Why Debt Currency Matters
A government’s debt can be stated in its own currency or in a foreign currency. That distinction matters because a change in the exchange rate can alter the domestic-currency value of a foreign-currency obligation even when the government has borrowed no additional money. If the domestic currency depreciates, more domestic currency is required to acquire each unit of foreign currency needed to repay that debt.
This is a valuation effect, not necessarily a new borrowing or a change in the foreign-currency amount owed. It can increase the measured debt stock and, if domestic-currency GDP is unchanged over the comparison, the debt-to-GDP ratio. The fiscal risk is greater when government revenues and assets are mainly in domestic currency while its debt payments are in foreign currency.
Debt denomination is not the same as the creditor’s location. A bond held by a foreign investor but payable in domestic currency does not acquire a higher domestic-currency principal merely because the exchange rate changes. Conversely, a foreign-currency bond held by a domestic investor remains a foreign-currency obligation of the government. The currency of payment determines the direct exchange-rate valuation effect.
Calculating the Valuation Effect
Suppose the exchange rate rises from \(E_0\) to \(E_1\), while the quantities of debt in each currency remain fixed. The change in domestic-currency debt is the change in the exchange rate multiplied by the foreign-currency debt. Domestic-currency debt does not change through this direct conversion.
If depreciation is measured as a fraction \(g\) of the initial exchange rate, then \(E_1=E_0(1+g)\). The foreign-currency component’s domestic-currency value rises by \(g\), but total debt rises by less than \(g\) when some debt is denominated in domestic currency.
The fraction \(E_0D^f/D_0\) is the foreign-currency share of debt measured at the initial exchange rate. Thus, with debt quantities unchanged, the percentage increase in total debt equals the depreciation rate multiplied by that initial share. This relationship is exact for the stated assumptions; it is not a claim that depreciation has no other effects on the economy.
Worked Example: Translating a Mixed-Currency Debt Stock
A government has domestic-currency debt of 70.00 billion units and foreign-currency debt of 12.00 billion euros. The initial exchange rate is 1.25 domestic-currency units per euro. The domestic currency then depreciates by 20.00%, with both debt quantities unchanged. Calculate total debt before and after depreciation and the percentage increase in total debt. All money amounts are in billions and are reported to two decimal places.
Method. Convert the foreign-currency debt at each exchange rate, then add the unchanged domestic-currency debt.
Initially, the domestic-currency value of the foreign debt is \(1.25 \times 12.00 = 15.00\). Initial total debt is therefore \(70.00 + 15.00 = 85.00\) billion domestic-currency units.
The new exchange rate is \(1.25 \times (1+0.20)=1.50\) domestic-currency units per euro. The converted foreign debt is \(1.50 \times 12.00=18.00\) billion. New total debt is \(70.00+18.00=88.00\) billion.
The increase is \(88.00-85.00=3.00\) billion. As a percentage of initial total debt, this is \((3.00/85.00)\times100=3.5294\%\), or 3.53% to two decimal places.
Check and trap avoided. Initially, the foreign-currency share is \(15.00/85.00=0.17647\). Multiplying this share by the 20.00% depreciation gives \(0.17647\times20.00\%=3.5294\%\), which matches the direct calculation. Applying 20.00% to all 85.00 billion would incorrectly treat domestic-currency debt as exchange-rate-sensitive.
Effect on the Debt-to-GDP Ratio
The debt-to-GDP ratio compares the domestic-currency value of public debt with domestic-currency GDP. For an immediate valuation calculation, one useful assumption is that nominal GDP and domestic-currency debt are held constant while the exchange rate changes. Under that assumption, any increase in translated foreign debt raises the ratio. In an actual economy, GDP, prices, interest costs, output, and fiscal balances may also change; the simple calculation isolates the direct conversion effect.
Worked Example: Depreciation and the Debt Ratio
A government has 60.00 billion units of domestic-currency debt and 40.00 billion units of foreign-currency debt. The initial exchange rate is 2.00 domestic-currency units per foreign-currency unit. Nominal GDP is 200.00 billion domestic-currency units. The domestic currency depreciates by 25.00%. Assume debt quantities and nominal GDP are unchanged apart from the direct currency conversion. Find the debt ratio before and after depreciation and its change in percentage points.
Method. Translate the foreign debt at each exchange rate, add domestic debt, and divide by the stated GDP.
Initially, translated foreign debt is \(2.00\times40.00=80.00\) billion. Total debt is \(60.00+80.00=140.00\) billion, so the initial ratio is \(140.00/200.00=0.70\), or 70.00%.
The new exchange rate is \(2.00\times1.25=2.50\). Translated foreign debt is \(2.50\times40.00=100.00\) billion. Total debt becomes \(60.00+100.00=160.00\) billion, and the new ratio is \(160.00/200.00=0.80\), or 80.00%.
The ratio increases by \(80.00\%-70.00\%=10.00\) percentage points. Relative to its initial value, the ratio rises by \(10.00/70.00=14.2857\%\), or 14.29% to two decimal places.
Check and trap avoided. Foreign debt initially represents \(80.00/140.00=57.1429\%\) of total debt. The total debt increase is \(25.00\%\times57.1429\%=14.2857\%\), consistent with the increase from 140.00 to 160.00. The ratio’s increase is 10.00 percentage points, not 10.00%; distinguishing these descriptions prevents a common reporting error.
Why the Exposure Formula Holds
The relationship between depreciation and total debt follows directly from the accounting definition of domestic-currency debt. It depends on the exchange rate applying to the foreign-currency liability, not on a separate assumption that every component of public debt changes.
At exchange rate \(E_0\), total debt is \(D_0=D^d+E_0D^f\).
If debt quantities are fixed and the exchange rate becomes \(E_1\), then \(D_1=D^d+E_1D^f\).
The domestic debt terms cancel, giving \(\Delta D=(E_1-E_0)D^f\).
If \(E_1=E_0(1+g)\), then \(\Delta D=gE_0D^f\). Dividing by \(D_0\) gives \(\Delta D/D_0=g(E_0D^f/D_0)\).
This derivation shows why the initial share of foreign-currency debt is central: it measures how much of the initial debt stock is directly revalued. If all debt is domestic-currency debt, that share is zero and the direct valuation effect is zero. If all debt is foreign-currency debt, the total stock rises by the full depreciation rate, provided the debt quantities are unchanged.
Worked Example: Debt Service and Currency Mismatch
A government owes 8.00 billion units of foreign currency. Its annual interest rate on that debt is 4.00%, and it must repay 1.50 billion units of principal during the year. It receives 0.50 billion units of annual public revenue in the same foreign currency; its other annual revenue is 100.00 billion domestic-currency units. The exchange rate rises from 4.00 to 5.00 domestic-currency units per foreign-currency unit. Assume the interest rate, principal repayment, foreign-currency revenue, and domestic-currency revenue are unchanged. Compare gross annual debt service and the net foreign-currency funding gap before and after depreciation.
Method. Calculate interest in foreign currency, add principal due, subtract the foreign-currency revenue to find the net gap, and convert both gross service and the gap at each exchange rate.
Annual interest is \(0.04\times8.00=0.32\) billion foreign-currency units. Gross annual debt service is \(0.32+1.50=1.82\) billion. After applying foreign-currency revenue of 0.50 billion, the net foreign-currency funding gap is \(1.82-0.50=1.32\) billion.
At the initial exchange rate of 4.00, gross service costs \(1.82\times4.00=7.28\) billion domestic-currency units. The net funding gap costs \(1.32\times4.00=5.28\) billion. Relative to domestic-currency revenue of 100.00 billion, these amounts are 7.28% and 5.28%, respectively.
At the new exchange rate of 5.00, gross service costs \(1.82\times5.00=9.10\) billion and the net funding gap costs \(1.32\times5.00=6.60\) billion. Relative to the same domestic-currency revenue, these are 9.10% and 6.60%. Thus gross service rises by 1.82 billion domestic-currency units, while the net gap rises by 1.32 billion.
Check and trap avoided. The foreign-currency revenue offsets part of the payment need because it is denominated in the same currency as debt service. It does not eliminate the mismatch: the government still needs 1.32 billion foreign-currency units. Counting the 0.50 billion as domestic-currency revenue without converting it would give an inconsistent comparison.
Currency Mismatch and Fiscal Vulnerability
A government has a currency mismatch when its foreign-currency obligations are not adequately matched by foreign-currency assets or reliable foreign-currency revenues. The relevant comparison is not simply the foreign-currency debt stock against all public resources. It asks whether the government can obtain the currency required for payments without an unusually large domestic-currency cost or difficult adjustments.
Foreign-currency assets or revenues can provide a partial hedge: when the domestic currency depreciates, their domestic-currency value may rise alongside that of foreign-currency liabilities. However, the hedge is only as strong as the amount, timing, accessibility, and currency match of those resources. A government with foreign-currency receipts that arrive after a large debt payment still faces a near-term funding need. The simple examples here assume the stated receipts are available when required.
The basic valuation result also has limits. It isolates the mechanical effect of translating an unchanged debt stock. It does not by itself predict whether depreciation will raise inflation, change interest rates, reduce output, affect tax revenue, or alter future borrowing. Those effects require additional assumptions and analysis. Nor does a higher translated debt ratio alone prove that a government cannot meet its obligations; it identifies one channel of exposure, not a complete solvency judgment.
For fiscal analysis, the composition of debt therefore matters alongside its total amount. Two governments with the same initial debt-to-GDP ratio can face different immediate valuation effects if their foreign-currency shares differ. A larger share, a sharper depreciation, or a weaker currency match between obligations and resources can make the budget more sensitive to exchange-rate movements.
Common Calculation Traps
- Using the wrong exchange-rate quotation. If \(E\) is domestic currency per foreign unit, depreciation means \(E\) rises. A quote defined in the opposite direction moves inversely.
- Applying the depreciation rate to all debt. The direct effect applies to the translated foreign-currency component; domestic-currency principal is unchanged under the stated assumptions.
- Confusing foreign-currency denomination with foreign ownership. Creditor residence does not determine the direct currency conversion.
- Changing the denominator without stating why. A calculated debt-ratio effect with fixed GDP is an immediate valuation comparison. If GDP changes, use the new GDP rather than assuming the old denominator still applies.
- Ignoring matching resources. Foreign-currency assets or revenues can offset some exposure, but only to the extent that they are available and aligned with the payment currency and timing.
Check Your Understanding
For each question, keep the exchange-rate quotation and the stated assumptions explicit.
- A government has domestic-currency debt of 90.00 million and foreign-currency debt of 20.00 million Swiss francs. The exchange rate is 1.10 domestic-currency units per franc, then the domestic currency depreciates by 10.00%. Find total debt before and after depreciation and the percentage increase. (Answer: 112.00 million initially; 114.20 million after; increase 1.96%.)
- Public debt consists of 300.00 billion domestic-currency units and 50.00 billion foreign-currency units. GDP is 500.00 billion domestic-currency units, and the exchange rate rises from 1.60 to 1.80. Assuming GDP and debt quantities remain fixed, calculate the debt ratios and their change in percentage points. (Answer: 76.00% initially; 78.00% after; increase 2.00 percentage points.)
- A government has domestic-currency debt of 100.00 billion and debt of 25.00 billion Canadian dollars. The exchange rate rises from 0.75 to 0.81 domestic-currency units per Canadian dollar. Calculate total debt before and after the change and the percentage increase. (Answer: 118.75 billion initially; 120.25 billion after; increase 1.26%.)
- A public entity has foreign-currency liabilities of 11.00 billion and foreign-currency assets of 3.00 billion. The exchange rate rises from 6.00 to 6.90 domestic-currency units per foreign unit. Assuming the quantities of assets and liabilities are fixed, calculate its net foreign-currency liability in domestic-currency value before and after depreciation. (Answer: 48.00 billion initially; 55.20 billion after; increase 7.20 billion.)
- Foreign-currency debt is 30.00% of a government’s initial total debt. If the domestic currency depreciates by 18.00% and all debt quantities are fixed, calculate the percentage increase in total debt from the direct valuation effect. (Answer: 5.40%.)