Simulate return-weighted rebalancing strategy
Company: Optiver
Role: Software Engineer
Category: Analytics & Experimentation
Difficulty: medium
Interview Round: Technical Screen
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.
Overview: 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.
Community answers
Answer by Michal Hug
import math
def simulate_return_weighted_rebalancing(prices):
"""
prices[i][t] = closing price of asset i on day t
Returns:
[mean_log_return, stddev_log_return]
"""
if not prices or len(prices[0]) < 2:
return [0.0, 0.0]
N = len(prices)
T = len(prices[0])
# Validate rectangular input
if any(len(row) != T for row in prices):
raise ValueError("prices must be a rectangular matrix")
# Portfolio value at close of day 0
V = 1.0
log_returns = []
# Period 0 -> 1 is 100% cash
log_returns.append(0.0)
# At close of day t, calculate returns from t-1 -> t,
# then apply those weights to the NEXT period t -> t+1.
#
# We only need periods through T-1.
for t in range(1, T - 1):
returns = [
prices[i][t] / prices[i][t - 1] - 1.0
for i in range(N)
]
positive_returns = [r for r in returns if r > 0]
total_positive = sum(positive_returns)
if total_positive > 0:
weights = [
r / total_positive if r > 0 else 0.0
for r in returns
]
else:
weights = [0.0] * N
# Portfolio return during t -> t+1
portfolio_return = sum(
weights[i] * (
prices[i][t + 1] / prices[i][t] - 1.0
)
for i in range(N)
)
V_next = V * (1.0 + portfolio_return)
log_returns.append(math.log(V_next / V))
V = V_next
mean = sum(log_returns) / len(log_returns)
variance = sum(
(x - mean) ** 2 for x in log_returns
) / len(log_returns)
stddev = math.sqrt(variance)
return [mean, stddev]