Chapter 0: Introduction
Question 1: Course Focus
What is the primary focus of Statistics of Financial Markets (SFM)?
Correct! SFM focuses on applying statistical methods to model and analyze financial market data.
Incorrect. The correct answer is C. SFM focuses on statistical modeling and analysis of financial data.
Question 2: Financial Data
Which type of data is most commonly analyzed in SFM?
Correct! SFM primarily works with financial time series such as prices, returns, and volatility data.
Incorrect. The correct answer is C. Financial markets generate high-frequency price and return data that is the focus of SFM.
Question 3: SFM vs Classical Statistics
What distinguishes SFM from classical statistics?
Correct! Financial data has unique characteristics like heavy tails, volatility clustering, and serial dependence that require specialized methods.
Incorrect. The correct answer is B. Financial data exhibits heavy tails, volatility clustering, and temporal dependence.
Question 4: Software Tools
Which software tool is primarily used in this course for data analysis?
Correct! Python is the primary programming language used for statistical analysis and data visualization in this course.
Incorrect. The correct answer is C. Python is the primary tool used in this course.
Question 5: Assessment
What is the assessment structure for this course?
Correct! The assessment is 70% final exam, 20% project, and 10% attendance/participation.
Incorrect. The correct answer is C. The assessment is 70% exam, 20% project, 10% attendance.
Question 6: Stylized Facts
What is a "stylized fact" of financial returns?
Correct! Heavy tails and volatility clustering are well-established stylized facts of financial return distributions.
Incorrect. The correct answer is C. Heavy tails and volatility clustering are key stylized facts.
Question 7: Course Topics
Which of the following is NOT a topic covered in SFM?
Correct! Double-entry bookkeeping is an accounting concept, not a topic in SFM.
Incorrect. The correct answer is C. Double-entry bookkeeping is not part of the SFM curriculum.
Question 8: Quantlets
What is the main purpose of a Quantlet in this course?
Correct! Quantlets are reusable, documented code snippets that implement specific statistical or computational procedures.
Incorrect. The correct answer is B. A Quantlet is a reusable, documented code snippet for statistical analysis.
Question 9: Heavy Tails
What does "heavy tails" mean in the context of financial returns?
Correct! Heavy tails mean that extreme events (large gains or losses) occur more often than the normal distribution would predict.
Incorrect. The correct answer is B. Heavy tails indicate more frequent extreme returns than predicted by the normal distribution.
Question 10: Academic Field
Which academic field combines statistics, finance, and programming as in SFM?
Correct! Quantitative finance and financial econometrics combine statistical methods, financial theory, and computational tools.
Incorrect. The correct answer is B. Quantitative finance / financial econometrics is the field that integrates these disciplines.
Chapter 1: Data Sources & Returns
Question 1: Simple Return
What is the formula for simple (net) return $R_t$?
Correct! The simple return is $R_t = (P_t - P_{t-1}) / P_{t-1}$, measuring the percentage change in price.
Incorrect. The correct answer is C. $R_t = (P_t - P_{t-1}) / P_{t-1}$.
Question 2: Log Return
What is the formula for log (continuously compounded) return $r_t$?
Correct! The log return is $r_t = \ln(P_t / P_{t-1})$, also known as the continuously compounded return.
Incorrect. The correct answer is B. $r_t = \ln(P_t / P_{t-1})$.
Question 3: Variance Drag
What is "variance drag" in the context of returns?
Correct! Variance drag means the geometric mean is lower than the arithmetic mean by approximately $\sigma^2/2$, eroding compounded wealth.
Incorrect. The correct answer is B. Variance drag is the gap between arithmetic and geometric mean returns ($\approx \sigma^2/2$).
Question 4: Log Returns Advantage
Why are log returns preferred for statistical modeling?
Correct! Log returns are time-additive ($r_{1:T} = \sum r_t$) and better approximated by the normal distribution than simple returns.
Incorrect. The correct answer is B. Log returns are additive over time and closer to normality.
Question 5: ADF Test
What does the Augmented Dickey-Fuller (ADF) test assess?
Correct! The ADF test has $H_0$: unit root (non-stationary) vs $H_1$: stationary.
Incorrect. The correct answer is B. The ADF test checks for a unit root, indicating non-stationarity.
Question 6: Jarque-Bera Test
What does the Jarque-Bera test evaluate?
Correct! The Jarque-Bera test checks normality by testing whether skewness $= 0$ and excess kurtosis $= 0$.
Incorrect. The correct answer is B. Jarque-Bera tests normality using skewness and kurtosis.
Question 7: Parkinson Estimator
Which volatility estimator uses the high-low price range?
Correct! The Parkinson (1980) estimator uses the daily high-low range: $\sigma^2_P = \frac{1}{4n\ln 2}\sum (\ln H_i - \ln L_i)^2$.
Incorrect. The correct answer is B. The Parkinson estimator uses high-low price ranges.
Question 8: Sharpe Ratio
What does a Sharpe ratio measure?
Correct! The Sharpe ratio is $S = (\bar{r} - r_f) / \sigma$, measuring risk-adjusted return.
Incorrect. The correct answer is B. The Sharpe ratio measures excess return per unit of risk.
Question 9: OHLC Data
What does OHLC data represent?
Correct! OHLC stands for Open, High, Low, Close — the four key prices recorded each trading period.
Incorrect. The correct answer is B. OHLC = Open, High, Low, Close prices per period.
Question 10: Leverage Effect
What is the "leverage effect" in financial markets?
Correct! The leverage effect describes the asymmetric response of volatility to negative vs. positive returns.
Incorrect. The correct answer is B. The leverage effect means negative returns increase volatility more than positive returns.
Chapter 2: Statistical Distributions for Financial Markets
Question 1: Normal Distribution
Which property makes the Normal distribution closed under addition (i.e., the sum of two independent normals is also normal)?
Correct! The Normal distribution is stable under addition: the sum of independent normal random variables is again normal, with parameters that add linearly.
Incorrect. The correct answer is B. The stability (additivity) property ensures that sums of independent normals remain normal.
Question 2: Stylized Facts
Which of the following is NOT a commonly observed stylized fact of financial return distributions?
Correct! Financial returns consistently deviate from normality. They exhibit fat tails, volatility clustering, and negative skewness — the Normal distribution fails to capture these features.
Incorrect. The correct answer is D. Returns do NOT follow a symmetric Normal distribution — this contradicts the well-documented stylized facts.
Question 3: Student-t Distribution
When fitting a Student-t distribution to daily equity returns, the estimated degrees of freedom typically fall in which range?
Correct! Empirical studies consistently find $\nu \approx 3$–$8$ for daily stock returns, indicating substantial tail heaviness while still having a finite variance ($\nu > 2$).
Incorrect. The correct answer is B. Daily equity returns typically yield $\nu \in [3, 8]$, capturing the fat-tail phenomenon.
Question 4: Skewed Student-t
What additional feature does the skewed Student-t distribution (Hansen, 1994) capture compared to the symmetric Student-t?
Correct! The skewed Student-t adds a skewness parameter $\lambda$, allowing the left tail (losses) to be heavier than the right tail (gains), matching the empirical asymmetry in equity returns.
Incorrect. The correct answer is B. The skewed Student-t captures the negative skewness commonly observed in equity return distributions.
Question 5: Stable Distributions
For a stable distribution with stability index $\alpha < 2$, which statement about moments is correct?
Correct! For $\alpha < 2$: $E[|X|^p] < \infty$ only when $p < \alpha$. The mean exists if $\alpha > 1$, but the variance is always infinite.
Incorrect. The correct answer is B. The variance is infinite for $\alpha < 2$; only fractional moments of order less than $\alpha$ exist.
Question 6: Extreme Value Theory
In the Peaks Over Threshold (POT) approach to EVT, which distribution is used to model exceedances above a high threshold?
Correct! The Pickands–Balkema–de Haan theorem shows that exceedances above a sufficiently high threshold follow a Generalized Pareto Distribution (GPD).
Incorrect. The correct answer is C. The GPD is the natural limit distribution for threshold exceedances in EVT. (GEV is used in the block maxima approach.)
Question 7: Model Selection
The Akaike Information Criterion (AIC) is defined as $\text{AIC} = -2 \ln L + 2k$. How should it be used for model selection?
Correct! Lower AIC indicates a better trade-off between goodness of fit ($-2 \ln L$) and model complexity ($2k$). Unlike likelihood ratio tests, AIC works for non-nested models too.
Incorrect. The correct answer is B. The model with the lowest AIC provides the best balance of fit quality and parsimony.
Question 8: Expected Shortfall vs VaR
What is the key advantage of Expected Shortfall (ES) over Value-at-Risk (VaR) as a risk measure?
Correct! ES (also called CVaR) is a coherent risk measure: it satisfies subadditivity ($\text{ES}(A+B) \leq \text{ES}(A) + \text{ES}(B)$), ensuring that portfolio diversification reduces measured risk. VaR can violate this property.
Incorrect. The correct answer is B. ES is coherent and satisfies subadditivity, unlike VaR which can penalize diversification.
Question 9: Basel Backtesting
Under the Basel framework, a bank uses 99% VaR over 250 trading days. How many exceedances are expected, and what is the “green zone” threshold?
Correct! At 99% confidence over 250 days, the expected number of exceedances is $250 \times 0.01 = 2.5$. The Basel traffic light test classifies: green (<5), yellow (5–9), red ($\geq$10).
Incorrect. The correct answer is B. Expected exceedances = 2.5, and the green zone requires fewer than 5 exceedances.
Question 10: GARCH-t Model
What does the GARCH(1,1)-t model capture that a simple Student-t distribution cannot?
Correct! GARCH(1,1)-t combines two features: the GARCH structure captures volatility clustering (time-varying $\sigma_t^2$), while Student-t innovations provide excess kurtosis even in the standardized residuals.
Incorrect. The correct answer is C. GARCH-t jointly models volatility clustering and fat tails through its conditional variance dynamics and t-distributed innovations.
