Strategy 5: Flexible Completion

Overview

The most advanced strategy, combining convex adaptive execution with optional partial completion. At the deadline, if prices are unfavorable, Strategy 5 can choose not to complete the full execution.

Type: Active / Convex + Flexible
Completion: Variable (85-100%)
Performance: +30-45 bps typical

Algorithm

Core Innovation

Strategy 5 is identical to Strategy 4 during execution, but at the deadline:

1. Check if minimum completion threshold is met
2. If price is unfavorable (above benchmark by threshold), stop
3. Otherwise, force complete as usual

Decision Logic

At max_duration:

\[ \text{skip\_forced} = \begin{cases} \text{true} & \text{if completion} \geq \text{min\_pct AND deviation} < \text{threshold} \\ \text{false} & \text{otherwise} \end{cases} \]

Where: - min_pct = Minimum completion percentage (e.g., 95%) - threshold = Unfavorable deviation threshold (e.g., -1%)

Parameters

Parameter	Default	Description
min_completion_pct	95%	Minimum required completion
unfavorable_threshold	-1%	Skip if deviation below this
beta, gamma	Same as S4	Convex parameters

Implementation

def strategy_5(prices, benchmarks, total_usd, min_dur, max_dur, target_dur,
               min_completion_pct=95.0, unfavorable_threshold=-0.01):
    """Flexible completion: can skip forced buying at bad prices."""

    # Same as Strategy 4 during execution...

    # At deadline (day = max_dur - 1):
    if usd_remaining > 0:
        current_completion = (total_usd - usd_remaining) / total_usd * 100
        deviation = (benchmark - price) / benchmark

        # Decision: force complete or skip?
        if (current_completion >= min_completion_pct and
            deviation < unfavorable_threshold):
            # Skip forced completion - prices unfavorable
            pass
        else:
            # Force complete remaining
            execute(usd_remaining)

Completion Trade-off

Min Completion	Behavior	Risk
100%	Same as Strategy 4	None
95%	Skip up to 5% at bad prices	Low
90%	Skip up to 10%	Medium
85%	Skip up to 15%	Higher

Execution risk

Lower min_completion means more USD may remain unexecuted. Ensure this aligns with your mandate.

Performance Profile

Metric	Typical Value (95% min)
Mean Performance	+30 to +45 bps
Std Dev	~80-100 bps
Avg Completion	97-99%
Min Completion	95%

When to Use

Ideal scenarios

• Flexible mandates without strict completion requirements
• When maximizing execution value is paramount
• Markets with occasional sharp adverse moves

Avoid when

• Mandate requires 100% completion
• Regulatory constraints on execution
• Low volatility markets (little benefit)

Comparison with Strategy 4

Aspect	Strategy 4	Strategy 5
Completion	Always 100%	Variable
Mean Performance	Lower	Higher
Worst-case	Forced buying	May not complete
Complexity	Medium	Higher

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(c) Joerg Osterrieder 2025