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For the bond market, this refers to a trade where you borrow and pay interest in order to buy something else that has higher interest. For example, with a positively sloped term structure (short rates lower than long rates), one might borrow at low short term rates and finance the purchase of long-term bonds. The carry return is the coupon on the bonds minus the interest costs of the short-term borrowing. Of course, if long-term interest rates unexpectedly rose(and long-term bond prices fell as a result), the carry trade could become unprofitable. Indeed, if this occured, there could be a number of investors trying to unwind the carry trade, which would involve selling the long-term bonds. It is possible that this could exacerbate the increase in long-term interest rates, i.e. push the rates even higher. For currency, you buy the currency that has the highest local short term interest rate. For more information on currency, see: Currency Carry Trade.
A trade of a security or a derivative where settlement occurs on the same trading day. This is fairly unusual; most contracts are settled between one and three days later. Generally speaking, cash contracts are most common in the last week of the calendar year when many trades must be settled sooner to guarantee tax advantages for one or both parties. It is also called a cash trade.