The carry of an asset is the return obtained from holding it (if positive), or the cost of holding it (if negative).
For instance, commodities are usually negative carry assets, as they incur storage costs or may suffer from depreciation, but in some circumstances, commodities can be positive carry assets if the market is willing to pay a premium for its demand.
This can also refer to a trade with more than one leg, where you earn the spread between borrowing a low carry asset and lending a high carry one.
Carry trades are not arbitrages: pure arbitrages make money no matter what; carry trades make money only if nothing changes against the carry's favor.
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