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 over some period (usually a year) by the standard deviation of returns for that exact period. You can also interpret it in p-value language: if the S&P 500 has a (yearly) Sharpe Ratio of 0.25, that corresponds to a p-value of 0.4 if we assume that everything is distributed normally 1 - NORM.DIST(0.25,0,1,1) = 0.4. This can be interpreted to mean that a leveraged portfolio of the risk-free asset (which has a Sharpe Ratio of 0) has a 40% chance of outperforming the S&P 500 in a given year. The p-values in finance are low (because the markets are pretty efficient), but the math is the same.

And if you think something is wrong with the math, I encourage you to discuss the math without talking about my "misinformed imagination".