CTA Statistical & Quantitative Methods 2 — Questions and Answers
Question 1: How does an Exponential Moving Average (EMA) differ most significantly from a Simple Moving Average (SMA)?
- The EMA applies equal weight to all data points in the calculation period
- The EMA requires significantly more historical data points to calculate
- The EMA gives progressively greater weight to more recent price data (Correct answer)
- The EMA is only calculated using opening rather than closing prices
Correct answer: The EMA gives progressively greater weight to more recent price data
An EMA applies exponentially greater weights to more recent prices, making it more responsive to recent price changes than an equally-weighted SMA.
Question 2: In hypothesis testing for trading system validation, what does a p-value of 0.05 indicate?
- The trading results have a 95% probability of being due to chance
- There is a 5% probability the results occurred by chance, indicating statistical significance (Correct answer)
- The system will generate a 5% annual return in the future
- The strategy data contains significant autocorrelation at the 5% level
Correct answer: There is a 5% probability the results occurred by chance, indicating statistical significance
A p-value of 0.05 means there is only a 5% probability the observed results occurred by chance, indicating the results are statistically significant at the 5% level.
Question 3: What does the Sharpe Ratio specifically measure in trading strategy evaluation?
- The total cumulative return generated by a portfolio
- The maximum peak-to-trough drawdown of a trading strategy
- The portfolio's correlation to its designated benchmark index
- The excess return earned per unit of total risk (standard deviation) (Correct answer)
Correct answer: The excess return earned per unit of total risk (standard deviation)
The Sharpe Ratio measures the excess return above the risk-free rate per unit of standard deviation, providing a risk-adjusted performance metric for comparing strategies.
Question 4: What does the Coefficient of Variation (CV) measure in financial analysis?
- The relative variability of returns expressed as a percentage of the mean return (Correct answer)
- The absolute level of portfolio risk in dollar terms
- The statistical correlation between two different asset classes
- The rate of change in implied volatility over time
Correct answer: The relative variability of returns expressed as a percentage of the mean return
The Coefficient of Variation expresses standard deviation as a percentage of the mean, enabling meaningful comparison of risk across securities with different price levels.
Question 5: What is 'overfitting' in the context of developing a technical trading system?
- Optimizing a model so precisely to historical data that it captures noise rather than true patterns, reducing future predictive power (Correct answer)
- Allocating positions across too many uncorrelated asset classes in a single portfolio
- Setting initial stop-loss levels too close to entry prices relative to market volatility
- Simultaneously applying an excessive number of technical indicators to a single price chart
Correct answer: Optimizing a model so precisely to historical data that it captures noise rather than true patterns, reducing future predictive power
Overfitting (curve-fitting) occurs when a trading model is calibrated too precisely to historical data, capturing random noise instead of genuine patterns and causing poor out-of-sample performance.
Question 6: In a linear regression channel applied to a price chart, what do the outer channel lines represent?
- Fibonacci retracement levels calculated from the regression trendline
- Price boundaries set at a specified number of standard deviations above and below the regression line (Correct answer)
- The average true range of price movement over the regression period
- Moving average crossover levels relative to the regression midline
Correct answer: Price boundaries set at a specified number of standard deviations above and below the regression line
A linear regression channel draws parallel lines at a specified standard deviation distance above and below the central regression line, creating statistically-derived price boundaries.
Question 7: What is the primary limitation of backtesting a technical trading strategy on historical data?
- Historical price data cannot be analyzed using standard statistical methods
- Historical data is generally insufficient in length to provide any meaningful results
- Past performance does not guarantee future results as market conditions and regimes change over time (Correct answer)
- Moving average calculations cannot be accurately applied to historical price data
Correct answer: Past performance does not guarantee future results as market conditions and regimes change over time
While backtesting evaluates historical performance, changing market conditions and structural shifts mean past performance does not reliably predict future results.
CTA Statistical & Quantitative Methods 2
How does an Exponential Moving Average (EMA) differ most significantly from a Simple Moving Average (SMA)?