The statement ' when a convertible bond is called, the bondholder must convert the bond or lose the appreciation achieved by the stock ' is false
Bonds are issued by the company as a source of raising capital. There are various types of bonds at can be issued by a company and they include callable bonds, convertible bonds, zero-coupon bonds, discount bonds, etc. They can be issued at par value, at a premium, or at a discount.
When a convertible bond is called by the issuer, it typically means that the company wants to redeem or buy back the bond from the bondholder before its maturity date.
This call provision allows the issuer to repurchase the bond at a specified call price.
However, the bondholder is not obligated to convert the bond into stock when it is called by the issuer.