Optiver·Software Engineer·Technical Phone Screen·Intermediate

Intermediate

Jul 2026

Summary

Optiver software engineer interview with a pretty dense quant-flavored coding problem. The kind of question where you think you understand it and then realize halfway through that the rebalancing logic is trickier than it looks.

Questions Asked (1)

You're given an N by T price matrix for multiple assets. Starting with some cash capital, compute daily simple returns, then for each day allocate portfolio weights proportional to positive returns only (zero weight for non-positive). If all returns are negative or zero, hold full cash. Rebalance daily with no transaction costs and fractional shares allowed. Return the mean and standard deviation of the daily log returns over the full period.

Algorithms & Data StructuresTechnical Trade-offs

Author's notes

The math description sounds clean on paper but actually implementing it correctly is another thing.

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AI HintsAI Generated

Suggested Approach

First, clarify the problem inputs and outputs, then outline the algorithm step-by-step: compute daily simple returns, determine weights based on positive returns, simulate portfolio value, and calculate log returns. Finally, discuss implementation details, edge cases, and complexity.

Pro tip: Emphasize the importance of handling edge cases like all returns being non-positive and ensuring numerical stability when computing log returns. Also, mention that you would validate the solution with a small example to catch off-by-one errors.

1. Clarify the problem

Confirm the input format (N assets, T days), starting capital, and that returns are computed from prices. Ask if the price matrix includes the initial day or only subsequent days.

2. Compute daily simple returns

For each asset and day (from day 1 to T-1), calculate the simple return as (price_t / price_{t-1}) - 1. Store these in a matrix of size N x (T-1).

3. Determine portfolio weights

For each day, consider only assets with positive returns. Allocate weights proportional to these positive returns, ensuring they sum to 1. If no positive returns, set all weights to 0 (hold cash).

4. Simulate portfolio value and compute log returns

Starting with initial capital, for each day compute the portfolio return as the weighted sum of asset returns. Update the portfolio value. Then compute the daily log return as ln(1 + portfolio_return).

5. Calculate mean and standard deviation

Compute the mean and standard deviation of the daily log returns over the full period. Use appropriate formulas (e.g., sample standard deviation) and discuss any assumptions.

Key Points to Mention

Handling of non-positive returns: zero weight and cash holding when all returns are non-positive.
Proportional weighting: weights sum to 1 and are based only on positive returns.
Daily rebalancing: portfolio is rebalanced each day, so weights are recalculated daily.
Log return calculation: use ln(1 + simple return) for each day.
Edge cases: first day has no previous price, so returns start from day 2; all returns non-positive; zero returns.
Complexity: O(N*T) time and space for storing returns and weights.

AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.