Katkat
Back

Choose Mean or Median for Trading Profit Metrics

Hudson River TradingSoftware Engineer · Technical Screen
MediumSoftware EngineerTechnical ScreenStatistics & Math

Last updated

This problem tests your understanding of statistical measures of central tendency, specifically how different distributions affect the choice between mean and median in high-frequency trading scenarios.

The Problem

Imagine you are building a monitoring dashboard for a high-frequency trading strategy. The strategy executes thousands of trades daily across various liquid assets. You need to provide a single metric that represents the 'typical' profit per trade for a given asset over the last hour.

Your manager suggests using the arithmetic mean to track performance because it is additive and aligns with total PnL. A junior developer suggests using the median because they are worried that sudden market spikes or 'fat-tail' events (extreme winning or losing trades) are skewing the daily averages.

Task

  1. Explain the statistical trade-offs between using the mean and the median in this context.
  2. Consider a scenario where your trading strategy has a 'stop-loss' mechanism that limits losses to a fixed amount, but profits are uncapped. How does this asymmetry affect the distribution of your profit data?
  3. Propose a metric or a combination of metrics that would give the most actionable feedback to the strategy developers without being misleading.

Guidelines

  • Assume the profit distribution is not necessarily normal.
  • Consider the implications of latency and computational complexity if the data stream is high-volume.
  • Focus on robustness against outliers versus the mathematical property of representativeness.

Hints

Hint 1

Consider the difference between a symmetric distribution and a skewed distribution when evaluating how the mean and median react to extreme values.

Hint 2

Think about the mathematical definition of 'total profit' and whether the median of individual trades relates linearly to the sum of all trades.

Hint 3

Recall that in financial time series, outliers often represent significant market regimes or system errors, which might be important to capture rather than ignore.

Follow-up questions

  • If we use a trimmed mean, how do we decide the optimal percentage of trades to discard from the tails?
  • How would your choice change if the primary purpose of the metric was for an automated risk-control system that triggers a circuit breaker?
  • How does the choice between mean and median change if you are analyzing trade latency (duration) instead of trade profit?