Converting from ProPhoto in Photoshop

ProPhoto's negative primaries [ Link ]

ProPhoto uses PCS of XYZ and its primaries have a* and b* values exceeding  the range  -128 to 127.  When converting color in Photoshop, color out of this Lab gamut  space would be cripped to the defined limits.



White Point for ProPhoto
Red: 0.797668, 0.288040, 0.000000
                   [Lab 60.608273, 139.168888, 104.497022]
Green: 0.135193, 0.711884, 0.000000
                   [Lab 87.576439, -186.694184, 150.993860]
Blue: 0.031342, 0.000092, 0.824905  
                   [Lab 0.082699, 90.249204, -172.271644]



ProPhoto colorants

Lack of appropriate Gamut Mapping

Example:

XYZ ( 16.010934 0.663729 138.946202 )
= Lab ( 5.995 180.014 -200.008 )
-->  Lab ( 5.995 127 -128) = aRGB ( 6.425 -67.615 207.751 )
-->  aRGB ( 6.425 0 207.751 )

see  [ link ]