All ACES Output transforms are more complex than simply a transform to the display space with a transfer function. They include s-shaped tone-mapping which expands the mid-tone contrast and compresses the highlights and shadows. The intent of this is to create a perceptual match between the scene in front of a camera (which may have bright highlights above 1.0 in relative linear exposure) and a display with a limited dynamic range which will be viewed in a different environment to the original scene.
Since there is no official Adobe RGB Output Transform, you would have to create one and add it to your OCIO config. Or use an Output Transform for a wide gamut SDR display space such as BT.2020, followed by a transform from that to Adobe RGB (1998).