Sandy McGuffog’s Solvency Invariant:
"In fractional reserve banking, the bank has assets to cover all its liabilities — assets equal reserves plus loans outstanding. Key point: Assets exceed/match liabilities. In full reserve cryptocurrencies, assets equal liabilities. In fractional reserve cryptocurrencies, the issuer has $10, and issues $100 of tokens... assets are less than liabilities. So no, they’re really not ok."
1. Traditional Fractional Bank
SOLVENT
Holds performing loans equal to deposits minus cash reserves
Assets
Cash Reserves:
$10.0M
Performing Loans:
$90.0M
Total Assets:
$100.0M
Liabilities & Equity
Deposits:
$100.0M
Paid Redemptions:
$0.0M
Net Balance:
$0.0M
Status: Fully Solvent. Initial $10M reserves satisfy first withdrawals. Remaining withdrawals met by rediscounting performing loans or central bank facility.
2. Full Reserve Stablecoin
1:1 BACKED
100% liquid fiat or short treasuries per issued token unit
Assets
Fiat Cash in Bank:
$100.0M
Loan Claims:
$0.0M
Total Assets:
$100.0M
Liabilities
Tokens in Circulation:
$100.0M
Tokens Burned:
$0.0M
Net Deficit:
$0.0M
Status: 100% Run Proof. Each token is redeemed 1:1 and burnt. Reserves decrease linearly with liabilities without discount or cliff.
3. Fractional Reserve Crypto
CRITICALLY INSOLVENT
Issues $100M "backed" tokens on only $10M reserve without real-economy loan book
Assets
Liquid Reserve Cash:
$10.0M
Enforceable Loans:
$0.0M
Actual Assets:
$10.0M
Token Liabilities
Tokens Issued:
$100.0M
Cumulative Deficit:
-$90.0M
Balance Sheet Gap:
-$90.0M
Insolvency Cliff at Step 2: Reserves exhausted after paying only $10.0M. Next $15.0M of requested redemptions fail completely. Zero loan assets to liquidate.
Step-by-Step Liquidity Run Mechanics
Observe what happens when customer withdrawals hit $25M against initial balance sheets:
Step 1: First $10M Withdrawn
ALL SURVIVE
Traditional Bank, Full Reserve Stablecoin, and Fractional Crypto all have $10M liquid cash. All three honor redemptions 1-for-1.
Step 2: Redemptions Exceed $10M (The Run Continues)
CRYPTO COLLAPSES
Fractional Crypto Issuer halts withdrawals at Step 2. It has no more reserves and no real debt claims to sell. Traditional Bank activates loan maturities / central bank window; Full Reserve simply pays from its remaining $90M cash.
Step 3: Extreme Stress (> $50M Run)
STRUCTURAL RESOLUTION
Full Reserve survives up to 100% without loss. Traditional Bank liquidates or pledges loan portfolio (with slight discount/haircut). Fractional Crypto leaves token holders recovering pennies on the dollar.
Solvency Audit & Counterfactual Summary
| Institution Architecture | Starting Assets | Liabilities | Run Demanded | Run Paid | Final Gap / Equity | Survival Outcome |
|---|