dbis_docs/gru_reserve_system/examples/Reserve_Calculation_Example.md

RESERVE CALCULATION EXAMPLE

Worked Example of Reserve Adequacy Calculation

Document Number: DBIS-GRU-EX-002
Version: 1.0
Date: [Enter date in ISO 8601 format: YYYY-MM-DD]
Classification: UNCLASSIFIED
Authority: DBIS Financial Operations Department

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SCENARIO

Calculate total reserves and reserve ratio for DBIS given the following reserve assets and liabilities.

Reserve Assets:

• XAU: 10,000 oz at $2,000/oz, weight = 1.0
• Bitcoin: 100 BTC at $50,000/BTC, weight = 0.9
• Ethereum: 500 ETH at $3,000/ETH, weight = 0.85
• US Treasury Bonds: $10,000,000 face value, present value = $10,200,000, weight = 1.0

Liabilities:

• Outstanding bonds: $30,000,000
• Currency in circulation: $5,000,000
• Other liabilities: $2,000,000
• Total liabilities: $37,000,000

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STEP 1: CALCULATE INDIVIDUAL ASSET VALUES

XAU Value

V_XAU = Q_XAU × P_XAU × F_XAU × W_XAU
V_XAU = 10,000 oz × $2,000/oz × 1.0 × 1.0
V_XAU = $20,000,000

Bitcoin Value

V_BTC = Q_BTC × P_BTC × W_BTC
V_BTC = 100 BTC × $50,000/BTC × 0.9
V_BTC = $4,500,000

Ethereum Value

V_ETH = Q_ETH × P_ETH × W_ETH
V_ETH = 500 ETH × $3,000/ETH × 0.85
V_ETH = $1,275,000

US Treasury Bonds Value

V_Bonds = PV_Bonds × W_Bonds
V_Bonds = $10,200,000 × 1.0
V_Bonds = $10,200,000

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STEP 2: CALCULATE TOTAL RESERVES

R_total = V_XAU + V_BTC + V_ETH + V_Bonds
R_total = $20,000,000 + $4,500,000 + $1,275,000 + $10,200,000
R_total = $35,975,000

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STEP 3: CALCULATE RESERVE RATIO

RR = R_total / L_total
RR = $35,975,000 / $37,000,000
RR = 0.972 (97.2%)

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STEP 4: ASSESS RESERVE ADEQUACY

Minimum Requirement:

R_min = L_total × RR_min
R_min = $37,000,000 × 1.0
R_min = $37,000,000

Current Status:

• Current reserves: $35,975,000
• Minimum required: $37,000,000
• Shortfall: $1,025,000
• Reserve ratio: 97.2%
• Status: BELOW MINIMUM (requires action)

Required Action:

• Increase reserves by minimum $1,025,000
• Target reserves: $44,400,000 (120% of liabilities)
• Additional required: $8,425,000 to reach target

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STEP 5: RISK-ADJUSTED RESERVES

Risk Factors:

• Concentration risk: Largest asset (XAU) = 55.6% of total (risk factor: 0.256)
• Liquidity risk: Liquid assets = 75% of total (risk factor: 0.25)
• Credit risk: All assets high quality (risk factor: 0.05)
• Market risk: Portfolio VaR = 2% (risk factor: 0.02)
• Operational risk: Low (risk factor: 0.05)

Aggregate Risk:

R_risk = 0.2 × 0.256 + 0.2 × 0.25 + 0.2 × 0.05 + 0.2 × 0.02 + 0.2 × 0.05
R_risk = 0.0512 + 0.05 + 0.01 + 0.004 + 0.01
R_risk = 0.1252 (12.52%)

Risk-Adjusted Reserves:

R_adj = R_total × (1 - R_risk)
R_adj = $35,975,000 × (1 - 0.1252)
R_adj = $35,975,000 × 0.8748
R_adj = $31,470,330

Risk-Adjusted Reserve Ratio:

RR_adj = R_adj / L_total
RR_adj = $31,470,330 / $37,000,000
RR_adj = 0.851 (85.1%)

Status: Risk-adjusted reserves also below minimum (85.1% vs. 100% required)

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CONCLUSION

The reserve system requires immediate action to increase reserves to meet minimum requirements. Both unadjusted and risk-adjusted reserves are below the 100% minimum threshold.

Recommendations:

1. Increase reserves by minimum $1,025,000 immediately
2. Target 120% reserve ratio ($44,400,000 total)
3. Diversify reserves to reduce concentration risk
4. Increase liquid assets to reduce liquidity risk

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END OF RESERVE CALCULATION EXAMPLE