Strategy 3: Discounted Benchmark

Overview

A conservative variant of Strategy 2 that uses a discounted benchmark for comparison. This makes the strategy more selective about when to accelerate, only buying aggressively at larger discounts.

Type: Active / Conservative-adaptive
Completion: Always 100%
Performance: +20-30 bps typical

Algorithm

Discounted Benchmark

Instead of comparing to raw TWAP, Strategy 3 uses a discounted version:

\[ \text{Adjusted Benchmark} = \text{TWAP} \times (1 - \text{discount}) \]

For a 50 bps discount: $$ \text{Adjusted} = \text{TWAP} \times 0.995 $$

Effect

• More conservative: Only speeds up when price is significantly below TWAP
• Higher bar: Requires ~0.5% discount before accelerating
• Reduced whipsaw: Less responsive to minor price fluctuations

Implementation

def strategy_3(prices, benchmarks, total_usd, min_dur, max_dur, target_dur,
               discount_bps=50):
    """Adaptive with discounted benchmark."""
    discount = discount_bps / 10000  # 50 bps = 0.005

    for t in range(max_dur):
        price = prices[t]
        raw_benchmark = benchmarks[t]

        # Apply discount to benchmark
        adjusted_benchmark = raw_benchmark * (1 - discount)

        # Compare price to discounted benchmark
        deviation = (adjusted_benchmark - price) / adjusted_benchmark

        # Same adaptive logic as Strategy 2...

Discount Selection

Discount (bps)	Effect
0	Same as Strategy 2
25	Slightly more conservative
50	Moderate selectivity
100	Very selective acceleration
200	Rarely accelerates

Recommended

A discount of 25-75 bps typically provides the best risk-adjusted performance.

Characteristics

Pros

• More consistent performance
• Lower variance than Strategy 2
• Reduces "false positive" accelerations
• Better for range-bound markets

Cons

• May miss small opportunities
• Slightly lower mean performance in trending markets
• Still forced to complete by deadline

Performance Profile

Metric	Typical Value
Mean Performance	+20 to +30 bps
Std Dev	~55-65 bps
Min	-80 to -120 bps
Max	+180 to +250 bps

The reduced variance makes Strategy 3 attractive for risk-sensitive mandates.

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(c) Joerg Osterrieder 2025