When an entity completes the construction or development of a self-constructed investment property that will be carried at fair value, the TRUE statement regarding the accounting treatment is as follows:

Any difference between the fair value of the property at the completion date and its previous carrying amount shall be recognized in profit or loss.

Upon completion of the construction or development, if the self-constructed investment property meets the criteria to be classified as investment property and will be subsequently measured at fair value, the difference between the fair value of the property at the completion date and its previous carrying amount (costs incurred during construction) should be recognized in profit or loss. This is in accordance with IAS 40 Investment Property, which specifies that when investment property is held for rental or capital appreciation, it should be measured at fair value through profit or loss. Therefore, upon transition to investment property, any such difference would be recognized in profit or loss.