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What is Carry Trade?
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.
Currency Carry Trade:
A carry trade where you borrow and pay interest in order to buy something else that has higher interest. For currencies, it might be that you borrow in Yen (where the interest rate might be low) and use the proceeds to purchase U.S. dollar long term debt. While the trade might produce a positive return, it is risky in two dimensions. First, U.S. rates could increase diminishing the value of the bond you purchased. Second, the exchange rate could take an unfavorable move effectively increasing your borrowing costs.