ETF5952 · Quantitative Methods for Risk Analysis

What ETF5952 covers

Ten chapters, one risk-analysis workflow. Each links to its free chapter guide, and the closed-book ETF5952 final (around June in the Monash Semester-1 exam period — confirm the date on Moodle) can draw a compute-and-interpret question from any of them, from Value-at-Risk and Expected Shortfall to GARCH volatility, backtesting and option pricing.

How ETF5952 is assessed

One-day parametric Value-at-Risk, as a return and in dollars

Key terms

Random variable vs realisation

A random variable (capital letters such as R_t or P_t) is the uncertain quantity before the outcome is known; a realisation (lowercase r_t, p_t) is a specific observed value. Risk analysis models the distribution of the random variable, then uses observed realisations to estimate it.

Log return

The continuously compounded return r_t = ln(P_t/P_t−1). Log returns are additive across time (a k-period log return is the sum of the one-period log returns), which is why the unit uses them for multi-period risk; simple returns are not additive.

Value-at-Risk (VaR)

The loss you expect to exceed only with probability p over a horizon, reported as a positive magnitude: VaR(p) = −q_p, where q_p is the p-quantile of the return distribution. For a small p the quantile is a negative return, so VaR comes out positive.

Expected Shortfall (ES)

The average loss given that the loss is in the worst-p tail: ES(p) = −E[R | R ≤ q_p]. ES is the mean beyond the VaR threshold, so ES(p) ≥ VaR(p) always, and it is the measure behind the Basel market-risk capital charge (2.5% ES).

Quantile

The value q_p a return falls below with probability p: F(q_p) = p, i.e. q_p = F⁻¹(p). A smaller p means a deeper tail, so q_0.01 < q_0.05 and the 1% VaR is larger than the 5% VaR.

Historical simulation

A non-parametric estimate that uses the empirical distribution of past returns: sort the observed returns and read the VaR off the ⌈pT⌉-th worst; ES is the average of that tail. It makes no distributional assumption but assumes the past window represents the future.

Monte Carlo simulation

Draw many returns from an assumed (or estimated) distribution, convert each to a portfolio value, and average the quantity of interest — e.g. expected utility or a tail loss. Used when no closed-form expression exists; simulate returns first, then map to wealth.

EWMA (RiskMetrics)

Exponentially Weighted Moving Average volatility: σ_t² = (1−λ)(R_t−1−μ)² + λσ_t−1², with the RiskMetrics daily default λ = 0.94. Weights decay geometrically; it is a GARCH with ω = 0 and no long-run anchor.

GARCH(1,1)

A volatility model σ_t² = ω + α(R_t−1−μ)² + βσ_t−1² that captures volatility clustering. If α+β < 1 it has a finite long-run variance σ̄² = ω/(1−α−β); α+β is the persistence.

Leverage effect / GJR-GARCH

The tendency of negative shocks to raise volatility more than equal positive shocks. GJR-GARCH adds an asymmetry term γ(R_t−1−μ)²·1{R_t−1 < μ}; γ > 0 confirms the leverage effect.

Square-root-of-time rule

Under constant (flat) volatility, h-period volatility scales as σ_h = √h·σ — variance scales with h, volatility with √h. It is only exact for i.i.d. or EWMA volatility, not for mean-reverting GARCH.

Certainty equivalent & risk premium

The certainty equivalent x_CE solves U(x_CE) = E[U(X)] — the guaranteed wealth as good as the gamble. The risk premium π = E[X] − x_CE; a risk-averse (concave-utility) investor has x_CE < E[X] and π > 0.

Arrow–Pratt risk aversion

The coefficient of absolute risk aversion A(w) = −U″(w)/U′(w). The minus sign is essential: for a risk-averse investor U″ < 0 and U′ > 0, so A(w) > 0. Concave utility is the defining feature of risk aversion.

VaR backtesting (coverage test)

An out-of-sample check that a VaR model has the right violation rate. A violation is r_t < −VaR_t(p); the unconditional-coverage (Kupiec) test compares the observed rate to p. Too many violations (π̂ > p) means the model underestimates risk.

ETF5952 FAQ

How to study for the exam

Treat ETF5952 as a compute-and-interpret unit: for every topic, learn the formula with its correct sign and quantile, work one clean number, then say what it means for the risk. The highest-yield core is the VaR/ES chain (parametric, historical-simulation and conditional) and the volatility models (EWMA, GARCH(1,1) and its long-run variance, GJR asymmetry), because they recur through backtesting and multi-period scaling. Drill the square-root-of-time rule (volatility × √h, variance × h) and the coverage-test direction (too many violations ⇒ risk underestimated) until they are automatic. Use the weekly Moodle quizzes to stay current, and treat Assignment 2 as your realistic exam rehearsal since it is written in the style of the final. In SWOTVAC, sit the free mock exam to time — budgeting minutes in proportion to marks, because the exam length is not published — then redo only what you missed. The exam is closed book, so rehearse the formulae from memory, and ask Sia to explain any step you cannot yet do by hand. Because ETF5952 Quantitative Methods for Risk Analysis is examined by Monash University with a single closed-book final that ranges across the whole syllabus, the surest revision is breadth with accuracy — one clean worked number per topic beats deep notes on any one.

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