BANK3011 · Bank Financial Management
Market Risk: DEAR and Value at Risk
Market risk is the Week 4 topic in BANK3011 Bank Financial Management at the University of Sydney, and it moves the analysis from the banking book to the trading book — positions marked to market every day where the danger is a sudden adverse price or yield move. The tool is Value at Risk (VaR) — the worst expected loss over a horizon, under normal conditions, at a set confidence level — and its one-day form, DEAR (Daily Earnings at Risk). You build DEAR from three multiplicative pieces, scale it across N days with the √N rule, and aggregate desks using the portfolio-DEAR-with-correlation formula. Because the exam provides a formula sheet, the marks are in choosing the right formula, using the correct tail multiplier and showing clean working — not in memorising equations.
What this chapter covers
- 011. Market risk & the trading book — value uncertainty from daily price and yield moves, measured over a short horizon and marked to market
- 022. Value at Risk (VaR) — the worst expected loss over a horizon, under normal conditions, at a given confidence level (Jorion's definition)
- 033. DEAR and its three components — dollar position × price sensitivity × adverse move; the last two multiply to the price volatility
- 044. The RiskMetrics (variance–covariance) model — assumes Normal returns; the 5% one-tail loss sits at 1.65σ (and 2.33σ for the 1% tail)
- 055. Equity DEAR — P × 1.65σ for a well-diversified market position with β ≈ 1
- 066. Fixed-income DEAR — −[D/(1+R)] applied to the adverse yield move; discount the face value to a market value first
- 077. N-day VaR — DEAR × √N under independent, identically distributed daily returns (√N, never N)
- 088. Portfolio DEAR with correlation — square-root aggregation; the diversification benefit that appears whenever ρ < 1
- 099. Three estimation approaches — RiskMetrics (parametric) vs historic (back) simulation vs Monte Carlo
DEAR, 10-day VaR and portfolio DEAR across a trading book
- +2(a) Equity DEAR = P × (1.65 × σ) = 40,000,000 × 1.65 × 0.018 = $1,188,000. This is the 5% one-day loss you would not expect to exceed.
- +2(b) 10-day VaR = DEAR × √N = 1,188,000 × √10 = 1,188,000 × 3.1623 = $3,756,812 (≈ $3.76m). Apply √N once, at the end — never √N to the volatility partway through.
- +1(c) Portfolio formula: DEAR_p = [DEAR_eq² + DEAR_fx² + 2ρ·DEAR_eq·DEAR_fx]^½ — the desk DEARs cannot simply be added unless ρ = 1.
- +1Terms: DEAR_eq² = 1.4113×10¹²; DEAR_fx² = 0.4900×10¹²; cross term = 2(0.2)(1,188,000)(700,000) = 0.3326×10¹².
- +1Sum and root: (1.4113 + 0.4900 + 0.3326)×10¹² = 2.2340×10¹²; DEAR_p = √(2.2340×10¹²) = $1,494,652.
- +1(d) Diversification benefit = simple sum − portfolio DEAR = (1,188,000 + 700,000) − 1,494,652 = 1,888,000 − 1,494,652 = $393,348.
Key terms
- DEAR (Daily Earnings at Risk)
- The one-day VaR: the trading loss expected to be exceeded only in the adverse tail (e.g. 5%). DEAR = dollar market value × price sensitivity × adverse market move.
- Value at Risk (VaR)
- The worst loss expected over an N-day horizon, under normal market conditions, at a given confidence level. It is a quantile, not a maximum — actual tail losses can exceed it.
- Price volatility
- The expected percentage change in a position's value in the adverse case — the product of the price sensitivity and the potential adverse move. DEAR = dollar position × price volatility.
- Confidence multiplier (1.65σ)
- Under Normally distributed returns the 5% one-tail loss lies 1.65 standard deviations below the mean; the 1% one-tail uses 2.33. VaR is one-sided (losses only), so it is not the two-tailed 1.96.
- RiskMetrics (variance–covariance) model
- The parametric approach that assumes returns are Normal with mean zero and turns a volatility into a loss via the 1.65σ multiplier. Fast, but understates fat tails.
- Historic (back) simulation
- Re-prices the current position on the actual past series of returns and reads the empirical 5% tail. It needs no distributional assumption but is limited by the length of the return history.
- Monte Carlo simulation
- Generates many synthetic return paths from an estimated covariance matrix and reads the tail. Flexible for options and non-linear books, but computationally heavy.
- Trading book
- The portfolio of marked-to-market positions (interest-rate, FX, equity, commodity) held for short-horizon trading — the book that market-risk VaR measures, as opposed to the held-to-maturity banking book.
Market Risk: DEAR and Value at Risk FAQ
Can AI help me with market risk, DEAR and Value at Risk?
Yes — ask Sia to walk through any DEAR or Value at Risk problem or concept step by step, the way University of Sydney tests it. Sia is an AI tutor that explains the method — why you price the bond before applying DEAR, why the horizon scales with √N, and how the correlation term shrinks a portfolio DEAR — so you can reproduce the working yourself under exam conditions.
What is the difference between DEAR and VaR?
DEAR (Daily Earnings at Risk) is simply the one-day VaR — the loss you expect to exceed only in the adverse tail over a single day. VaR is the same idea over a longer horizon: N-day VaR = DEAR × √N. So DEAR is the building block, and VaR is DEAR scaled up over time.
Why is VaR scaled by √N and not N?
Under the assumption that daily returns are independent and identically distributed (i.i.d.), variance adds over N days, so the standard deviation — and therefore the loss — grows with the square root of time. Multiplying DEAR by N (instead of √N) massively overstates the risk. Note the caveat: a trending market grows faster than √N (so √N understates) and a mean-reverting one grows slower.
Why can't I just add the DEARs of two trading desks?
Because adding is only correct when the desks are perfectly correlated (ρ = 1). With ρ < 1 the cross term in DEAR_p = [DEAR₁² + DEAR₂² + 2ρ·DEAR₁·DEAR₂]^½ is smaller, so the portfolio DEAR sits below the simple sum. That gap is the diversification benefit — a real reduction in risk that adding would ignore.
Which multiplier do I use — 1.65 or 2.33?
Match the multiplier to the stated confidence, and remember VaR is one-tailed (losses only). The 5% one-tail uses 1.65σ; the 1% one-tail uses 2.33σ. The two-tailed 1.96 belongs to a different (95% two-sided) question, so using it for VaR is a common silent error.
Is the DEAR / VaR formula on the BANK3011 exam formula sheet?
Yes — the University of Sydney final exam provides a formula sheet that includes DEAR, the N-day VaR √N scaling and the portfolio DEAR with correlations, so you are not expected to memorise them. The marks reward choosing the right formula, using the correct tail multiplier and showing clean working. Always confirm the current formula sheet on Canvas before the exam.
Studying with AI? Sia — free AI financial modeling tutor works through BANK3011 step by step.
Exam move
Treat market risk as a formula-application topic: because the exam hands you a formula sheet with DEAR, N-day VaR and portfolio DEAR, the marks come from picking the right formula and laying out each line cleanly. Fix the three-piece structure of DEAR in your head — dollar position × price sensitivity × adverse move — then drill both faces of it: the equity form (P × 1.65σ) and the fixed-income form (price the bond first, then apply −[D/(1+R)] to the adverse yield move). Practise the √N scaling and the two- and three-asset portfolio DEAR until the setup is automatic, and always sanity-check that the portfolio DEAR is below the simple sum whenever ρ < 1. Keep a short list of the recurring traps (modified duration vs D/(1+R), the 1.65 vs 2.33 multiplier, √N vs N, VaR as a minimum-not-maximum, discounting the face value first) because the short-answer section rewards knowing why a method works. When a step won't click, ask Sia to explain that exact move step by step rather than looking up an answer.
