From true contribution details we learn that:
1 - “The goal of TC metric is to estimate how much a user’s signal improves or detracts from the returns of Numerai’s portfolio”
This is not correct. TC estimates how much a user’s stake should change so that the user’s signal (which is stake weighted) maximizes the returns of Numerai’s portfolio. In other words, to improve the returns of Numerai’s portfolio the weight (stake) of the user’s signal for that round should be stake+TC.
stake+TC is the signal contribution to that round, not TC alone. This mistake has important consequences if we use TC alone as payout.
By the way, this signal contribution doesn’t express how much a model is good in its predictions. It simply says how much of this signal is required so that combined with the others makes a good portfolio. Maybe the model is bad, but it combines well with the rest.
2 - “With TC as the payout metric, a user’s stake would increase if their model increased portfolio returns and decrease (burn) if the model reduced returns”
This is not correct. With TC as the payout metric, a user’s stake would increase or decrease so that the stake is adjusted until it reaches the optimal value that maximizes Numerai’s portfolio returns. At that point TC will become 0. And when TC is 0 the model contribution to the portfolio will be simply the stake. Interestingly enough, if the stake of a model is already at the optimal value and the user increases the stake ,the next round TC would be the negative value of the stake increase (assuming no other changes take place).
Is there a better payout scheme? Maybe the payout should be proportional to “stake + TC”, the actual signal contribution. If we compute “stake + TC” as percentage of the total tournament stake we have an estimate of a model importance in the portfolio. The payout could be something related to this value, but I have some doubts that would work. The problem is that “stake + TC” express how much the model is required by the portfolio but from the user perspective the stake is how much their want to invest in their model. If a user decides to double their stake what happens to the TC of all the other models?
A possible improvement to the current TC, stake and payout scheme is the following.
TC alone is responsible to define the contribution of a model to the Numerai’s portfolio. Stake is not used anymore in this context. However TC computation has to change: Numerai initially sets the TC of all models to 0 (or any value for that matter), then, at each round, it computes the optimal portfolio using TC as model initial weight. In the next step the gradient is computed and finally TC value is updated with this gradient. So TC at round end is TC of previous round + the gradient (TC[n+1] = TC[n] + gradient). This change in TC calculation makes it a full representation of a model contribution to the Numerai’s portfolio. TC expresses how much Numerai needs a model.
Payout can now be a function of TC, where TC is scaled with respect of the total amount of TCs in the tournament. Oversimplyfing, if Numerai is willing to pay A amount of NMR at each round, the payout could be computed as: Payout = (TC/TotalTournamentTCs) * A
Stake is just there for the user and it’s not part of the reward/punish mechanic. The stake earn/burn mechanic as a “the survive of the fittest” mechanic is interesting, but it is not required anymore: Numerai is already able to quantify what is the optimal model weight required to compute the best portfolio: it’s TC computed as I described above. If TC goes to 0 then a model gets 0 NMR reward, no need to burn NMR (at least not for this purpose, but I can see that a similar mechanic is still needed for the NMR ecosystem. I don’t have an answer for that yet).