This is a linkpost for http://putanumonit.com/2017/01/29/significantly-invested/
That's a very confused post.
Let's start with the obvious -- the Sharpe ratio is not a test statistic (and does not lead to a p-value). To observe this note that the calculation of a test statistic involves a very important input -- the number of observations. Your denominator is not volatility, it's volatility divided by the square root of n. The Sharpe value does not care about the number of observations at all. So statements like
Each (arbitrary and useless) p-value cutoff corresponds to a test statistic cutoff which translates to a Sharpe Ratio cutoff above which an investment strategy is “significant” enough to brag about in front of a finance professor
are just figments of your misinformed imagination. In reality, having a strategy with a Sharpe of, say, 1 is very very good (the Sharpe ratio of the S&P500 this century is somewhere around 0.25).
In general, people in finance don't care about the p<0.05 (even when it's statistically "valid") because that threshold assumes a stable and unchanging underlying process which in the financial markets is very much not the case.
A test statistic involves dividing some measurement by the standard deviation of that same measurement.
When you calculate a p-value for a number of observations, you commonly take the average result and the standard deviation of the average, which equals the standard deviation of a single measurement divided by the square root of n. You can also calculate a test statistic and a p-value for a single observation, in which case you have just one result and one standard deviation.
This is what you do when calculating the Sharpe Ratio: you divide excess return...