Portfolio Analyzer v2 - Efficient Frontier
← v1 (Simple Model) galoy.io

EFFICIENT FRONTIER ANALYSIS

Efficient Frontier Portfolio Analyzer

Model the risk-return tradeoff of bitcoin-backed vs. traditional loans using Yield-to-Maturity calculations, recovery rate modeling, and return distribution analysis. This builds the foundation for efficient frontier visualization.

YTM-Based Returns
Recovery Rate Modeling
Return Distribution
Efficient Frontier

Traditional Loan Parameters

6.00%
3%15%
36
12120
1.00%
0%3%
2.00%
0%10%
50%
0%100%

Typical Recovery Rates:
• Commercial Real Estate: 50-65%
• Equipment: 40-55%
• Unsecured: 20-35%

Traditional Loan

YTM Analysis
Yield to Maturity (YTM) 7.14%
Nominal Rate 6.00%
+ Origination (annualized) +0.33%
= Gross YTM 6.33%
Net Spread (- CoF) 2.33%

Bitcoin-Backed Loan

YTM Analysis
Yield to Maturity (YTM) 12.00%
Nominal Rate 10.00%
+ Origination (annualized) +2.00%
= Gross YTM 12.00%
Net Spread (- CoF) 8.00%

Efficient Frontier

Phase 2
100% Traditional (long only)
100% Bitcoin (long only)
Optimal (max Sharpe)
Full Hyperbola (-100% to +200%)

The hyperbola shows all possible portfolios including short positions. The efficient frontier is the upper-left edge where you get maximum return for each volatility level.

0% BTC
-100% BTC (short) 50/50 +200% BTC (levered)

Expected Return

1.29%

Volatility

7.33%

Sharpe Ratio

0.18

vs Optimal

—

Key Portfolios

100% Traditional

1.29%

σ: 7.33%

Optimal (100% BTC)

7.92%

σ: 0.80%

100% Bitcoin

7.92%

σ: 0.80%

Frontier Insights

Loading analysis...

Recovery Rate Modeling

Traditional Loan Recovery
Recovery Rate 50%
Loss Given Default (LGD) 50%

Based on historical empirical data for collateral type

Bitcoin-Backed Recovery
BTC Price Scenario Stable (0%)
Collateral Value at Default 100% of initial
Recovery Rate 100%
Loss Given Default (LGD) 0%

Calculated from LTV, liquidation threshold, and BTC price scenario

BTC Recovery Calculation:

Recovery = min(1, (Collateral Value × BTC Price Change) / Loan Amount)

With 50% LTV, collateral = 2.00× loan value. At 0% price change: Recovery = 100%

Expected Return Distribution

Traditional Loan Returns
Performing Scenario 98.0% probability
Return = YTM +2.33%
Default Scenario 2.0% probability
Return = Recovery - 1 -50.00%
Expected Return (E[R]) 1.29%
Volatility (σ) 7.21%
Sharpe Ratio 0.18
Bitcoin-Backed Loan Returns
Performing Scenario 99.0% probability
Return = YTM +8.00%
Default Scenario 1.0% probability
Return = Recovery - 1 +0.00%
Expected Return (E[R]) 7.92%
Volatility (σ) 0.79%
Sharpe Ratio 10.00

Return Distribution Model:

E[R] = (1 - PD) × YTM + PD × (Recovery - 1)

σ = √[PD × (1-PD) × (YTM - (Recovery-1))²]

Where PD = Probability of Default, YTM = Yield to Maturity (net of CoF), Recovery = Recovery Rate

Risk-Return Summary (Phase 1 Foundation)

Metric Traditional Bitcoin-Backed Difference

Coming in Future Phases

  • • Phase 3: Historical scenario analysis across different time periods
  • • Phase 4: Multi-period frontier evolution visualization
  • • Phase 5: Statistical validation and dominance testing

Phase 1 Model Notes

YTM accounts for origination fees annualized over loan term
BTC recovery calculated dynamically based on LTV and price scenario
Returns assume loans perform to maturity or default (binary outcome)
Volatility derived from return distribution across scenarios

This model is for illustrative purposes only and does not constitute financial advice.