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Strategy 2: Adaptive Execution

Overview

An adaptive strategy that adjusts daily execution based on the current price relative to the rolling TWAP benchmark. Buy more when prices are favorable (below benchmark), less when unfavorable.

Type: Active / Price-adaptive
Completion: Always 100%
Performance: +15-25 bps typical

Algorithm

Core Logic

  1. Calculate rolling TWAP benchmark up to current day
  2. Compare current price to benchmark
  3. If price < benchmark: speed up (buy more)
  4. If price > benchmark: slow down (buy less)
  5. Ensure completion by max_duration

Execution Multiplier

\[ \text{multiplier} = \begin{cases} \text{speedup} & \text{if } P_t < \text{TWAP}_t \\ \text{slowdown} & \text{if } P_t > \text{TWAP}_t \end{cases} \]

Where: - Speedup range: 1.0 to MAX_SPEEDUP (5x default) - Slowdown range: 0.1 to 1.0

Urgency Factor

As the deadline approaches, urgency increases:

\[ \text{urgency} = \frac{\text{days\_remaining}}{\max(\text{usd\_remaining} / \text{base\_daily}, 1)} \]

Implementation

def strategy_2(prices, benchmarks, total_usd, min_dur, max_dur, target_dur):
    """Adaptive execution: buy more when cheap, less when expensive."""
    base_daily = total_usd / target_dur
    usd_remaining = total_usd

    for t in range(max_dur):
        price = prices[t]
        benchmark = benchmarks[t]
        deviation = (benchmark - price) / benchmark

        # Adaptive multiplier
        if deviation > 0:  # Price below benchmark (favorable)
            multiplier = 1.0 + deviation * MAX_SPEEDUP
        else:  # Price above benchmark (unfavorable)
            multiplier = max(0.1, 1.0 + deviation)

        # Urgency adjustment
        days_left = max_dur - t
        if days_left <= 5 and usd_remaining > base_daily * days_left:
            multiplier = max(multiplier, usd_remaining / (base_daily * days_left))

        daily_usd = min(base_daily * multiplier, usd_remaining)
        # ... execute and track

Characteristics

Pros

  • Exploits price discounts systematically
  • Self-adjusting to market conditions
  • Guaranteed completion
  • Moderate risk profile

Cons

  • May delay execution in rising markets
  • Performance depends on volatility
  • Can be forced to buy at deadline

Performance Profile

Metric Typical Value
Mean Performance +15 to +25 bps
Std Dev ~60-70 bps
Min -100 to -150 bps
Max +200 to +300 bps

Key Insight

Strategy 2 generates alpha by systematically buying more at discounts and less at premiums, creating a slight positive skew in the performance distribution.

(c) Joerg Osterrieder 2025