As I understand, Quantopian's objectives can all be expressed in broad lines of thought. Their prime objective is to maximize their multi-strategy portfolio(s). I view it as a short-term operation like trying to predict some alpha over the short-term (a few weeks) where long-term visibility is greatly reduced and adopt a "we will see what turns out attitude" with a high probability of some long-term uncertainty.

I would prefer that this portfolio optimization problem be viewed as a long-term endeavor where their portfolio(s) will have to contend with the Law of diminishing returns (alpha decay), that the portfolios compensate for it or not. It is a matter of finding whatever trading techniques needed or could be found to sustain the exponential growth of their growing portfolio of strategies.

A trading portfolio can be expressed by its outcome:\(\;\) **Profits** \(\,\) = \(\displaystyle{\int_{t=0}^{t=T}H(t) \cdot dP}\).

The integral of this payoff matrix gives the total profit generated over the trading interval (up to terminal time T) whatever its trading methods and whatever its size or depth. Saying that it will give the proper answer no matter the number of stocks considered and over whatever trading interval no matter how long it might be (read over years and years even if the trading itself might be done daily, weekly, minutely, or whatever).

The strategy \(H_{mine}\) becomes the major concern since \(\Delta P\) is not something you can control, it is just part of the historical record. However, \(H_{mine}\), will fix the price at which the trades are recorded. All those trading prices becoming part of the recorded price matrix \(P\).

You can identify any strategy as \(H_{k}\) for \(k \subset {1, \dots, k} \). And if you want to treat multiple strategies at the same time, you can use the first equation as a 3-dimensional array where \(H_{k}\) is the first axis. Knowing the state of this 3-dimensional payoff matrix is easy: any entry is time-stamped and identified by \(h_{k,d,j}\) thereby giving the quantity held in each traded stock \(j\) within each strategy \(k\) at time \(t\).

How much did a strategy \(H_{k}\) contribute to the overall portfolio is also easy to answer:

\(\quad \quad \displaystyle{w_k = \frac{\int_{0}^{T} H_{k} \cdot dP}{ \int_{t=0}^{t=T}H(t) \cdot dP}}\).

And evidently, since \(H(t)\) is a time function that can be evaluated at any time over its past history the weight of strategy \(w_{k}\) will also vary with time.

Nothing in there says that \(w_{k}\) will be positive. Note that within Quantopian's contest procedures, a non-performing strategy (\(w_{k} < 0 \)) is simply thrown out.

Understandably, each strategy \(H_{k}\) can be unique or some variation on whatever theme. You can force your trading strategy to be whatever you want within the limits of the possible, evidently. But, nonetheless, whatever you want your trading strategy to do, you can make it do it. And that is where your strategy design skills need to shine.

Quantopian can re-order the strategy weights \(w_{k}\) by re-weighing them on whatever criteria they like, just as in the contest with their scoring mechanism and declare these new weights as some alpha generation "factor" with \(\sum_1^k a_k \cdot w_{k}\). And this will hold within their positive strategies contest rules: \( \forall \, w_k > 0\).

Again, under the restriction of \(\, w_k > 0\), they could add leveraging scalers based on other criteria and still have an operational multi-strategy portfolio: \(\sum_1^k l_k \cdot a_k \cdot w_{k}\). The leveraging might have more impact if ordered by their expected weighing and leveraging mechanism: \(\; \mathsf{E} \left [ l_k \cdot a_k \cdot w_{k} \right ] \succ l_{k-1} \cdot a_{k-1} \cdot w_{k-1} \). But, this might require that their own weighing factors \(\, a_k \) offer some predictability. However, I am not the one making that choice having no data on their weighing mechanism.

Naturally, any strategy \(H_{k}\) can use as many internal factors as it wants or needs. It does not change the overall objective which is having \(\, w_k > 0\) to be considered not only in the contest but to have it high enough in the rankings to be considered for an allocation.

Evidently, Quantopian can add any criteria it wants to its list including operational restrictions like market-neutrality or whatever. These become added conditions where strategy \(H_{k}\) needs to comply with, otherwise, again it might not be considered for an allocation.

The allocation is the real prize, the contest reward tokens should be viewed as such, a small for "waiting" reward for the best 10 strategies in the rankings: \( H_{k=1, \dots, 10}\,\) out of the \( H_{k=1 \, , \dots, \, \approx 300}\) participating.