Strategy Overview

The simulator implements five share buyback execution strategies, ranging from simple uniform execution to sophisticated adaptive algorithms.

Strategy Comparison

Strategy	Approach	Adaptivity	Completion	Best For
S1 Uniform	Fixed daily amounts	None	100%	Baseline
S2 Adaptive	Price-responsive	Linear	100%	General use
S3 Discount	Discounted benchmark	Linear	100%	Conservative
S4 Convex	Exponential scaling	Convex	100%	Aggressive
S5 Flexible	Convex + partial	Convex	Variable	Maximum value

Key Concepts

Benchmark (TWAP)

All strategies use Time-Weighted Average Price (TWAP) as the benchmark:

\[ \text{TWAP} = \frac{1}{T} \sum_{t=1}^{T} P_t \]

This rolling benchmark updates daily and represents the "fair" average price.

Performance Measurement

Performance is the difference between what you paid (VWAP) and the benchmark (TWAP):

\[ \text{Performance (bps)} = \frac{\text{TWAP} - \text{VWAP}}{\text{TWAP}} \times 10000 \]

Execution Window

• Min Duration: Earliest the execution can complete
• Max Duration: Deadline - must complete by this day
• Target Duration: Sweet spot between min and max

Strategy Evolution

graph LR
    A[S1: Uniform] --> B[S2: Adaptive]
    B --> C[S3: Discount]
    B --> D[S4: Convex]
    D --> E[S5: Flexible]

Each strategy builds on previous ones:

1. S1 establishes the baseline (uniform execution)
2. S2 adds price adaptivity (buy more when cheap)
3. S3 modifies the benchmark with a discount
4. S4 uses convex (exponential) scaling for bigger bets on discounts
5. S5 allows partial completion to avoid forced buying at bad prices

Choosing a Strategy

For most use cases

Strategy 4 (Convex) offers the best risk-adjusted returns for typical market conditions.

For conservative mandates

Strategy 3 (Discount) with a small discount provides consistent outperformance with lower variance.

For maximum performance (with risk)

Strategy 5 (Flexible) with 90-95% min completion can significantly outperform but may not fully execute.

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(c) Joerg Osterrieder 2025