My question might be a well-known problem, or already discussed in this forum, but I don't know what keyword to search for, so I leave a question in here. Sorry if it is duplicated.
So, let me explain the problem with an example,
Suppose that I have a group of models which predict the future's market price in stock trading, and want to select the best model that has the highest sharpe ratio in backtesting, simulation on the past data frames.
Thus, I decide to divide the past trade periods by month, and get N trade periods.
Then, the problem is, finding the model that has 'great' sharpe ratio on all N trade periods.
The easiest way to select the best model is to find the average sharpe ratio per month. However, if the selected best model by averaging has the incredibly high sharpe ratio on single month and bad on other periods, I want to say that it is not the 'optimal' solution.
Suppose that N=2, then I can draw a Cartesian coordinate of x-axis: sharpe ratio on a trade period, and y-axis: sharpe ratio on the other trade period. Then, what I want to do is to find the point that is close to the line, y=x, and also, far from the (0,0). Obviously, there are some points that are indistinguishable from what is better by Pareto optimality. But, let's assume that the only points that are k distances away from y=x are indistinguishable.
Then, how can I find the 'optimal' points for N trade periods?
In fact, I'm bad at mathematical formulation, so there would be unclear sentences, or definitions, feel free to leave comments.
Thanks!
