You may as well analyse the skewness and kurtosis of the period of time PnL by having 3rd and 4th times of $Y_t$ respectively. Presumably you are going to conclude that for 2 collection with equivalent expectation and variance, you'll like the 1 with beneficial skew or reduced kurtosis, but https://andresnjydi.mybjjblog.com/how-much-you-need-to-expect-you-ll-pay-for-a-good-pnl-46790935