ETF5952 Quantitative Methods for Risk Analysis
The Complete Exam Bible · S1 2027ETF5952 Overview
- Monash University
- S1 2027
- 10 chapters
- Statistics
ETF5952 Quantitative Methods for Risk Analysis is Monash University’s postgraduate financial-risk unit, run by the Department of Econometrics and Business Statistics and taught in R.
- Assessed by In-class Quizzes (best 10 of 12, weekly online) 10% + 4 more
- Key terms Random variable vs realisation, Log return, Value-at-Risk (VaR), Expected Shortfall (ES)
- How to prepare
Treat ETF5952 as a compute-and-interpret unit: for every topic, learn the formula with its correct sign and quantile…
- Most asked Where can I find past exam papers or practice for ETF5952?
How ETF5952 is assessed
| Component | Weight | Format |
|---|---|---|
| In-class Quizzes (best 10 of 12, weekly online) | 10% | Individual online quiz, weekly Fri 23:55 |
| Assignment 1 (Exercise) — group answer sheet 50% + individual oral Q&A 50% | 10% | Group + Individual oral |
| Assignment 2 (Exercise) — individual written answer sheet, exam-style at-home | 15% | Individual written |
| Assignment 3 (Project) — group report (<=4pp PDF) 50% + individual oral Q&A 50% | 25% | Group + Individual oral |
| Final Examination | 40% | Centrally scheduled, invigilated, closed book, individual |
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.
Risk, Uncertainty and Random Variables
States of the world, random variables vs realizations, pmf/pdf/CDF, moments (mean, variance, skewness, kurtosis), sample estimators, prices and returns as random variablesThis is the opening topic of ETF5952 Quantitative Methods for Risk Analysis at Monash University, and it lays the probability foundation the rest of the unit is built on.
- Risk vs uncertainty - risk is uncertainty you can describe with probabilities; the unit models risk as a random variable
- States of the world - the future lands in one of several states, each with a probability; a random variable assigns a number to each
- Random variable X vs realisation x - capital letters are the (random) model of the future, lowercase are the observed data
- pmf, pdf and CDF - discrete mass p(x)=Pr(X=x), continuous density with Pr(a≤X<b) as area, and F(x)=Pr(X≤x)
- Mean and variance - μ=E[X] locates the distribution; Var(X)=E[(X-μ)²] and volatility σ measure its spread
- Skewness and kurtosis - the 3rd and 4th moments: negative skew = heavier downside tail, kurtosis > 3 = fatter-than-normal tails
Utility Theory and Decision-Making Under Risk
Expected utility, Jensen's inequality, concave=risk-averse, certainty equivalent, risk premium, Arrow-Pratt absolute risk aversionIn ETF5952 Quantitative Methods for Risk Analysis at Monash University, this chapter is the bridge from describing risk to acting on it: how a rational investor turns a whole distribution of returns into a single ranked choice.
- Expected utility E[U(X)] = Σ pᵢ U(xᵢ): score a gamble by the average utility of its outcomes, then pick the highest
- Utility is ordinal: a positive-affine rescaling Ũ = aU + b (a > 0) leaves the ranking unchanged, and a sure payoff y has E[U(y)] = U(y)
- Jensen's inequality: U concave ⇒ U(E[X]) ≥ E[U(X)]; U convex ⇒ U(E[X]) ≤ E[U(X)]
- Risk attitude ⇔ curvature: risk-averse = concave = U''< 0; risk-neutral = linear = U''= 0; risk-loving = convex = U''> 0
- Certainty equivalent x_CE: the sure wealth with the same utility as the gamble, U(x_CE) = E[U(X)]
- Risk premium π = E[X] − x_CE: positive for a risk-averse investor (x_CE < E[X]), zero if risk-neutral, negative if risk-loving
Financial Risk and Returns
Simple vs log returns, log-return additivity, return frequencies and time aggregation, i.i.d. assumptionThis is the measurement layer of ETF5952 Quantitative Methods for Risk Analysis at Monash University: the topic that turns a price series into the returns on which every later risk measure is computed.
- Simple vs log return - simple R_t = (P_t - P_{t-1})/P_{t-1}; log r_t = ln(P_t/P_{t-1}); both are dimensionless fractions of the base price
- Gross return and the link - gross return = P_t/P_{t-1} = 1 + R_t, so r_t = ln(1 + R_t) and R_t = e^(r_t) - 1: two encodings of one price move
- Log returns are always ≤ simple returns - they agree for small moves and diverge as moves grow (a gain: r < R; a loss: |r| > |R|)
- Rebuilding the price - roll forward with P_{t+1} = P_t(1 + R_{t+1}) or P_{t+1} = P_t·e^(r_{t+1})
- Log-return additivity - the k-period log return is the SUM of the one-period log returns; simple returns instead COMPOUND (multiply the gross returns)
- Return frequencies - returns are measured daily, weekly, monthly or annually, and must be aggregated to move between frequencies
Estimating Return Distributions: Monte Carlo, Parametric and Non-parametric
Monte Carlo simulation for expected utility, parametric distribution models, empirical distribution, normal and Student-tThis chapter of Monash University's ETF5952 Quantitative Methods for Risk Analysis tackles the problem underneath every risk number: the next return RT+1 is drawn from an unknown distribution F, and expected utility, VaR and Expected Shortfall are all expectations under F.
- The estimation problem: R_{T+1} ~ unknown F, and every risk measure is an expectation under F
- Three routes to F: Monte Carlo simulation, parametric (Normal / Student-t), non-parametric (empirical)
- Monte Carlo for expected utility: draw N returns, convert to wealth, average U, choose the higher E[U]
- Simulate returns then map to wealth: P = P_T(1+r) for simple returns, P = P_T·e^r for log returns
- Parametric location-scale model: R = μ + σZ, quantile q_p = μ + σ z_p, VaR(p) = −(μ + σ z_p)
- Normal quantiles z_0.05 = −1.645, z_0.01 = −2.326; the 1% VaR always exceeds the 5% VaR
Downside Risk Measures: Value-at-Risk and Expected Shortfall
Quantiles, VaR definition VaR(p)=-q_p, parametric/historical-simulation/bootstrap VaR, Expected Shortfall, ES>=VaRThis chapter of Monash University's ETF5952 Quantitative Methods for Risk Analysis quantifies downside risk with the two measures the unit builds the rest of the course on: Value-at-Risk (VaR) and Expected Shortfall (ES).
- Quantiles of the return distribution: q_p = F⁻¹(p), with small p giving a negative (bad) return
- The VaR definition VaR(p) = −q_p, read as a positive loss magnitude
- Parametric VaR in location-scale form: −(μ + σ z_p), with z_0.05 = −1.645, z_0.01 = −2.326
- Student-t (fat-tailed) VaR: fatter tails give a larger VaR than the normal for the same μ, σ
- Historical-simulation VaR: the ⌈pT⌉-th worst sorted return, negated (round pT up)
- Bootstrap VaR: resample returns with replacement, take the p-quantile, negate
Conditional Mean, Volatility and Time-Varying Risk
Information set, conditional distribution/mean/variance, rolling-window volatility, conditional VaR and ES, historical simulationThis is the time-varying-risk core of ETF5952 Quantitative Methods for Risk Analysis at Monash University: the topic that stops treating risk as a fixed number and makes it move with the market.
- Information set - I_t = {r_1,...,r_t} collects everything known at time t and GROWS over time; every conditional quantity is an expectation given I_t
- Conditional vs unconditional distribution - the unconditional distribution averages over all time; the conditional distribution F_{t+1|t} uses today's state, so it widens in a storm
- Conditional mean, variance, volatility - E_t(R_{t+1}), Var_t(R_{t+1}) and σ_{t+1|t} = √Var_t; the mean is ~flat while the variance moves
- Volatility clustering - large moves bunch with large, calm with calm; the return model R_t = μ + σ_t Z_t puts all the time-variation in σ_t
- Rolling-window (moving-average) volatility - σ-hat²_{t+1|t} = (1/m)Σ(r_{t-i} - μ-hat)²; short m is reactive, long m is smooth
- Conditional quantile and VaR - q_p solves Pr(R_{t+1} ≤ q_p | I_t) = p, and VaR(p) = -q_p is a positive loss; normal case VaR = -(μ + σ z_p)
Volatility Models: EWMA, GARCH and GJR-GARCH
Volatility clustering, EWMA (RiskMetrics lambda=0.94), GARCH(1,1) long-run variance, leverage effect, GJR-GARCH asymmetryIn ETF5952 Quantitative Methods for Risk Analysis at Monash University, this chapter models the conditional variance σt2 = Var(Rt | It−1) — the fact that the size of return swings changes over time and clusters.
- Volatility clustering: time-varying conditional variance vs a roughly constant conditional mean
- The constant-mean return model R_t = μ + σ_t Z_t and the squared mean-adjusted shock
- Rolling-window (moving-average) volatility: equal weights, sharp cut-off, short vs long window
- EWMA: recursive form σ_t² = (1−λ)(R_{t−1}−μ)² + λ σ_{t−1}², geometric weights, no cut-off
- The RiskMetrics rule λ = 0.94 for daily data (set, not estimated)
- GARCH(1,1): ω, α (reaction), β (persistence); stationarity α + β < 1
Multi-Period Risk and the Square-Root-of-Time Rule
Return aggregation, h-period mean and variance, square-root-of-time volatility scaling, GARCH multi-step forecastsThis topic from ETF5952 Quantitative Methods for Risk Analysis at Monash University answers the practical question every risk figure eventually faces: a volatility, Value-at-Risk or Expected Shortfall estimated over one day has to be reported over a longer horizon h — a 10-day capital figure, a monthly forecast.
- Return aggregation - because log returns add across time, the h-period return is the sum of the one-period log returns, R(t+h,h) = Σ R(t+j)
- h-period mean - under a constant conditional mean the expectation of the sum is μ(h) = hμ, so the mean scales linearly with the horizon
- h-period variance - for conditionally uncorrelated returns the variance of the sum is the sum of the one-step variances (covariance terms vanish)
- Square-root-of-time rule - if every one-step variance equals a constant σ², the h-period variance is hσ² and the volatility is √h × σ
- Variance scales with h, volatility with √h - the single most common slip is scaling volatility (or VaR) linearly in h
- Scaling a VaR - scale μ by h and σ by √h, then recompute VaR; scaling VaR directly by √h is exact only when the drift is zero
Model Risk and VaR Backtesting
Misspecification vs estimation risk, AIC/BIC, estimation windows, hit sequence, unconditional/independence/conditional coverage tests, Kupiec, Basel ESThis topic sits near the end of ETF5952 Quantitative Methods for Risk Analysis at Monash University, where the unit turns from building risk models to trusting them.
- Model risk - the risk the model itself misleads; it splits into misspecification and estimation risk
- Misspecification risk - the wrong structure (e.g. a Normal model for fat-tailed returns); a bias more data cannot cure
- Estimation risk - the right structure but imprecise parameters from a finite sample; shrinks as T grows
- AIC and BIC - penalised-likelihood criteria; choose the SMALLEST; BIC penalises complexity more so favours simpler models
- Estimation windows - fixed, recursive (expanding) and rolling schemes for re-estimating parameters out-of-sample
- Hit sequence - the 0/1 record where a hit is a return worse than the forecast VaR; expected hits = T₀·p
Option Pricing and Option Risk
Call/put payoffs, one-period binomial no-arbitrage, hedge ratio, risk-neutral valuation, lognormal prices, Black-Scholes call/put, comparative staticsThis chapter of Monash University's ETF5952 Quantitative Methods for Risk Analysis is the derivatives capstone: it turns the return-distribution machinery of the earlier weeks into an option price and a hedge.
- European payoffs at maturity: call C_T = max{S_T − K, 0}, put P_T = max{K − S_T, 0}, floored at zero
- One-period binomial, no-arbitrage: two states s_u, s_d and a risk-free rate r_f
- Hedge ratio (delta): x = (C_u − C_d) / (s_u − s_d), the shares that make the portfolio risk-free
- Risk-neutral probability q = (S₀ e^{r_f} − s_d)/(s_u − s_d) and price c₀ = e^{−r_f}[q C_u + (1−q) C_d]
- Replication and risk-neutral valuation give the SAME no-arbitrage price
- Lognormal prices: ln(S_{t+τ}/S_t) ~ N(τμ, τσ²), with the mean correction E[S] = S_t e^{τμ + ½τσ²}
In ETF5952 you learn to characterise risk using probability and statistics, then quantify it with Value-at-Risk (VaR) and Expected Shortfall (ES), and to implement and evaluate risk models — historical and Monte-Carlo simulation, EWMA and GARCH volatility models, and VaR backtesting and stress testing — before extending to option pricing and option risk.
Assessment at Monash University combines weekly Moodle quizzes and three R-based assignments (10% + 15% + 25%) with a 40% closed-book final examination in the Semester-1 central exam period (around June; confirm the exact date on Moodle).
This free guide maps every ETF5952 topic to its exam thread so your SWOTVAC revision goes straight to the marks that build your WAM — work each risk measure by hand, and ask Sia to explain any step you get stuck on.
Worked example · free
One-day parametric Value-at-Risk, as a return and in dollars
- +1Write the parametric VaR formula. In location-scale form R = μ + σZ, the p-quantile is qp = μ + σzp, so the loss magnitude is VaR(p) = −qp = −(μ + σzp).
- +15% VaR: VaR(0.05) = −(0.0004 + 0.018·(−1.645)) = −(0.0004 − 0.029610) = 0.02921, i.e. 2.921%.
- +1Convert to dollars: 0.02921 × $500,000 = $14,605 — the 1-day loss you expect to exceed only 5% of the time.
- +11% VaR: with z0.01 = −2.326, VaR(0.01) = −(0.0004 + 0.018·(−2.326)) = 0.04147, i.e. 4.147% → 0.04147 × $500,000 = $20,734.
- +1Compare and read it: the 1% VaR ($20,734) exceeds the 5% VaR ($14,605) because the 1% quantile sits further into the left tail. VaR is reported as a positive loss, and the deeper tail always gives the larger number.
Key terms
- Random variable vs realisation
- A random variable (capital letters such as Rt or Pt) is the uncertain quantity before the outcome is known; a realisation (lowercase rt, pt) 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 rt = ln(Pt/Pt−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) = −qp, where qp 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 ≤ qp]. 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 qp a return falls below with probability p: F(qp) = p, i.e. qp = F−1(p). A smaller p means a deeper tail, so q0.01 < q0.05 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: σt² = (1−λ)(Rt−1−μ)² + λσt−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 σt² = ω + α(Rt−1−μ)² + βσt−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(Rt−1−μ)²·1{Rt−1 < μ}; γ > 0 confirms the leverage effect.
- Square-root-of-time rule
- Under constant (flat) volatility, h-period volatility scales as σh = √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 xCE solves U(xCE) = E[U(X)] — the guaranteed wealth as good as the gamble. The risk premium π = E[X] − xCE; a risk-averse (concave-utility) investor has xCE < 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 rt < −VaRt(p); the unconditional-coverage (Kupiec) test compares the observed rate to p. Too many violations (π̂ > p) means the model underestimates risk.
ETF5952 FAQ
Can AI help me study ETF5952?
Yes — used well, AI is a strong study partner for a technical unit like ETF5952. Sia can walk you through a VaR or Expected Shortfall calculation step by step, explain why a GARCH model mean-reverts while EWMA does not, check your reasoning on a backtesting question, or re-derive a worked example with different numbers so you can practise.
It explains the method and the intuition rather than handing you final answers, so you build the skill the closed-book exam actually tests. Always follow Monash University’s assessment and academic-integrity rules on Moodle — use AI to learn, not to complete assessed work for you.
Where can I find past exam papers or practice for ETF5952?
Official past papers, when released, live in the Monash University Library exam database and on the ETF5952 Moodle page; your best in-unit preview is Assignment 2, which is written “in the style of the final examination.” This free guide adds a full mock exam of re-authored, worked problems that mirror the exam’s compute-and-interpret style — VaR and ES, EWMA/GARCH volatility, square-root-of-time scaling, backtesting and option pricing — without copying any real paper.
You can also ask Sia to generate fresh practice questions on any topic and explain each step.
What can Sia do that a textbook can't?
A textbook explains one method one way; Sia adapts to your exact question. Paste a VaR sum you got wrong and it will find the slip — a flipped sign, the wrong quantile, or variance scaled by h instead of volatility by √h — and explain the fix.
It can re-explain the same idea at a different level, generate new numerical examples, connect utility theory to the risk premium, or turn a formula into a plain-English risk statement. It works through problems with you step by step; it will not sit your exam or guarantee a grade.
Is ETF5952 hard?
It is demanding but predictable. ETF5952 Quantitative Methods for Risk Analysis is a postgraduate quantitative unit at Monash University that layers probability, statistics and financial econometrics, and it is taught in R — but no prior programming is assumed. Most of the difficulty is precision: getting the sign, the quantile and the time-scaling right under exam pressure.
Because the exam is compute-and-interpret across a defined syllabus, steady weekly practice on the worked methods (VaR/ES, EWMA/GARCH, backtesting, options) makes it very manageable.
Is the ETF5952 exam open or closed book?
The final examination is closed book. It is worth 40%, individual, invigilated and centrally scheduled in the Monash Semester-1 exam period, so you need the VaR/ES definitions, the EWMA and GARCH recursions, the square-root-of-time rule and the option formulae in your head.
The exam duration is not stated in the unit materials, so plan your time in proportion to the marks and confirm the exact date, time and length on Moodle / the Monash exam timetable.
Is there a hurdle in ETF5952?
The unit information states the final examination has no hurdle, and no component-level hurdle is stated for the quizzes or assignments. Standard Monash University practice is that you need an aggregate pass overall, so treat any minimum-mark rule as “confirm on Moodle” — the authoritative source is your current ETF5952 unit guide.
What's examined in ETF5952?
The final covers the whole unit (Learning Outcomes 1–4): describing risk with random variables and moments, utility theory and risk aversion, simple vs log returns, estimating return distributions by simulation and parametric/non-parametric methods, Value-at-Risk and Expected Shortfall, conditional and time-varying volatility (EWMA, GARCH, GJR-GARCH), multi-period risk and the square-root-of-time rule, model risk and VaR backtesting, and option pricing and option risk.
Assignment 2 previews the style; confirm the current scope on Moodle.
Questions students ask in each ETF5952 chapter
- What is the difference between a random variable and its realisation, and why does it matter?
- A random variable (written with a capital letter, like R for a return) is the model of an uncertain future quantity: it has a whole distribution of possible values with probabilities, and therefore an expectation and a variance. A realisation (lowercase, like the return you actually observed yesterday) is the single number it turned out to be, with no distribution of its own. It matters because risk - variance, expected loss, VaR - is a property of the random variable, which you then estimate from a sample of past realisations. Speaking of 'the variance of yesterday's return' mixes the two up and is a common exam error. Chapter 01 · Risk, Uncertainty and Random Variables
- Why do investors maximise expected utility instead of expected wealth?
- Because expected wealth ignores attitude to risk. A risk-averse investor feels a loss more than an equal gain (diminishing marginal utility), so a fair gamble can have positive expected wealth yet negative expected utility. Ranking by E[U(X)] captures that trade-off: it is why such an investor can rationally prefer a sure 102 to a risky project with an expected 104. Rank on utility, then read off the certainty equivalent and risk premium to see how much the risk costs. Chapter 02 · Utility Theory and Decision-Making Under Risk
- What is the difference between a simple return and a log return, and when should I use each?
- A simple (net) return R_t = (P_t - P_{t-1})/P_{t-1} is the ordinary percentage price change and is the natural way to describe the return on a portfolio at a single point in time or across assets held together. A log return r_t = ln(P_t/P_{t-1}) = ln(1 + R_t) is the continuously compounded version and is the one to reach for whenever you aggregate over TIME, because log returns add across periods while simple returns compound. The two agree for small moves and diverge as moves get larger. In ETF5952 the working default is the log return, but read each question carefully - a dollar-P&L or single-period portfolio question may want the simple return. Chapter 03 · Financial Risk and Returns
- When should I use Monte Carlo instead of a parametric formula?
- Use the parametric formula when a closed form exists — for example VaR(p) = −(μ + σ z_p) under a Normal or standardised Student-t. Reach for Monte Carlo when there is no closed form: any non-linear utility U(P), an option-like payoff, or a multi-asset portfolio. You draw N returns from your estimated distribution, convert to wealth, and average the quantity; the same simulated sample also gives VaR (sort the losses) and ES (average the worst tail). The trade-off is simulation error, which shrinks only like 1/√N, so use a large N. Chapter 04 · Estimating Return Distributions: Monte Carlo, Parametric and Non-parametric
- Why is Expected Shortfall always at least as large as Value-at-Risk?
- Because ES averages returns that are all at or below the quantile q_p, the average sits at least as far into the tail as q_p itself. Negated, the tail mean is greater than or equal to the VaR threshold, so ES(p) ≥ VaR(p), with equality only in degenerate cases. That is also why the Basel framework now uses a 2.5% ES for bank capital — it captures the size of tail losses, not just how often they occur. Chapter 05 · Downside Risk Measures: Value-at-Risk and Expected Shortfall
- What is the difference between conditional and unconditional VaR, and why does it matter?
- An unconditional VaR treats the return distribution as fixed and averages over all time, so it produces a single risk number that sits still through calm and crisis alike. A conditional VaR is computed from the conditional distribution given the information set I_t, so it uses today's estimated volatility: when a fresh shock enters the rolling window the conditional volatility jumps and the VaR rises, and when markets calm the shock eventually drops out and the VaR falls. Because financial volatility clusters, the unconditional number badly understates risk during a turbulent period and overstates it afterwards, which is exactly why ETF5952 emphasises the time-varying, conditional version. Chapter 06 · Conditional Mean, Volatility and Time-Varying Risk
- When is the GARCH long-run variance formula σ̄² = ω/(1−α−β) actually valid?
- Only when the persistence α + β is strictly less than 1. That condition guarantees the process is stationary and the geometric series behind the unconditional variance converges. If α + β ≥ 1 — as in EWMA, where α + β = 1 exactly — there is no finite long-run variance to revert to, and quoting a number for σ̄ would be wrong. Always state the check before you compute the anchor. Chapter 07 · Volatility Models: EWMA, GARCH and GJR-GARCH
- Why does volatility scale with the square root of time but the mean scales with the horizon itself?
- Both come from writing the h-period return as a sum of the one-period returns. The expectation of a sum is the sum of expectations, so with a constant mean μ the h-period mean is hμ - it scales linearly with h. For the variance, when the returns are uncorrelated the variance of the sum is the sum of the variances, so with a constant one-step variance σ² the h-period variance is hσ². Volatility is the square root of variance, so the h-period volatility is √(hσ²) = √h × σ. That is the square-root-of-time rule: variance adds linearly, volatility grows with the square root. Scaling volatility linearly in h is the classic error and badly overstates multi-period risk. Chapter 08 · Multi-Period Risk and the Square-Root-of-Time Rule
- What is the difference between misspecification risk and estimation risk, and which one does more data fix?
- Misspecification risk means you chose the wrong model form - for instance a Normal model for returns that really have fat tails or a leverage effect - so the model is biased in a way that persists no matter how much data you have; more data does not fix it, only changing the model does. Estimation risk means the form is right but the parameters are imprecise because they came from a finite sample; this error is a variance that shrinks as the sample size T grows, so more data does help. A useful exam line is that a simpler model carries less estimation risk but more misspecification risk, and a richer model the reverse, which is exactly the bias-variance trade-off that AIC and BIC try to balance. Chapter 09 · Model Risk and VaR Backtesting
- Why do the hedge-ratio (replication) and risk-neutral methods give the same option price?
- Because both are the same no-arbitrage argument. Replication builds a portfolio of the stock and a bond that reproduces the option's two possible payoffs; that portfolio must cost what the option costs, or a free lunch exists. Rearranging that price algebraically gives exactly the discounted risk-neutral expectation c₀ = e^{−r_f}[q C_u + (1 − q) C_d]. So the two answers are identical by construction — computing both is a built-in check on your arithmetic. Chapter 10 · Option Pricing and Option Risk
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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