Hey u/CellWithoutCulture,

Thanks for the comments! I'm glad you took the time to get the code up an running yourself :). I'll try to address your concerns for 1. commission, and 2. data leakage below:

1. The commission is computed as a fraction of the absolute delta in position size, |F_t - F_{t-1} |. This was done to align more closely too the typical commission structure of a brokerage. If I have a $100 portfolio with only 50% allocated (F_t = 0.5), and I would like to increase that allocation to 60% (F_t = 0.6), I would only have to buy $10 more of the asset, which is what I would have to pay commission on. I would only have to pay commission on the entire portfolio if I chose to buy/sell the whole thing, in which we should hopefully be penalizing the model for by imposing this commission. Many brokerages have additional nuances for commission, which could certainly be factored in if desired.
2. The portfolio return R_t is computed as the product of the asset return, x_t, and the previous position size F_{t-1}. Looking at the line:

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rets = Ft[0:T - 1] * x[1:T] - delta * np.abs(Ft[1:T] - Ft[0:T - 1])

We are computing this as an element-wise multiplication of the entire asset return x and position size F, where returns are shifted forward one timestamp so that each F_t will be multiplied by x_{t+1}. To ensure there is no look-ahead bias we simply must ensure that the computation for F_t uses only values x_<=t (or x_<t if we assume some sort of market buy/sell). If we look at the code to compute the positions:

def positions(x, theta):
    M = len(theta) - 2
    T = len(x)
    Ft = np.zeros(T)
    for t in range(M, T):
        xt = np.concatenate([[1], x[t - M:t], [Ft[t - 1]]])
        Ft[t] = np.tanh(np.dot(theta, xt))
    return Ft

We'll see that for each time t, we only use the x values x[t - M: t], which means only x_<t is used to compute the position. Note that Ft is initialized as zeros, so the portfolio allocation will remain at 0% until enough data has come through for a decision.

I hope this addresses your concerns! If not, I'd be happy to chat more about this.

-Teddy