QFC Quantitative Finance Algorithmic Trading & Data Science 2 — Questions and Answers
Question 1: In pairs trading, what statistical condition must hold between two assets for the strategy to be theoretically sound?
- The assets must have identical volatility
- The asset price series must be cointegrated (Correct answer)
- The assets must belong to the same sector
- The correlation coefficient must exceed 0.9
Correct answer: The asset price series must be cointegrated
Cointegration ensures a stable long-run relationship between asset prices, meaning deviations from equilibrium are mean-reverting.
Question 2: Which order type is most commonly used in algorithmic trading to avoid market impact when executing large orders?
- Market orders
- Stop-loss orders
- TWAP or VWAP sliced child orders (Correct answer)
- Limit orders at the ask price
Correct answer: TWAP or VWAP sliced child orders
TWAP/VWAP algorithms slice large parent orders into smaller child orders over time to minimize market impact and tracking error.
Question 3: What does the Sharpe ratio measure in the context of a trading strategy?
- Total return relative to benchmark
- Risk-adjusted return per unit of total volatility (Correct answer)
- Maximum drawdown relative to average return
- Return per unit of downside deviation
Correct answer: Risk-adjusted return per unit of total volatility
The Sharpe ratio is calculated as (portfolio return - risk-free rate) / standard deviation of excess returns.
Question 4: In the context of high-frequency trading (HFT), what is 'latency arbitrage'?
- Exploiting price differences across geographically distant exchanges using fiber optic cables
- Using faster data feeds to trade ahead of slower market participants acting on stale prices (Correct answer)
- Arbitraging the bid-ask spread on illiquid securities
- Taking advantage of delayed settlement times between asset classes
Correct answer: Using faster data feeds to trade ahead of slower market participants acting on stale prices
Latency arbitrage involves HFT firms using speed advantages to detect and trade before slower participants can update their orders.
Question 5: Which machine learning technique is best suited for predicting a continuous financial variable like next-day stock returns?
- K-nearest neighbors classification
- Random forest regression (Correct answer)
- Naive Bayes classifier
- Support vector machine with RBF kernel for classification
Correct answer: Random forest regression
Random forest regression is an ensemble method well-suited for continuous output prediction with non-linear feature relationships common in financial data.
Question 6: What is the primary purpose of applying a Kalman filter in algorithmic trading?
- To detect regime changes in volatility
- To recursively estimate latent state variables from noisy observations (Correct answer)
- To calculate optimal portfolio weights under transaction costs
- To backtest trading signals on historical data
Correct answer: To recursively estimate latent state variables from noisy observations
The Kalman filter provides optimal recursive estimates of hidden state variables (e.g., dynamic hedge ratios) by combining model predictions with noisy measurements.
Question 7: In backtesting, what is 'look-ahead bias' and why is it problematic?
- Using too short a historical window for parameter estimation
- Incorporating future information into historical signal calculations, inflating apparent performance (Correct answer)
- Overfitting model parameters to the training set
- Ignoring transaction costs in performance calculations
Correct answer: Incorporating future information into historical signal calculations, inflating apparent performance
Look-ahead bias occurs when a backtest uses data that would not have been available at the time of the trade, producing unrealistically optimistic results.
QFC Quantitative Finance Algorithmic Trading & Data Science 2
In pairs trading, what statistical condition must hold between two assets for the strategy to be theoretically sound?