# PRP-34: Arbitrage Pricing Theory (APT) Model Framework
## Context & Motivation
**Integration Goal**: Implement flexible multi-factor APT framework extending beyond Fama-French.
**User Requirement**: Support arbitrary factor models with customizable risk factors.
**Technical Challenge**: Design extensible framework for various factor specifications.
## Requirements
### APT Framework
1. **Factor Registry**: Dynamic factor registration system
2. **Custom Factors**: User-defined factor specifications
3. **Factor Loading Matrix**: N assets × K factors
4. **Orthogonalization**: Handle factor correlations
### Extensibility
1. **Plugin Architecture**: Easy addition of new factors
2. **Factor Combinations**: Mix different factor models
3. **Time-Varying Loadings**: Dynamic factor exposures
4. **Factor Timing**: Conditional factor models
## Implementation Blueprint
### Phase 1: Framework Design
1. Create `src/factors/apt.rs`
2. Define `Factor` trait for extensibility
3. Implement `APTModel` with factor registry
4. Add factor loading matrix management
### Phase 2: Factor Implementation
1. Create macro factors (GDP, inflation)
2. Add sector factors
3. Implement statistical factors (PCA)
4. Add custom factor support
### Phase 3: Model Integration
1. Integrate with data generator
2. Add factor model selection
3. Create factor analysis tools
4. Implement factor timing logic
## Success Criteria
### Validation Gates
```bash
# Test APT framework
cargo test apt_framework
cargo test custom_factors
# Test extensibility
cargo test factor_plugin_system
```
### Implementation Metrics
- [ ] Support 10+ simultaneous factors
- [ ] Factor orthogonalization working
- [ ] Custom factor integration < 50 LOC
- [ ] Performance scaling linear with factors
## Dependencies & References
**Prerequisites**:
- Complete PRP-32 and PRP-33 first
- Provides foundation for complex models
**Research Sources**:
- APT literature and implementations
- Factor model repositories
- Barra risk model documentation
**Design Patterns**:
- Plugin architecture patterns
- Trait-based extensibility
- Registry pattern implementation
## Implementation Tasks
### Phase 1: Framework (3-4 hours)
1. Design trait system
2. Implement registry
3. Create loading matrix
4. Add orthogonalization
### Phase 2: Factors (2-3 hours)
1. Implement core factors
2. Add factor builders
3. Create validation
4. Test combinations
### Phase 3: Integration (1-2 hours)
1. Generator integration
2. Add selection logic
3. Create examples
4. Document API
## Risk Mitigation
- Start with well-known factors
- Validate factor orthogonality
- Include factor diagnostics
- Provide factor templates
## Success Score
**6/10** - Complex extensible framework requiring careful architectural design.