More Return With Less Risk? by Kim Zussman
There are many examples of historically profitable strategies which have LESS risk, if you define risk as volatility. (Of course volatility is not risk if you could know there will be profits after period-X, and know what capitalization it takes to survive to X) Notably various above-moving-averages (see below from prior post):
SP500 daily (1951-p). Using the rules buy at close if at today's close 50DMA>200DMA: sell at close if at today's close 50DMA<200DMA (and stay long while 50DMA>200DMA). Here is comparison of mean daily returns (in market =1, out of market =0):
Two-Sample T-Test and CI: ret, 50>200
Two-sample T for ret
50>200 N Mean StDev SE Mean0 4633 0.0000 0.0121 0.00018 T=-2.15
1 10301 0.00044 0.00832 0.000082
(all positive returns for the period contained in the rule)
And the returns while in-market are significantly less volatile:
Test for Equal Variances: ret versus 50>200
95% Bonferroni confidence intervals for standard deviations
50>200 N Lower StDev Upper
0 4633 0.0118321 0.0121078 0.0123962
1 10301 0.0081929 0.0083209 0.0084528
F-Test (normal distribution)
Test statistic = 2.12, p-value = 0.000
Levene's Test (any continuous distribution)
Test statistic = 388.07, p-value = 0.000