I have 4 different investing schemes. I’m changing universal parameters, back testing, and evaluating the average returns of these 4 schemes.
Unfortunately the “average” performance doesn’t treat each scheme equally because the existing returns are not equal. If one scheme is doing 50% and the others are in the 10% area, changes in the parameters become dominated by the leading scheme and the lesser scheme's progress gets ignored.
I need an index of the 4 that measures each scheme's progress equally. A 40% increase in any scheme should produce a 10% increase in this index regardless of how far that scheme is ahead of or behind the others.
The average performance would be important for investing. For tuning the system however, I need to see how universal parameter changes affect each scheme and I need a fair index to evaluate and to decide whether to keep these changes or discard them. Is there a formula or a function for such an index?
Thanks much, roofman6
If $b_1,b_2,b_3,b_4$ are the scheme's performances before a change and $a_1,a_2,a_3,a_4$ are their performances after a change, then the percentage change in scheme $i$ is $a_i/b_i-1$. So your overall index's increase can be the sum of these, which is $$ \frac{a_1}{b_1}+\frac{a_2}{b_2}+\frac{a_3}{b_3}+\frac{a_4}{b_4}-4. $$ Alternatively, you can compute the product $$ \frac{a_1}{b_1}\frac{a_2}{b_2}\frac{a_3}{b_3}\frac{a_4}{b_4}; $$ an answer of $1$ is the neutral response, and anything larger indicates progress on average.