What Is a Worked Example of Carry Relationship in Forex? (With Assumptions)

Direct answer

A worked example of carry relationship is a number-based scenario that translates the interest-rate difference between two currencies into an estimated “carry” amount, using stated assumptions for rates, holding period, costs, and currency conversion. The key idea is that the interest differential is only one component; exchange-rate movements and practical costs can dominate the overall outcome.

Mechanism or definition

Carry relationship (often called currency carry) compares two currencies by asking: if you hold currency A and fund (pay) currency B, what is the interest-rate difference over time? In simplified terms, the potential carry comes from:

1. Interest-rate differential: the difference between the interest yield available on currency A and the interest cost of funding in currency B.
2. Time and compounding basis: how the interest is prorated over the holding period (for example, based on a day-count convention) and how it is settled/rolled.
3. Conversion back to your base currency: the interest you earn or pay is usually realized and valued in specific currencies, then converted at prevailing exchange rates.

A “worked example” should therefore specify: the two interest rates being compared, the notional size, the holding period, the day-count assumption, the exchange rate used for conversion, and any extra costs (spreads/fees) assumed in or out.

Evidence or example (fully numeric scenario)

Below is one transparent scenario. It is not a forecast; it is a mechanical illustration.

Assumptions

• You compare Currency A vs Currency B.
• You hold the position for 30 days.
• Notional: 100,000 units of Currency A.
• Annual interest rates (simple annualized assumptions):
  • Currency A earns 3% per year.
  • Currency B costs 1% per year.
• Day-count: use a simple approximation of 30/365 for the 30-day period.
• FX spot rate for conversion during the illustration: 1 unit of Currency B = 1.2000 units of Currency A.
• No additional costs (so we isolate interest carry only). In reality, providers may include transaction costs and overnight financing adjustments.
• No FX price change during the 30 days is assumed for the interest-only math. (This is a limitation; see below.)

Step-by-step carry calculation (interest differential)

1. Interest differential rate = 3% − 1% = 2% per year.

2. 30-day carry amount in Currency A terms (interest-only):

   • Carry ≈ 100,000 × 0.02 × (30/365)
   • (30/365) ≈ 0.08219
   • Carry ≈ 100,000 × 0.02 × 0.08219 ≈ 164.38 units of Currency A.

3. Convert to Currency B terms for comparison (using the stated FX rate):

   • If 1 B = 1.2000 A, then 1 A = 0.8333 B.
   • Carry in Currency B ≈ 164.38 × 0.8333 ≈ 136.98 units of Currency B.

What this shows

This scenario demonstrates how a positive interest differential can create a positive carry figure under fixed FX and ignoring all costs. If the exchange rate moves against you, the overall result can differ even when the interest differential remains positive.

Limitations and risks (material failure modes)

A worked example is useful for mechanics, but carry relationship has several limitations:

• FX move risk: Even if the interest differential is positive, depreciation of the held currency (or appreciation of the funded currency) can outweigh interest carry. The worked example’s “no FX change” assumption is a major simplification.
• Provider and execution details: Actual financing/overnight adjustments depend on market conventions and how a provider computes and applies them. Fees, spreads, and roll timing can reduce or change realized carry.
• Day-count and compounding conventions: Different instruments and providers may use different conventions for prorating interest. Changing the day-count basis changes the numerical output.
• Rollover timing: Carry is typically realized through overnight or periodic adjustments. If your holding period crosses roll or billing boundaries, realized carry may not match a simple 30-day prorated estimate.
• Regime changes: Historical relationships do not guarantee future results. Interest differentials can compress or reverse, and volatility can increase, altering how carry translates into returns.

Verification and next question

To verify a carry relationship calculation independently, check that your assumptions match the environment you are analyzing:

• Confirm the interest-rate inputs you used and the day-count/proration method. - Confirm whether any provider-specific overnight financing adjustments or fees should be included. - Verify the conversion basis (which currency the interest is valued in and how it is converted).