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

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

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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.

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.
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.
• From table, “Fill The Most At Best Prices” works:Lovedlets the fund pocket9.6 BP (\$98k) per order on average, whileHatedlets fund pocketonly 7.0 BP (\$72k) per order, on average.
• Loved Algo Is Better… RIGHT?

Loved fills more, at lower prices than Hated...

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

7.2 BP =

370k/ 500MM

7.7 BP =

390k/ 500MM

... But ??

* 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?
• 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.
• Answer: Yes, 2.4 BP of Loved’s vanished with its strategy’s negative CORRELATION with the net return term
• Getting a lot done for great prices NOT the ONLY goal.
• Should have moved more carefully into favorable prices.
• 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.
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 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.

Fund’s alpha

Hated Slipp

Optimal Slipp

Optimal Net (orthogonal with fill)

Loved Slipp

• 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.
Loved’s Behavior: Anomalous Slippage X Opp Cost Trade-Off

Notice How

Stock

Returns

Increase

While Slippage

Does Not

Indeed, the hardest but most rewarding trades are those ending in big returns. So “spending” slippage with those trades should be more than compensated by bigger net returns and smaller opp costs

This anomalously “up and down” curve reflects the fact that either traders are misestimating future returns or not counting on them when they do exist.

For appropriate strategy, slippage should DECREASE with opportunity costs (or, equivalently, INCREASE with stock returns).

• Important: Just for this and the next slide we consider POSITIVE COST (SLIPP OR OPP) AS BAD.
The Correct Slippage X Opp Cost Trade-Off: Decreasing
• Now slippage does DECREASE with opportunity cost.
• Left part of strategy has higher slipp + opp cost figures. But this is more than made up by right part.
Correlation Defies Intuition About Buying As Much For As Cheap As Possible
• Loved: Executed a lot (80%) at CHEAP prices. Negative correlation between fill rates and net alpha ruined effort.Cherry picking bad investments at high slippages.
• Hated: Executed less (70%) at EXPENSIVE prices. But positive correlation between fill rates and net alpha made up for slippage.Selectively smart about opportunities..

Fund’s alpha

Hated Slipp

Optimal Slipp

Optimal Net (orthogonal with fill)

Loved Slipp

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
• 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.
Controlling Our Demanding of Market Liquidity Use: Market Impact Forecasting
• Market Impact: Relationship Between Trading Intensity And Premium Paid For Liquidity
• Allows Division of Slippage into “Market” And “Trader or Algo” Parts  Useful both for real time trading as well as for backtesting.
Good Strategy Design: Use Some Alpha Forecast (If Possible) With Right TC Management
• Strategy: MAXIMIZE FORECAST NET RETURNS; BLUE TRIANGLE = strategy’s choice of shares
• Strategy Rightly Bullish: But, aware of transaction costs, does not “go all the way”.
• Net Result: Improves on trader’s performance, highly damaged by high transaction costs (8 min)
• When looking for price improvement, manage opportunities to be passive.
A Plot with Real Data
• Limit Price has stronger influence
• Same data as before (first row).
Bad Order Placement And Planning: Example
• Algo should mind average ask size for stock.

COX market order cost: 50 ¢/share

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.
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

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).

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

Introductory Example:Who Performed Better?

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

• Avg Cost:
• Hated Algo:-36BP
• Loved Algo:-11BP
• Conclusion:
• Loved Better Than Hated.
• Obvious, right?

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

Looking More Closely...
• Indeed, Loved’s Average of-11BP Better Than Hated’s -36BP.
• 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.

• Avg Cost:
• Hated:-36BP
• Loved:-11BP
• But Hated better for each stock. How come?
• 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

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).