You are given an N×T matrix prices where prices[i][t] is the end‑of‑day price of asset i on day t (t = 0…T− 1). Start with total capital C in cash on day 0. For each day t ≥ 1, compute simple returns r_i(t) = prices[i][t]/prices[i][t−1] − 1. If all r_i(t) ≤ 0, hold 100% cash for the next day. Otherwise, set next‑day portfolio weights proportional to the positive returns: w_i(t) = r_i(t) / Σ_{j: r_j(t) > 0} r_j(t) for r_i(t) > 0, and w_i(t) = 0 otherwise. Rebalance at the close of day t using these weights; fractional shares and zero transaction costs are allowed. Let V_t be portfolio value at the close of day t. The daily log return for period t→t+1 is ln(V_{t+1}/V_t). Compute and return [mean_log_return, stddev_log_return] over all T−1 daily log returns.

Simulate return-weighted rebalancing strategy evaluates metric design, causal reasoning, experiment setup, diagnostics, SQL/statistical checks, and recommendations in a realistic interview setting. A strong answer states assumptions, handles edge cases, explains trade-offs, and shows how to validate the result clearly.

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Simulate return-weighted rebalancing strategy

Problem: Momentum-weighted daily log-return statistics

You have N assets with end-of-day prices over T trading days. Let prices[i][t] be the closing price of asset i on day t (i = 0..N−1, t = 0..T−1). You start with total capital C in cash at the close of day 0. Fractional shares and zero transaction costs are allowed.

At each day t ≥ 1:

Compute simple returns r_i(t) = prices[i][t] / prices[i][t−1] − 1.
Set next-day portfolio weights for period t→t+1 as follows:
- If all r_i(t) ≤ 0, hold 100% cash for the next day (i.e., all asset weights are 0).
- Otherwise, assign weights only to assets with positive returns, proportional to those returns: w_i(t) = r_i(t) / Σ_{j: r_j(t) > 0} r_j(t) if r_i(t) > 0; else w_i(t) = 0.
Rebalance at the close of day t using these weights.

Let V_t denote portfolio value at the close of day t. The daily log return for period t→t+1 is ln(V_{t+1}/V_t). Note:

For t = 0, there are no prior-day returns; treat period 0→1 as 100% cash (log return 0).

Task: Compute and return [mean_log_return, stddev_log_return] over all T−1 daily log returns L_t = ln(V_{t+1}/V_t), for t = 0..T−2.

Assume prices are positive. If T < 2, return [0.0, 0.0].

Constraints & Assumptions

Preserve the scope, facts, inputs, and requested outputs from the prompt above.
If the prompt leaves a detail unspecified, state a reasonable assumption before relying on it.
Keep the answer interview-ready: concise enough to present, but concrete enough to implement or evaluate.

Clarifying Questions to Ask

Clarify the business objective, unit of analysis, time window, exposure definition, and primary metric.
State assumptions about instrumentation, randomization, sample size, and data quality.
Separate descriptive analysis from causal claims.

What a Strong Answer Covers

A metric framework with primary, guardrail, and diagnostic metrics.
A credible analysis or experiment design with clear assumptions and bias checks.
SQL/statistical logic for segmentation, variance, confidence, and data validation where relevant.
An actionable recommendation that explains trade-offs and next steps.

Follow-up Questions

What sanity checks would you run before trusting the result?
How would you handle novelty effects, seasonality, or selection bias?
What decision would you make if metrics disagree?