Risk = possibility actual outcome differs from expected, focused on losses
Knight (1921): risk = measurable probabilities; uncertainty = probabilities not reliably measurable
Four stages: identify, measure, manage, monitor, then loop
Four treatments: avoid, retain, mitigate, transfer
Top-level umbrella: market, credit, liquidity, operational risk
Market risk = losses from moves in prices and rates
Credit risk = loss when a counterparty fails to pay
Operational risk = loss from failed processes, people, systems, or external events
Normal distribution: fully described by mean and standard deviation
VaR = the loss not exceeded with probability $c$ over a set horizon
Assumes normal returns; VaR is a multiple of volatility
Drift $\mu$ is negligible over short horizons, material over long ones
Scale across horizons with $\mathrm{VaR}_J = \mathrm{VaR}_1\sqrt{J}$
Normal-model VaR is exactly proportional to $z$
Local (delta) valuation: $\Delta V \approx \delta\,\Delta S$, fast but linear
Replay past return scenarios on today's portfolio
Simulate many model-generated scenarios, then reprice
Returns are leptokurtic: kurtosis above the normal value of 3
Parametric: fast, data-light, but assumes normality and linearity
VaR is a threshold loss, not the maximum loss
Four axioms: monotonicity, subadditivity, positive homogeneity, translation invariance
ES = mean loss in the worst (1 - alpha) tail, i.e. average loss beyond VaR
Black swan: rare, extreme impact, explained only in hindsight (Taleb 2007)
Apply the VaR quantile idea to variables other than trading P&L
Dynamic VaR updates its inputs (mainly volatility) over time
Returns cluster in volatility; GARCH(1,1) models conditional variance
Exception (violation): a day whose loss exceeds the VaR
Kupiec (1995) proportion-of-failures = unconditional-coverage test
Christoffersen (1998) tests conditional coverage = frequency + independence
Implied volatility makes the model price equal the option market price
Reporting quality: faithful, relevant, neutral representation of the firm
Reporting quality lies on a spectrum, not a binary
Legal accounting choices move reported numbers in predictable directions
Earnings management reports a target profit, not true performance
Earnings myopia: short-termism that chases near-term benchmarks
Red flags are warning signs, not proof of wrongdoing
Quality assessment is a disciplined multi-step process
Beneish M-score: eight ratios combined into a manipulation probability
Earnings = CFO + accruals; accruals = net income − CFO
Altman Z-score (1968): five ratios scaled by total assets
SRV = how widely returns scatter around their own mean
Main direction: higher volatility raises distress likelihood
Moderators change the slope of the volatility-distress link, not its level
Return standard deviation: dispersion of close-to-close returns
Lower leverage shrinks the asset-to-equity volatility multiplier
Liquidity = ease of trading fast, in size, near fair value
Liquidity risk: loss from not trading fast at a fair price
Volume = shares (or dollars) traded over a period
Spread = ask minus bid, the cost of an instant round trip
Depth = quantity tradable near the current price without moving it
Quoted spread = posted ask minus bid
Turnover = trading volume / shares outstanding (or float)
Amihud ILLIQ = average of |daily return| / daily dollar volume
Fire sale = forced rapid selling below fundamental value to raise cash
Sovereign risk = a government failing to service its debt in full and on time
Firms can be liquidated under bankruptcy law; sovereigns cannot
Benchmark government bonds are default-risk-free in their home currency, not risk-free
Three economic pillars: growth, public finances, external position
Fiscal balance = revenue minus expenditure (a yearly flow)
Current account = trade balance plus net income and transfers
Politics governs willingness to pay; economics governs ability
Moody's, S&P, Fitch, and DBRS rate sovereign ability and willingness to pay
Sovereign stress transmits beyond the government bond market
Risk that one failure disrupts the whole financial system, harming the real economy
Unsystematic = firm-specific, diversifiable (averages away in a portfolio)
Exogenous risk: shock originates outside the system (pandemic, war, disaster)
Contagion: transmission of distress across the financial network
Procyclicality: the financial system amplifies the business cycle
Fire sale: forced selling below fundamental value when buyers are constrained
SIFI: failure threatens the system via size, interconnectedness, complexity, substitutability
CoVaR: VaR of the system conditional on institution i’s state
MES: expected equity loss of a firm given a market tail event
Stress test: capital adequacy under a severe but plausible adverse scenario
Micro = individual firm safety; macro = whole-system stability
"Dark side of efficiency": cost-cutting via weaker risk controls raises risk
Minsky (1992): "stability is destabilizing", calm breeds fragility