CFA Level II Exam · Currency Exchange Rates: Understanding Equilibrium Value

Carry Trade and Forward Rate Bias Explained

Updated 7 October 2026 · Fact-checked

A carry trade borrows in a low-yield currency and invests in a high-yield currency. It profits when the high-yield currency does not depreciate by the interest differential. Forward rate bias is the empirical failure of uncovered interest parity, which lets the trade earn positive average returns, with occasional sharp crashes.

Understand Carry Trade and Forward Rate Bias

Start with uncovered interest rate parity (UIP). It says the expected change in the spot rate offsets the interest rate gap. The high-yield currency is expected to depreciate by about the interest differential. If UIP held, investors earn the same expected return in any currency, and no strategy would earn a free premium.

Covered interest rate parity (CIP) is different. It is a no-arbitrage condition: the forward rate is set by the interest differential. So the forward points tell you the interest differential. Under CIP, the forward rate of a high-yield currency trades at a discount to spot.

If UIP held, the forward rate would be an unbiased predictor of the future spot rate. The evidence shows UIP tends to fail over short to medium horizons, and the forward rate is a biased predictor on average. High-yield currencies, on average, do not depreciate as much as the forward rate implies, and sometimes they appreciate. This is forward rate bias: the forward discount overstates the depreciation that actually occurs on average.

The carry trade exploits this. You borrow the funding currency (low interest rate), convert to the investment currency (high interest rate), and earn the interest differential. You keep the profit if the investment currency falls by less than the differential. You can do it unhedged in the spot market, or equivalently by buying the high-yield currency forward.

The risk is a negative skew. Returns are small and steady for long stretches, then a sudden fall in the investment currency, often during a global risk-off episode, wipes out many months of carry. Return distributions show negative skewness and excess kurtosis (fat tails), so standard deviation understates the crash risk. Carry trades are also tied to leverage and liquidity: when volatility rises, funding dries up, and many investors unwind at once, which deepens the fall. Carry returns are best seen as compensation for bearing crash risk, and a Sharpe ratio can look attractive before a crash.

Key formulas to remember

Uncovered interest rate parity: E(%ΔS) ≈ i(price currency) − i(base currency); With S = price currency per unit of base currency. A positive E(%ΔS) means the base currency is expected to appreciate and the price currency to depreciate. The higher-rate currency is expected to depreciate, whichever one it is. If i_price > i_base, the price currency is expected to depreciate. If i_base > i_price, E(%ΔS) is negative and the base currency is expected to depreciate.
Covered interest rate parity: F = S × (1 + i_price) ÷ (1 + i_base); Holds by arbitrage. The forward premium or discount approximately equals the interest differential. Exactly, F ÷ S − 1 = (1 + i_price) ÷ (1 + i_base) − 1. The higher-rate currency trades at a forward discount.
Carry trade return (unhedged, one period): R ≈ i_invest − i_fund + %ΔS_invest-currency; %ΔS here is the percentage change in the value of the investment currency measured in the funding currency, so a positive number means the investment currency gained. This is not the same sign convention as ΔS in the UIP formula when the investment currency is the price currency. Exact: (1 + i_invest)(1 + %ΔS) − (1 + i_fund) in funding-currency terms.
Break-even depreciation: %ΔS = −(i_invest − i_fund) = i_fund − i_invest (approx.); The investment currency can fall by the carry, i_invest − i_fund, before the carry is wiped out. The %ΔS figure is negative because it is a fall. It uses the same convention as the carry trade return formula: the change in the investment currency's value in funding-currency terms.
Forward rate bias condition: Under UIP: F = E(S future). With bias: E(S future) ≠ F; High-yield currencies trade at a forward discount but depreciate less than that on average.

How to solve Carry Trade and Forward Rate Bias questions

Use this order for any carry trade or forward bias item in a vignette.

1Identify the funding currency (lower rate) and the investment currency (higher rate) from the exhibit. Check the quote convention (price per base).
2Compute the interest differential over the holding period. Scale annual rates by the period length.
3Compute the currency move: percent change in the investment currency against the funding currency. Invert the quote if needed.
4Add the carry and the currency move to get the return in funding-currency terms. Use the exact form if the question gives large moves.
5Compare the actual move with the forward discount or UIP-implied move to judge whether UIP held or the trade gained.
6For risk questions, name negative skewness, fat tails, leverage, and unwinding in risk-off periods. Do not rely on standard deviation alone.

Quickest way: Carry minus currency move

When to use it: Any numeric carry trade return where rates and spot moves are small.

Carry = high rate − low rate, for the period.
Currency move = percent change of the high-yield currency against the funding currency.
Return ≈ carry + currency move.
The trade breaks even when the currency falls by the carry.
If the quote is price per base, a rise in the quote means the base currency appreciated. Flip the sign if your investment currency is the price currency.

Common mistakes in Carry Trade and Forward Rate Bias

Treating UIP as an observed fact and expecting the high-yield currency to depreciate.
UIP and CIP sound alike, and the text states UIP as a model.
Fix: Remember CIP holds by arbitrage. UIP is a prediction that often fails, which is forward rate bias.
Getting the sign of the currency move wrong because of the quote direction.
Quotes are price currency per base, and students read a rising number as appreciation of the wrong currency.
Fix: Write the quote as price/base first. A higher number means the base currency has gained. Then decide which currency you hold.
Using annual rates for a shorter holding period.
Rates in exhibits are quoted annually.
Fix: Scale the differential to the period, for example multiply by 3/12 for three months, before adding the currency move.
Concluding that carry is risk-free because average returns are positive.
Strong Sharpe ratios in calm years hide tail risk.
Fix: Describe the return as compensation for crash risk: negative skew, excess kurtosis, and unwinds when volatility rises.
Saying forward rate bias means CIP is violated.
Both involve forward rates and interest differentials.
Fix: CIP is intact. The bias is that the forward rate is a poor predictor of the future spot rate.

Worked examples

Example 1

A fund borrows in currency JPY at 0.5% a year and invests in currency AUD at 4.5% a year, unhedged, for one year. AUD/JPY spot moves so that AUD falls 2.0% against JPY over the year. (a) What is the approximate return in JPY terms, and what is the exact return? (b) How large a fall in AUD breaks even? (c) Was the outcome in line with UIP if the one-year forward showed AUD at a discount of about 3.8% (the exact CIP figure, close to the 4.0% rate gap)?

Show the solution

Carry = 4.5% − 0.5% = 4.0%.
Approximate return ≈ 4.0% + (−2.0%) = 2.0%.
Exact return = 1.045 × 0.98 − 1.005 = 1.0241 − 1.005 = 0.0191, or about 1.9%.
Break-even fall in AUD ≈ the carry = about 4.0%. The exact CIP-based figure is 1.005 ÷ 1.045 − 1 ≈ −3.8%, so the approximation is close.
UIP implied AUD would fall by about the forward discount, roughly 3.8% to 4.0%. It fell only 2.0%, so AUD depreciated less than the forward implied.
This is one outcome. Forward rate bias is a finding about average results over many periods, so a single observation cannot demonstrate it.

Answer: (a) About 2.0% approximately (1.9% exactly). (b) About 4.0% (about 3.8% exactly). (c) No. The depreciation was smaller than UIP predicted. This single outcome is consistent with the pattern of forward rate bias and gave a profitable carry trade, but it does not demonstrate the bias.

Example 2

An investor funds in USD at 1.0% and invests in MXN at 7.0% for six months. The exchange rate is quoted as USD per MXN: spot 0.0500 at the start and 0.0470 at the end. (a) What is the six-month carry? (b) What is the currency return on MXN in USD terms? (c) What is the approximate total return, what is the exact return, and what does this show about risk?

Show the solution

Six-month carry = (7.0% − 1.0%) × 6/12 = 3.0%.
The quote is USD per MXN, so MXN changed from 0.0500 to 0.0470 USD: 0.0470 ÷ 0.0500 − 1 = −6.0%.
Approximate total return = 3.0% − 6.0% = −3.0%.
Exact return: six-month rates are 3.5% on MXN and 0.5% on USD. (1.035)(0.94) − 1.005 = 0.9729 − 1.005 = −0.0321, or about −3.2%.
The currency loss exceeded the carry, so the trade lost money in USD terms.

Answer: (a) 3.0%. (b) −6.0%. (c) About −3.0% approximately (about −3.2% exactly). A currency fall larger than the carry produces a loss, showing the crash and negative skew risk of carry trades.

Exam tips

Always find the quote convention in the exhibit before computing the currency move. Most wrong answers come from direction errors.
Check whether the question asks for the return in funding-currency terms or investment-currency terms.
For risk questions, pick answers mentioning negative skewness, fat tails, and unwinding in high-volatility periods, not low standard deviation.
If a statement says the forward rate is an unbiased predictor of the future spot rate, that is UIP. Evidence of forward rate bias contradicts it.
Scale annual rates to the holding period. A one-quarter question will not use the full annual differential.

Carry Trade and Forward Rate Bias: frequently asked questions

What is a carry trade in CFA Level II?

It is a strategy that borrows in a low-interest currency and invests in a high-interest currency to earn the interest differential. It profits if the high-yield currency does not depreciate by that differential. It can be done with spot positions or by buying the high-yield currency forward.

What is forward rate bias?

It is the empirical finding that the forward rate is a biased predictor of the future spot rate. High-yield currencies tend to depreciate less than the forward discount implies. This is a failure of uncovered interest rate parity.

Why is the carry trade risky if it earns positive average returns?

Returns are negatively skewed with fat tails. Many small gains can be wiped out by a sudden currency fall, often when market volatility rises and investors unwind leveraged positions together.

How do I calculate carry trade return?

Add the interest differential for the period to the percentage change in the investment currency against the funding currency. Get the sign of the currency move right from the quote convention. The trade breaks even when the currency falls by about the carry.