You might find this response from Ted Smith of interest in response to just the opposite question: Why Is There A Loss Of Volume With DSD Files?
tedsmithChief digital dude
There isn’t - in fact DSD allows for more volume than PCM in that it can go above 0dBFS (0 dB full scale) and as we know PCM is unforgiving when music tries to go above full scale.
Some DSD material is mastered with less compression than the PCM releases. Comparing multiple SACDs which have a CD layer that matches the DSD layer is a way around this (tho not all SACDs with CD layers have the CD layer derived from the DSD layers.)
There also might be something like a volume setting somewhere in your chain that’s affecting PCM but not DSD. You might try running the Bit Perfect test to see if something is affecting the PCM’s levels. (See http://www.psaudio.com/ps_how/how-to-run-a-bit-perfect-test-with-directstream/ in the Support/How To’s part of the web site.)
You also might be accidentally converting DSD to PCM in your transport/player software - in order to deal with DSD that’s louder than 0dBFS often there is a setting for how much to lower the volume level to avoid clipping as it’s converted to PCM. Verify that when you play DSD that the display on the DS indicates DSD (or DoP.)