Foreign Exchange Exposure & Risk Management (Quick Revision)
1. Quotation Rules & Cross Currency Chain
1. Direct to Indirect Quote Inversion:
$$\text{Direct Bid} = \frac{1}{\text{Indirect Ask}}; \quad \text{Direct Ask} = \frac{1}{\text{Indirect Bid}}$$2. Synthetic Cross Rates:
$$\left(\frac{A}{B}\right)_{\text{Bid}} = \left(\frac{A}{C}\right)_{\text{Bid}} \times \left(\frac{C}{B}\right)_{\text{Bid}} = \frac{(A/C)_{\text{Bid}}}{(B/C)_{\text{Ask}}}$$ $$\left(\frac{A}{B}\right)_{\text{Ask}} = \left(\frac{A}{C}\right)_{\text{Ask}} \times \left(\frac{C}{B}\right)_{\text{Ask}} = \frac{(A/C)_{\text{Ask}}}{(B/C)_{\text{Bid}}}$$3. Forward Swap Points Rule:
- Ascending Points ($\text{Bid} < \text{Ask}$) $\implies$ ADD Points (Premium)
- Descending Points ($\text{Bid} > \text{Ask}$) $\implies$ SUBTRACT Points (Discount)
4. Annualized Premium / Discount:
$$\%\text{ Premium/Discount} = \frac{F - S}{S} \times \frac{12}{m} \times 100$$2. International Parity Relationships
| Theorem | Direct Quote Formula ($\text{Domestic/Foreign}$) | Core Takeaway |
|---|---|---|
| Interest Rate Parity (IRP) | $$\frac{F}{S} = \frac{1 + r_D \cdot t}{1 + r_F \cdot t} \approx 1 + (r_D - r_F)t$$ | Currency with lower interest rate trades at a forward premium. |
| Purchasing Power Parity (PPP) | $$\frac{E(S_t)}{S_0} = \frac{1 + I_D}{1 + I_F} \approx 1 + (I_D - I_F)$$ | Expected spot change equals inflation differential. |
| International Fisher Effect (IFE) | $$\frac{E(S_t)}{S_0} = \frac{1 + r_D}{1 + r_F} \approx 1 + (r_D - r_F)$$ | Higher nominal interest rate implies expected currency depreciation. |
3. Covered Interest Arbitrage & Triangular Arbitrage
Covered Interest Arbitrage (CIA) Decision Rule:
- If $\text{Forward Premium} > (r_D - r_F) \implies$ Foreign currency forward is Overvalued.
Strategy: Borrow Domestic $\to$ Convert Spot $\to$ Invest Foreign $\to$ Sell Foreign Forward. - If $\text{Forward Premium} < (r_D - r_F) \implies$ Foreign currency forward is Undervalued.
Strategy: Borrow Foreign $\to$ Convert Spot $\to$ Invest Domestic $\to$ Buy Foreign Forward.
4. Forward Cover vs. Money Market Hedge (MMH)
| Parameter | Exporter (Foreign Receivable) | Importer (Foreign Payable) |
|---|---|---|
| Forward Contract | Sell foreign currency at Forward Bid: $$\text{Inflow} = \text{Receivable} \times F_{\text{Bid}}$$ | Buy foreign currency at Forward Ask: $$\text{Outflow} = \text{Payable} \times F_{\text{Ask}}$$ |
| Money Market Hedge (MMH) | 1. Borrow $FC = \frac{\text{Receivable}}{1 + r_{FC}^{\text{borrow}} \cdot t}$ 2. Convert Spot at Bid. 3. Invest in Domestic at $r_D^{\text{deposit}} \cdot t$. |
1. Deposit $FC = \frac{\text{Payable}}{1 + r_{FC}^{\text{deposit}} \cdot t}$ 2. Buy Spot at Ask. 3. Borrow Domestic at $r_D^{\text{borrow}} \cdot t$. |
| Currency Option | Buy Put Option (Guaranteed floor with upside participation). | Buy Call Option (Capped maximum cost with downside participation). |
5. FEDAI Forward Contract Cancellation & Extension
| Contract Event | Offsetting Market Rate Applied by Bank | Net Cash Settlement Formula |
|---|---|---|
| Forward Sale Cancelled on Due Date | Prevailing Spot TT Buying Rate | $\text{Gain / Loss} = (\text{Contract Rate} - \text{Spot TT Buying}) - \text{Charges}$ |
| Forward Purchase Cancelled on Due Date | Prevailing Spot TT Selling Rate | $\text{Gain / Loss} = (\text{Contract Rate} - \text{Spot TT Selling}) - \text{Charges}$ |
| Early Cancellation (before due date) | Prevailing Forward Rate for Residual Maturity | Difference between Contract Rate and Residual Forward Rate. |
| Early Delivery | Execute at contracted rate; charge Swap Loss + Interest on Outlay | $\text{Outlay Interest} = \text{Outlay} \times \text{PLR} \times \frac{\text{Days}}{365}$ |
| Extension / Rollover | 1. Cancel old contract at Spot TT Buying/Selling. 2. Book new contract at prevailing Forward rate. |
Two-step settlement. |
6. High-Frequency Exam Traps & Pointers
- Bank Perspective: In every merchant transaction, the bank buys low (Bid) and sells high (Ask). Importers buy from bank at Ask; Exporters sell to bank at Bid.
- Margin Direction: Bank always deducts margin from Bid (paying less to customer) and adds margin to Ask (charging more from customer).
- Direct vs Indirect Formula: When quote is direct ($\text{Domestic/Foreign}$), domestic interest is in numerator: $\frac{F}{S} = \frac{1+r_D}{1+r_F}$. If quote is indirect ($\text{Foreign/Domestic}$), foreign interest is in numerator!
- Exchange Position vs Nostro Cash: Forward contracts affect Exchange Position immediately, but DO NOT affect Nostro Cash until physical settlement.