See this two equity curves, they correspond a two investment funds:

And the

DrawDowns:

Both have the same target pattern, but with different risk.

B is more profitable but it's obvious also has more variability of results.

Just looking at the graphs, we can think that A has more quality in terms of the negative part of the results (less variability, less deviation, less DD, etc).

So, will not miss us that applying SQN formula, we get:

(With european notation; "." as the thousands separator and "," as decimal separator.)

SQN(A) = 2,10

SQN(B) = 1,60

Moreover and by other way, we have to know that their expectancies (at this end point of the study interval) are resp.: 0,172 and 0,044.

So, for now, we could say that A is better than B.

At the time of completion this study (recently), they presented this returns:

Return(A, %) = 8,45

Return(B, %) = 13,34

These are instant returns. By the way, and I can speak from experience with them, one could conclude (now supported by the graphs) that when things goes bad, goes bad equally for both. And usually they are able to overcome the DDs and became profitables. In these latter situations, B gives more satisfaction...

So, in this conditions, I thought something was wrong with SQN. Also trying things with other funds I conclude the same; it seems something can be improved.

Perhaps we would want to weight the SQN based formula with something directly related to the return, and avoiding imbalances, also weighting with something relevant to the DDs.

Returns and MaxDD appears in first instance as a possible solution. We would have (with new name):

With this new expression, we have:

System Value (A) = 0,2662

System Value (B) = 0,3144

This result looks better ; B better than A after all said (

**DDs are not so different, but the return is better for B much larger than the DD is worse**).

__But__
this expression has two drawbacks IMO:

* Returns are instantaneous results. They could varies over time hiding a longer term profile, so it would be better something more careful with the longer term returns profile.

* Max DD has some drawbacks for calculation, mainly because when starting running a system, it needs some time to abandon DDs proportionally absurd (all you know). And to avoid this, it needs human considerations because very different views in each case and this makes it very difficult a pure algorithmic treatment (something very important).

So, what can we have better?.

Let's replace the instantaneous return by the slope of the straight line fitting the equity curve.

Also let's replace the Max DD by the area

covered by the DD curve. But, as slope is a 1-dimensional magnitude and an area is 2-dimensional, let's involve it in a square root.

And also, inspired by the idea of

Sortino ratio, as we are primarily interested in the uncertainty at the left of the average result more than at its right side, let's replace the

standard deviation, by other, just considering the "downside risk".

Deviation at "left side":

Where r(sub)i is each result lower than the average, and NDown is the number of them over the total.

Now, with all of this, we have:

or rearranged (as preferred):

In our example, with standard deviation:

System Value (A) = 0,00011536

System Value (B) = 0,00017881

And with downside risk:

System Value (A) = 0,00011133

System Value (B) = 0,00017842

Not so different in this case but could it be cases with more relevant approach.

The following is to do an extensive use of the formula and subject it to criticism (expected to be useful btw). All feedback will be appreciated.

The first possible improvement could be a power factor ten (¿10e5?), to get more friendly values. But the use will say.

From my side it will be embeded in other project, that is to make a selector algorithm for selection of interesting investment funds, from a large database of asset values.