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

Introduction The 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 Hate Learning 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 24 h later.

Loved Algo Does Seem To Deserve Love • • “Flipping” Exercise: Buy at arrival plus slippage (that is, traded price), sell at 24 h 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 (\$98 k) per order on average, while Hated lets fund pocket only 7. 0 BP (\$72 k) per order, on average. Loved Algo Is Better… RIGHT?

Looking More Closely: Potential Profit If Flipped Shares Next Day* Loved fills more, at lower prices than Hated. . . 7. 2 BP = 370 k/ 500 M M 7. 7 BP = 390 k/ 500 M M • • 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. . But ? ?

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?

“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. •

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. 000 x)200 -1 annual returns. Simple setup, but illustrates power of 1 BP saved.

The Conclusion From Love X Hate: Algorithms Depend Enormously On Appropriate TC Mgmt – Investment/Trading Together: The Trading X Alpha Orthogonality Principle • Graphic Interpretation: 5 point slippage and alpha Fund’s numbers can be represented as alpha vectors. Hated Slipp • Correlations fill, net angle • Conclusions: Optimal Slipp Optimal Net • Loved: traded more when (orthogonal with alpha smaller neg correl should not jump so hard at fill) Loved Slipp better prices; be less afraid of unfavorable prices. • Vectors: slippage, alpha and fill rate’s numbers • Hated: traded more at good 5 vectors. Correlations can be represented as R alphas pos correl could angles between those vectors can be shown trade some slippage for higher to be equivalent quantities. net even when forecasting well. • Since cannot see in R 5, 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 Idea When 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 • 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. • 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

Investment & Trading Frontiers Connected: Losing Sight Of Alpha May Ruin Trade TC Mgmt • 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 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

Part III: Love And Hate Again Being 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 400 k, 1 MSFT 10 k). . . - Loved Algo gets the “beach breeze” (1 COG 400 k, 9 MSFT 10 k). . .

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 MSFT better than Loved In the table above, B’s average’s superiority comes into question.

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 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

Should Be Able To Compare At Level Playing Fields • Different algos, say from different brokers, may enjoy different perceptions in the buyside 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).