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Analytics & Experimentation questions require understanding of core concepts and practice. PracHub provides solutions with explanations to help you master analytics & experimentation interviews.

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This is a medium difficulty Analytics & Experimentation question, commonly asked during Technical Screen rounds at Optiver.

What role is this question designed for?

This question is commonly asked for Software Engineer candidates at Optiver during technical interviews.

Simulate return-weighted rebalancing strategy

Quick Overview

This question evaluates competency in quantitative portfolio analytics within the Analytics & Experimentation category, focusing on time-series manipulation, numerical computation of log-returns, and implementation of a momentum-weighted daily rebalancing strategy under edge conditions.

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].

Quick Overview

Problem: Momentum-weighted daily log-return statistics

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].

Simulate return-weighted rebalancing strategy

Quick Overview

Problem: Momentum-weighted daily log-return statistics

Solution

Comments (0)

Simulate return-weighted rebalancing strategy

Quick Overview

Problem: Momentum-weighted daily log-return statistics

Solution

Comments (0)