By defining the probability distribution as the historical distribution of one-year returns, you're severely warping the possibility space. Imagine two experime

By defining the probability distribution as the historical distribution of one-year returns, you're severely warping the possibility space. Imagine two experiments: Experiment A: you flip a coin 1000 times. You estimate the probability that the coin flips heads, and use this to estimate the odds of flipping 10 heads in a row. Experiment B: you flip a coin 10 times. You repeat that experiment 100 times. You use the results of that experiment to estimate the odds of flipping 100 heads in a row (by looking at how many times it occurred, and dividing by 100). Assuming reasonable results and a fair coin, you'll conclude from experiment A that the probability of a heads flip is around 50%, and that the odds of getting 10 heads in a row are (1/2)^10. In experiment B, ~90% of the time you'll conclude that it's impossible to flip 10 heads in a row, and ~10% of the time (in the cases where you did flip 10 heads in a row at least once) you'll overestimate the likelihood of doing it again by a factor of 10 (at 1%, instead of the true value, <0.1%). So when you only look at annual returns, you're effectively looking at an aggregate of 365 daily returns (or 365*6.5 hourly returns).