^{6} Merton, Robert, C., On Estimating the Expected Return on the Market: An Exploratory Investigation, Journal of Financial Economics 8 (1980) 323-361. See appendix A, pages 355-357. To see why you can’t get around this inconvenient truth, note that in continuous time, the number of years of observation, using the annual Sharpe Ratio (SR) as an input is 2*(1.645/SR)^2, where 1.645 is the 95% cumulative probability level in a Normal distribution. If we sample more frequently, f times per year, the required number of periods goes to 2*(1.645/(SR/sqrt(f)))^2 = 2f*(1.645/SR)^2. So, we'll need to observe f times as many periods as when we look annually, which is exactly how many more periods we get to observe by breaking the year into f intervals.

^{7} A comprehensive list of these would be long, and would include publication bias, base-rate bias, pervasive data 'snooping,' survivorship bias, non-normal distributions, out-of-the-money option selling, mean-reversion and benchmark mis-specification, to name a few.

^{8} Paraphrased from Harvey, Liu, Zhu, '……and the Cross-Section of Expected Returns,' (2015), on

SSRN,

*'Hundreds of papers and hundreds of factors attempt to explain the cross-section of expected returns. Given this extensive data mining, it does not make any economic or statistical sense to use the usual significance criteria for a newly discovered factor, e.g., a t-ratio greater than 2.0. [95% confidence]. …A newly discovered factor needs to clear a much higher hurdle, with a t-ratio greater than 3.0 [99.7% confidence]. Echoing a recent disturbing conclusion in the medical literature, we argue that most claimed research findings in financial economics are likely false.'*
^{9} See our Elm paper on return-chasing

here. Return Chasing results in the well-documented phenomenon of investor (aka dollar-weighted) returns being significantly lower than fund (aka time-weighted) returns. See Morningstar's 'Mind the Gap' notes and Dalbar's annual investor behaviour reports.

^{10} See

'The Most Important Number You Won't Find in the WSJ' for more discussion about driving your portfolio with eyes open and forward looking.