?

• Answer:• Hated beats Loved

hand-to-hand and is thus better than Loved. Simple average is misleading due to uneven assignment of easy (MSFT) and hard (COG).

Hated trades COG better than Loved

Hated trades MSFT better than Loved

Number of TradesAlgo COG, 400,000 MSFT, 10,000Hated 9 1Loved 1 9

Should Be Able To Compare At Level Playing Fields

• Different algos, say from different brokers, may enjoy different perceptions in the buy-side firm which uses them.

• The firm may apply one algo for certain trade characteristics and other algo for other characteristics.

• For fair comparisons – and best use of algos – such possible differences should be taken into account.

Conclusions

• What looks good when seen in isolation may not be as good when seen as part of a process. Algos should be consistent with investment.

• TC management follows some basic ideas. Adapting the efficient frontier to adaptive trading (as in algos) goes beyond simple rules of thumb to include the investment plan.

• Comparing algos should take into account possible differences in their applications, even for similar type algos (like, two IS algos).