# 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

---

## 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

---

## 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
```

---

## 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
```

---

## STEP 3: CALCULATE RESERVE RATIO

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

---

## 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

---

## 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)

---

## 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

---

**END OF RESERVE CALCULATION EXAMPLE**