Suppose I have a function of a varying values represented by randomness. A stock or price of a commodity would be a good example.
What is the average return for that stock on any given interval of prices?
Let average return be defined as the most likely return achieved given two bounds.
I've come up with an initial hypothesis for my average value function.
Let $A$ be the average value.
Let $x_i \in [0,M]$ Where $M$ is the most recent index for a price.
$$A = \sum_{x=0}^M \frac{1}{M} \sum_{y=x}^M \frac{1}{M -y+x} f(x,y) $$
Let $f(x,y)$ be the return using an arbitrary strategy between the intervals $[x,y]$
Is this a good indicator for any return? Does this say more about the stock or commodity or the strategy itself?