Carry

Carry is the most unifying idea in cross-asset systematic trading: it defines an expected return that can be measured for any asset from prices alone, before making a single forecast. Koijen, Moskowitz, Pedersen, and Vrugt's insight was that the FX carry trade, the bond roll-down, and commodity backwardation are all the same strategy, buy high-carry, sell low-carry, and that this simple mechanical signal earns a premium across every asset class.

The general definition

Carry is the return an asset earns if its price stays unchanged. Formally, decompose an asset's expected return into carry plus expected price appreciation:

$\underbrace{\mathbb{E}[r_{t+1}]}_{\text{expected return}} = \underbrace{C_t}_{\text{carry}} + \underbrace{\mathbb{E}[\Delta \text{price}]}_{\text{expected appreciation}}.$

Carry $C_t$ is observable today, it is a mechanical function of current prices (spot vs. forward, yield, roll). Expected appreciation is unobservable and requires a forecast. The carry trade bets that the unobservable part averages to roughly zero, so realized returns track the observable carry, equivalently, that markets do not fully offset high carry with anticipated adverse price moves. Whenever that offset fails to fully materialize, carry earns a premium.

Carry across asset classes

The power of the framework is that one formula specializes to each market:

• FX. For a currency with local rate $r^*$ against home rate $r$, holding it via a forward, covered interest parity gives forward $F = S\,\frac{1+r}{1+r^*}$, so

$C^{\text{FX}}_t \approx r^* - r = \text{the interest-rate differential} = \frac{S_t - F_t}{F_t}.$

You earn the forward discount, high-rate currencies have positive carry. Efficient-markets theory (uncovered interest parity, UIP) says high rates should be offset by expected depreciation, so carry should earn nothing. UIP fails badly in the data, the "forward premium puzzle", and that failure is the FX carry premium.

• Fixed income / rates. Carry is the yield plus the roll-down: if the yield curve is upward-sloping and static, a bond ages into lower yields and gains price. $C^{\text{bond}} \approx y_t + \text{roll-down} - r_f$, capturing term-premium harvesting.

• Commodities. Carry is the negative of the roll return between futures. In backwardation (spot above futures) you roll into cheaper contracts and earn positive carry; in contango you pay. $C^{\text{cmdty}}_t \approx \frac{F_{\text{near}} - F_{\text{far}}}{F_{\text{far}}}$. This is the commodity roll yield.

• Equities. Carry is the expected dividend (or futures basis) yield net of financing.

In every case, high carry = "the market is paying you to hold this," and the cross-asset carry factor goes long the high-carry assets and short the low-carry ones.

Carry as a risk premium

Why would a purely mechanical signal earn money? Because carry loads on a specific, nasty risk: carry trades earn small, steady gains punctuated by large crashes. Their return distribution is negatively skewed, "picking up nickels in front of a steamroller." Brunnermeier, Nagel, and Pedersen showed FX carry crashes coincide with spikes in volatility and funding illiquidity (VIX up, funding markets seize), unwinding violently as leveraged carry positions are liquidated together. Lustig, Roussanov, and Verdelhan identified a common "global" risk factor priced in the carry cross-section.

So carry is compensation for bearing crash and liquidity risk, you are the insurance seller. This explains three empirical regularities at once: the premium is positive on average (insurance pays), returns are negatively skewed (occasional large claims), and drawdowns cluster in crises (Regime Detection matters enormously). It also explains why carry and Trend Following are natural complements: trend is long convexity and tends to profit in the same crises where carry crashes, so a carry-plus-trend book smooths the tail.

Worked example: FX carry

You go long AUD (rate 4%) and short JPY (rate 0%), a classic carry pair. Your carry is $C \approx 4\% - 0\% = 4\%$/year, earned as long as AUD/JPY does not fall. Suppose over a year AUD/JPY is flat: you pocket the 4%. Now a risk-off shock hits; leveraged carry books unwind, AUD/JPY drops 15% in weeks. Your year is $4\% - 15\% = -11\%$, a loss many times your average monthly gain. This asymmetry, years of +4% then one year of −11%, is the signature of the carry premium and the reason raw Sharpe overstates its attractiveness once you account for skew.

Failure modes

• Negative skew and crash risk. The defining flaw: Sharpe ratios look great until the tail event, which is precisely when your investors and lenders pull capital. Sizing on volatility alone under-prices this, you must budget for the crash.
• Funding and crowding. Carry is a leveraged, crowded trade; when funding tightens everyone unwinds at once, turning a diversifiable position into a systemic one.
• Regime dependence. Carry thrives in calm, low-volatility regimes and dies in risk-off; conditioning on volatility or overlaying trend materially improves it.
• Carry ≠ free lunch. High carry often signals genuine risk (a currency with 30% rates is not a gift). Distinguishing compensated carry from a value-trap-style impairment is the real skill, linking carry to The Value Factor thinking.

In interviews

Define carry as the return if prices don't move, and show you can specialize it: FX carry = interest-rate differential / forward discount, bond carry = yield + roll-down, commodity carry = backwardation/roll yield. The conceptual question is "why does carry make money?", because UIP and its analogs fail, and carry is a risk premium for negatively-skewed crash and funding-liquidity risk; you are selling disaster insurance. Strong candidates note the diversification with trend-following (trend is long the tail carry is short) and warn that volatility-based sizing understates carry's true risk because the danger lives in the skew, not the variance. See Factor Investing for how carry sits among the other cross-asset premia.