QFC Quantitative Finance Algorithmic Trading & Data Science 3 — Questions and Answers
Question 1: What does the Hurst exponent measure in financial time series analysis?
- The degree of mean reversion or trend persistence in a time series (Correct answer)
- The rate of volatility clustering in returns
- The tail heaviness of the return distribution
- The optimal lag for autocorrelation analysis
Correct answer: The degree of mean reversion or trend persistence in a time series
A Hurst exponent H > 0.5 indicates trending (persistent) behavior, H < 0.5 indicates mean reversion, and H = 0.5 indicates a random walk.
Question 2: Which regularization technique in linear regression is most appropriate when many predictors are expected to have zero effect on the target variable?
- Ridge (L2) regularization
- Lasso (L1) regularization (Correct answer)
- Elastic net regularization
- Principal component regression
Correct answer: Lasso (L1) regularization
Lasso (L1) regularization produces sparse solutions by driving irrelevant coefficients exactly to zero, making it ideal for feature selection.
Question 3: In market microstructure, what does the 'adverse selection' component of the bid-ask spread represent?
- The broker's compensation for providing liquidity
- The market maker's compensation for inventory risk
- The cost of trading with better-informed counterparties (Correct answer)
- The exchange fee charged per transaction
Correct answer: The cost of trading with better-informed counterparties
Adverse selection cost reflects the risk that the market maker's counterparty possesses private information, leading to losses on subsequent price moves.
Question 4: What is the 'volatility smile' in options markets and what does it imply about the Black-Scholes model?
- Implied volatility is highest for at-the-money options, implying BS overprices them
- Implied volatility varies with strike price, implying the lognormal return assumption is violated (Correct answer)
- Historical volatility is always lower than implied volatility, implying a volatility risk premium
- Realized volatility smiles are consistent with Black-Scholes assumptions
Correct answer: Implied volatility varies with strike price, implying the lognormal return assumption is violated
The volatility smile shows that implied volatilities differ across strikes, indicating that real return distributions have fat tails and/or skewness not captured by the lognormal model.
Question 5: Which gradient boosting hyperparameter most directly controls the bias-variance trade-off in financial prediction models?
- Number of estimators (n_estimators)
- Learning rate (shrinkage)
- Maximum tree depth (Correct answer)
- Subsample fraction
Correct answer: Maximum tree depth
Maximum tree depth controls model complexity directly — shallow trees (low depth) give high bias/low variance, while deep trees give low bias/high variance.
Question 6: In the Almgren-Chriss framework for optimal execution, what is the fundamental trade-off being optimized?
- Alpha decay versus transaction costs
- Market impact costs versus timing risk from price uncertainty (Correct answer)
- Bid-ask spread versus order size
- Short-term momentum versus mean reversion
Correct answer: Market impact costs versus timing risk from price uncertainty
Almgren-Chriss optimizes a mean-variance objective balancing the cost of market impact (execute fast) against the risk of adverse price moves while waiting (execute slowly).
Question 7: What is 'survivorship bias' in the context of evaluating quantitative trading strategy performance?
- Including only the best-performing months in performance reporting
- Building a dataset from currently existing securities, omitting those that were delisted or went bankrupt (Correct answer)
- Overfitting to the most recent market regime
- Using a benchmark that only includes top-performing assets
Correct answer: Building a dataset from currently existing securities, omitting those that were delisted or went bankrupt
Survivorship bias inflates backtested returns because failed or delisted stocks are excluded, making historical strategy performance appear better than it was.
QFC Quantitative Finance Algorithmic Trading & Data Science 3
What does the Hurst exponent measure in financial time series analysis?