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# PRP-33: CAPM (Capital Asset Pricing Model) Implementation
## Context & Motivation
**Integration Goal**: Implement CAPM for systematic risk-based return generation.
**User Requirement**: Generate asset returns based on market beta and risk-free rate.
**Technical Challenge**: Maintain consistent beta relationships across multiple assets.
## Requirements
### CAPM Components
1. **Risk-Free Rate**: Configurable base rate
2. **Market Return**: Systematic market return generation
3. **Beta Calculation**: Asset-specific systematic risk
4. **Alpha Generation**: Excess returns beyond CAPM prediction
### Multi-Asset Support
1. **Beta Matrix**: Support multiple assets with different betas
2. **Correlation Preservation**: Maintain market correlations
3. **Dynamic Beta**: Support time-varying betas
4. **Portfolio Analytics**: CAPM-based portfolio metrics
## Implementation Blueprint
### Phase 1: CAPM Core
1. Create `src/factors/capm.rs`
2. Define `CAPMModel` struct
3. Implement expected return calculation
4. Add beta configuration options
### Phase 2: Market Generation
1. Generate market return series
2. Apply asset betas
3. Add idiosyncratic risk component
4. Implement alpha generation
### Phase 3: Analytics
1. Add beta estimation tools
2. Create Sharpe ratio calculator
3. Implement security market line
4. Add performance attribution
## Success Criteria
### Validation Gates
```bash
# Test CAPM implementation
cargo test capm_model
cargo test portfolio_beta
# Validate returns
cargo test capm_expected_returns
```
### Implementation Metrics
- [ ] Beta preservation accuracy > 95%
- [ ] Market correlation maintained
- [ ] Sharpe ratios realistic
- [ ] Alpha generation configurable
## Dependencies & References
**Prerequisites**:
- Can build on PRP-32 factor infrastructure
- Requires market return generator
**Research Sources**:
- Modern Portfolio Theory references
- CAPM empirical studies
- Beta estimation methodologies
**Rust Libraries**:
- Leverage digifi's CAPM functions
- Use existing statistics modules
- Build on factor model framework
## Implementation Tasks
### Phase 1: Core CAPM (2-3 hours)
1. Implement CAPM model
2. Add return calculation
3. Create beta management
4. Write tests
### Phase 2: Generation (2-3 hours)
1. Generate market returns
2. Apply beta transformation
3. Add idiosyncratic risk
4. Test correlations
### Phase 3: Analytics (1-2 hours)
1. Add metrics calculation
2. Create analysis tools
3. Document usage
4. Add examples
## Risk Mitigation
- Validate beta ranges (typically 0.5-2.0)
- Ensure positive risk premiums
- Handle edge cases (zero beta)
- Provide sensible defaults
## Success Score
**8/10** - Well-established model with clear implementation path and existing library support.