Note that beta is benchmarked to SPY. I tested between 2002-2020 and found a negative sharpe ratio for all six. The returns are pretty abysmal. The inverse returns (high-beta/high-vol) were pretty reasonable, as one could imagine.
There's so much academic research on this anomaly but as far as I can tell, it was never done on a L/S dollar neutral portfolio, only long only.
What I was expected to find was a higher Sharpe ratio for the low-vol/low-beta portfolio and when levered up to the same beta or vol level, higher absolute returns. I have found nothing of the sort, and am a little disturbed.