TRUE. On the initial exercise date, if the call price is low the owner of the put-on-a-call may exercise and sell the call. But then the buyer is short a call option, which has theoretically unlimited loss if the asset price later rises and the long option holder can exercise for a gain on the second date.

By contrast, the other compound option types have limited downside:

• call-on-a-call and call-on-a-put: if exercised, the buyer only ends up with an option.
• put-on-a-put: the loss is limited to the strike price if the asset goes to zero.