Interest Rate Differentials and Carry

Interest rate differentials are the gravitational force of currency markets. They determine forward points, drive carry trade flows, and explain why some currencies persistently trade at forward discounts. When JPY rates sit at 0.5% and AUD rates at 4.35%, that 3.85% gap creates measurable arbitrage relationships and trading opportunities. The point is: currency markets aren't independent of rates—they're deeply connected through arbitrage constraints that you can calculate precisely.

How Rate Differentials Drive Forward Points

Forward exchange rates aren't predictions of future spot rates. They're mathematically derived from spot rates and interest rate differentials through a no-arbitrage relationship.

The mechanism:

If you can borrow in one currency, convert to another, invest there, and lock in the return with a forward contract, you shouldn't earn more than the risk-free rate. Otherwise, arbitrage would eliminate the opportunity instantly.

Forward points formula:

Forward Points = Spot × (r_quote - r_base) × Time

Where:

• r_quote = Interest rate of quote currency (annualized)
• r_base = Interest rate of base currency (annualized)
• Time = Fraction of year to settlement

Example: AUD/USD forward points

Given:

• Spot AUD/USD: 0.6550
• AUD rate: 4.35%
• USD rate: 5.25%
• Time: 3 months (0.25 years)

Forward Points = 0.6550 × (0.0525 - 0.0435) × 0.25 Forward Points = 0.6550 × 0.0090 × 0.25 Forward Points = 0.0015 (15 pips, premium)

3-month forward = 0.6550 + 0.0015 = 0.6565

Interpretation: AUD trades at a forward premium against USD because USD rates are higher. If you buy AUD forward, you pay more than spot—offsetting the yield advantage of holding USD.

Uncovered Interest Parity: The Theory

Covered interest parity (CIP) is an arbitrage relationship—it holds by construction because traders enforce it. Uncovered interest parity (UIP) is a theoretical expectation that often fails empirically.

UIP states: The expected future spot rate should move to offset the interest rate differential. A currency with higher rates should depreciate by the rate differential.

The formula:

E[S_future] = S_spot × (1 + r_domestic) / (1 + r_foreign)

Example (theoretical):

• Spot USD/JPY: 150.00
• USD rate: 5.25%
• JPY rate: 0.50%
• 1-year forward: 143.37 (reflecting differential)

UIP predicts: In one year, spot USD/JPY should trade near 143.37. The dollar should depreciate against yen by approximately 4.4% to offset the yield advantage.

Reality check: UIP consistently fails. Empirical studies find that high-yield currencies appreciate rather than depreciate over short horizons. This failure is why carry trades generate positive returns—they exploit UIP violations.

The durable lesson: UIP is a theoretical benchmark, not a trading rule. Its systematic failure creates the carry trade opportunity.

Carry Trade Mechanics

A carry trade borrows in a low-yielding currency (the funding currency) and invests in a high-yielding currency (the target currency). Profit comes from the interest rate differential, provided the exchange rate doesn't move against you.

Basic structure:

1. Borrow JPY at 0.5% for one year
2. Convert JPY to AUD at spot
3. Invest AUD at 4.35% for one year
4. At maturity: Convert AUD back to JPY to repay loan

Net carry = Target rate - Funding rate = 4.35% - 0.50% = 3.85%

The risk: If AUD/JPY falls by more than 3.85%, your currency loss exceeds your carry gain.

Why traders don't hedge: Hedging with a forward contract would eliminate the carry. The forward points exactly offset the rate differential (covered interest parity). Unhedged carry trades are bets that UIP fails—that high-yield currencies won't depreciate by the full differential.

Worked Example: JPY-Funded AUD Carry Trade

Setup:

• Investment: Borrow JPY 100,000,000 at 0.5% for one year
• Spot AUD/JPY: 97.50
• AUD deposit rate: 4.35%

Step 1: Convert to AUD

AUD amount = JPY 100,000,000 / 97.50 = AUD 1,025,641

Step 2: Invest AUD for one year

Interest earned = AUD 1,025,641 × 4.35% = AUD 44,615 Total AUD at maturity = AUD 1,025,641 + 44,615 = AUD 1,070,256

Step 3: Calculate JPY owed

Principal + interest = JPY 100,000,000 × (1 + 0.5%) = JPY 100,500,000

Step 4: Calculate breakeven exchange rate

Breakeven AUD/JPY = JPY owed / AUD available Breakeven = 100,500,000 / 1,070,256 = 93.90

If AUD/JPY stays above 93.90, the trade profits. The maximum AUD depreciation tolerable before loss is:

(97.50 - 93.90) / 97.50 = 3.69%

This matches the carry (minus compounding adjustments).

Scenario analysis:

The point is: Carry trades profit in stable or risk-on environments but suffer severe losses during risk-off episodes when funding currencies strengthen.

Rate Differential Calculation Framework

Step-by-step for any currency pair:

1. Identify base and quote currencies
2. Find relevant short-term rates:
   • Use SOFR for USD
   • Use TONA for JPY
   • Use cash rate for AUD
   • Use 3-month interbank rates for approximation
3. Calculate differential: Quote rate - Base rate
4. Calculate annualized carry: Differential × notional
5. Calculate breakeven depreciation: Differential / (1 + base rate)

Current rate differential examples (as of late 2024):

Reading the table: Negative differential means selling the quote currency and buying the base currency earns carry.

Carry Trade Risks: When Depreciation Exceeds Carry

Carry trades exhibit a distinctive return profile: steady small gains punctuated by large sudden losses. This pattern reflects the risk-on/risk-off dynamic.

Historical stress episodes:

Why losses are sudden:

1. Carry trades are crowded—many traders hold similar positions
2. Risk-off triggers force simultaneous unwinds
3. Funding currencies (JPY, CHF) are safe havens—they strengthen in crises
4. Leverage amplifies moves

Risk metrics for carry trades:

• Carry-to-volatility ratio: Annualized carry divided by annualized volatility. Above 0.5 is attractive; below 0.3 is risky.
• Maximum adverse move: Calculate how much depreciation wipes out one year of carry.
• Correlation with risk assets: High correlation means carry adds to portfolio risk, not diversification.

A → B → C chain:

Risk-off event → JPY/CHF demand surge → Carry positions unwind → Additional selling pressure → Funding currencies spike

Detection Signals: Carry Trade Stress

Warning signs that carry trade conditions are deteriorating:

• VIX spikes above 20 (risk appetite falling)
• JPY strengthening despite rate differential
• Credit spreads widening (risk-off behavior)
• EM currencies weakening broadly
• Carry-to-volatility ratio declining (vol rising faster than carry)

The point is: carry trades require monitoring risk conditions, not just rate differentials. High carry means nothing if the currency crashes.

Common Mistakes

Mistake 1: Assuming carry is risk-free return

Carry is compensation for currency risk. High carry currencies tend to depreciate during stress, partially offsetting the income.

Mistake 2: Ignoring funding costs and rollover

Broker rollover rates include spread. Your actual carry may be 0.5-1% less than the theoretical rate differential.

Mistake 3: Overleveraging carry positions

A 4% carry with 10x leverage looks like 40% return—until a 10% currency move causes a 100% loss.

Mistake 4: Ignoring correlation

Multiple carry trades (long AUD, long BRL, long MXN, short JPY) are correlated. They all fail simultaneously in risk-off episodes.

Checklist: Evaluating Carry Trade Opportunities

Essential (before entering any carry position)

• Calculate exact rate differential using current reference rates
• Determine breakeven currency move (how much depreciation wipes out carry)
• Check current VIX and credit spreads for risk environment
• Size position to survive historical maximum adverse moves

High-Impact (for systematic carry trading)

• Track carry-to-volatility ratio over time
• Monitor central bank policy trajectory (will differential persist?)
• Diversify funding currencies (not all JPY-funded)
• Set stop-losses based on currency moves, not P&L

Your Next Step

Calculate the current rate differential for a currency pair you follow. Then calculate how much the target currency would need to depreciate to eliminate one year of carry. Compare that to the pair's historical volatility—is the carry worth the risk?

Calculation template:

1. Rate differential = Target rate - Funding rate
2. Breakeven depreciation = Differential / (1 + Funding rate)
3. Historical annual volatility = Standard deviation of daily returns × sqrt(252)
4. Carry-to-volatility ratio = Differential / Annual volatility

If the ratio is above 0.5 and risk conditions are stable, the carry trade may be attractive. Below 0.3, you're not being compensated adequately for the volatility.

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Related: Spot vs. Forward FX Markets | Using Currency Futures and Options | Carry Trade Mechanics and Risks

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Sources: Bank for International Settlements (2022). FX and OTC Derivatives Markets Survey. | Federal Reserve Bank of St. Louis (2024). FRED Interest Rate Data.