Optimization criteria: integral of "underwater"
Can we have an optimization criteria that penalties the integral of the min(equity curve, balance) that is below the max balance of the test?
Replies 5
Sure.
variant 1) w=sum(d_i) where d_i is an equity measure that is lower than max balance up to the time i
then the optimization criteria is something like total_gain/w
Note: Measurements ABOVE the max balance up to time sample i are ignored and are not part of the sum.
variant 2 (generates smoother equity curved)
w=sum(r_i) where r_i is the measurement that is below the *fitted line* from the start to the last equity.
Note: Measurements ABOVE the fitted line are ignored and are not part of the sum.
the penalty can then also be total_gain/w
consider also gain/(1+w) just in case w is zero.
or gain/ln(2+w)
let me know if I can clarify more
Sure.
variant 1) w=sum(d_i) where d_i is an equity measure that is lower than max balance up to the time i
then the optimization criteria is something like total_gain/w
Note: Measurements ABOVE the max balance up to time sample i are ignored and are not part of the sum.
variant 2 (generates smoother equity curved)
w=sum(r_i) where r_i is the measurement that is below the *fitted line* from the start to the last equity.
Note: Measurements ABOVE the fitted line are ignored and are not part of the sum.
the penalty can then also be total_gain/w
consider also gain/(1+w) just in case w is zero.
or gain/ln(2+w)
let me know if I can clarify more
Something similar to R-squared, but ignoring the up-side, right?
Or do you want to take only one d_i after each new balance maximum?
Why to analyze balance and not a previous equity maximum?
Can you make some draft in Excel (better on Google Drive) so we can discuss it with real example?
Good question: I indeed use the equity and not balance (just checked my code).
Balance would eventually be better, because it would not penalize times when equity is higher than the balance.
Have a look at this code. It expects an array of ALL equity sample points from the whole backtest (so I track these somewhere else)
Good question: I indeed use the equity and not balance (just checked my code).
Balance would eventually be better, because it would not penalize times when equity is higher than the balance.
Have a look at this code. It expects an array of ALL equity sample points from the whole backtest (so I track these somewhere else)
I have similar code to collect equity values.
What's the next step? How to calculate integral of "underwater" given the array of equity values?
Interesting idea! Do you have formula for this?