There is a sentence in the schweser material that I do not get;
"Callable bonds give the issuer the option to call back the bond; the investor is short the call option."
When the author states the investor shorts the call option, does he mean when the investors sells the bond to the bondholder. As far as I understand, the option gives the issuer the privilege to buy the bond back which is a long the call option.
Yes, if the issuer exercises the option, the investor has to give back the bond to the issuer in exchange of the principal initially invested. If the investor decides to buy callable bonds then they are short the call option. The investor is short the call option because if the issuer decides to exercise the option, the investor has the obligation to sell back the bond to the issuer at a pre-specified price (interest rate). It is similar to if you are short on an equity call option. When an investor sells an equity call option, they accept the risk that the stock may increase in price. If the stock price does increase, then the issuer of the call option needs to purchase the stock at a higher price (market price) if they are not covered and sell it at a lower price (the strike price of the call option). In this case, the issuer buys a call option from the issuer, so the investor is short the call by definition.