Callable bond
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A callable bond is a bond that can be called (redeemed) by the issuer prior to its maturity, on certain call dates, at the call price. In other words, on the call dates, the issuer has the right, but not the obligation, to buy back the bonds from the bond holders at the call price. Technically speaking, the bonds are not really bought and held by the issuer, but cancelled immediately.
Call price will usually exceed the par or issue price. In certain cases, mainly in the high-yield debt market, there can be a substantial premium. See there for more details.
The issuer has an option, for which he pays in the form of a higher coupon rate. If interest rates in the market have gone down at the time of the call date, the issuer will be able to refinance his debt at a cheaper level, so will call the bonds. Another way to look at it is that as interest rates have gone down, the price of the bond has gone up. Therefore, it is advantageous to buy the bonds back at the par. What this means exactly is that a callable bond will always be sold at the highest price but to the most prominent bidder. The issue regarding the bond will almost always result in detrimental circumstances for the parties involved in the merger or acquistion of the bond.
The investor has the benefit of a higher coupon than he would have had with a bullet (non-callable) bond. On the other hand, if interest rates go down, the bonds get called, and he can only invest at the lower rate. This is comparable to selling an option—you get a premium upfront, but you have downside if the option gets exercised.
The largest market for callable bonds is that of issues from the government sponsored entitites, better know as U.S. Agencies. They own a lot of mortgages and mortgage-backed securities. In the U.S. mortgages are usually fixed rate, and can be prepaid early without cost, contrary to other countries. If rates go down, a lot of home owners will refinance at a lower rate. This means that the Agencies lose assets. By issuing a large number of callable bonds, they have a natural hedge, as they can then call their own issues and refinance at a lower rate.