Risk — Pomegra Wiki

How to Calculate a Hedge Ratio A hedge ratio is the size of a derivative position needed to offset the risk of an underlying exposure. The minimum-variance hedge ratio uses correlation and volatility to minimize residual risk.

How to Calculate Value at Risk (VaR) How to calculate Value at Risk: historical simulation, variance-covariance, and Monte Carlo methods with worked examples.

How to Calculate Value at Risk: A Simple Example Walk through the three main VaR methods—historical simulation, variance-covariance, and Monte Carlo—with worked numerical examples.

Idiosyncratic Risk Idiosyncratic risk — also called unsystematic or firm-specific risk — is the risk unique to a single company or small group of companies. It can be eliminated through diversification, unlike market risk.

Implied Volatility as a Forward-Looking Risk Measure How implied volatility from options markets reflects future risk expectations better than historical volatility, and when to use it as a near-term gauge.

Incremental Value at Risk The marginal risk contribution of adding a new position to an existing portfolio, measured as the change in portfolio VaR.

Index Concentration Risk How passive index investing can lead to concentrated portfolio exposures due to market-cap weighting and portfolio clustering.

Inflation Hedging Asset allocation and derivative strategies designed to preserve purchasing power during periods of rising prices.

Inflation Risk Inflation risk is the exposure to losses in purchasing power when investment returns do not keep pace with inflation, or when inflation rises unexpectedly, eroding real returns.

Inflation Risk in Fixed Income Inflation risk is the erosion of real purchasing power in fixed-rate bond coupons and principal payments, affecting returns most harshly in long-duration, low-coupon securities.

Interest Rate Cap vs Swap as a Hedge Compare interest rate caps and swaps for hedging floating-rate debt: cost, flexibility, maximum payout, accounting, and when each hedge fits a borrower's risk profile.

Interest Rate Hedging Mitigating bond and debt sensitivity to rate changes through derivatives or offsetting positions.

Interest Rate Risk for Bond Ladders How a staggered maturity structure in bond ladders reduces interest rate risk compared to single-duration portfolios and how to size the rungs.

Interest Rate Risk in the Banking Book (IRRBB) How regulators measure interest rate risk in the banking book (IRRBB) under Basel standards, tracking bank sensitivity to rate shifts and economic value impact.

Interest-Rate Risk Interest-rate risk is the exposure of a bond portfolio to losses from rising interest rates, which cause bond prices to fall, or gains from falling rates, which cause prices to rise.

Internal Ratings-Based Approach A Basel II/III method that allows banks to use proprietary models of default probability and loss-given-default to set their own regulatory capital requirements.

Jump Risk The discontinuous, price-gap hazard that standard diffusion models systematically underestimate, causing sudden large moves.

Jump Risk in Options Pricing How sudden discontinuous price moves create losses that delta-hedging cannot prevent, and why jump risk is priced into options.

Kelly Criterion A mathematical formula that calculates the optimal fraction of a bankroll to bet on each wager to maximise long-run capital growth.

Kupiec Proportion-of-Failures Test A binomial statistical test that checks whether a VaR model's observed exception rate matches its claimed confidence level.

Legal Risk Losses from unenforceable contracts, litigation, regulatory fines, adverse court rulings, or statutory penalties.

Legal Risk in Financial Contracts Legal risk is the possibility that a financial contract is unenforceable, misinterpreted, or triggers regulatory penalties. It arises in derivatives, lending, and cross-border agreements.

Leverage Ratio Requirement A Basel III regulatory floor that caps bank balance-sheet size relative to Tier 1 capital, independent of risk-weighting.

Leverage Ratio Requirements: Small Banks vs Large Banks Understand why large banks face enhanced leverage ratio rules while community banks have simpler requirements.

Liquidity Coverage Ratio Explained The LCR measures whether a bank can survive a 30-day funding crisis. Learn what counts as a high-quality liquid asset and how regulators set the threshold.

Liquidity Crisis A situation where assets cannot be quickly converted to cash at fair-value prices, forcing sellers to accept steep discounts or face inability to meet obligations.

Liquidity Risk Liquidity risk is the danger that an investment position cannot be sold quickly without suffering a significant loss. It arises when the market for an asset is thin, has few buyers, or trades at a wide bid-ask spread.

Liquidity Risk vs Credit Risk Understand the difference between liquidity risk (inability to sell assets quickly at fair value) and credit risk (borrower default), and how they interact during market stress.

Liquidity-Adjusted Value at Risk How liquidity-adjusted VaR accounts for market impact costs when exiting illiquid positions, correcting standard VaR's systematic underestimation of tail risk.

Liquidity-Adjusted VaR (LVaR) How standard Value at Risk understates risk for illiquid positions and methods to adjust VaR for bid-ask spreads and liquidation horizons.

Longevity Risk in Defined Benefit Pensions What is longevity risk in defined benefit pensions? Learn how beneficiaries living longer than expected increases pension fund obligations and threatens solvency.

Loss Given Default The fraction of a loan or bond exposure actually lost when a borrower defaults, accounting for recovery from collateral and liquidation.

Lower Partial Moment A family of downside risk measures that raises below-target deviations to any chosen power order, generalizing semi-variance and enabling flexible tail-weighting.

Macro Hedging Portfolio-wide risk reduction against broad macroeconomic shocks affecting all asset classes simultaneously.

Margin Call A broker's demand that a leveraged investor deposit additional collateral or liquidate positions to cover accumulated losses and restore minimum margin requirements.

Margin of Safety in Risk Management How margin of safety in risk management works as a capital buffer principle and position-sizing rule, distinct from value-investing discount thresholds.

Marginal Value at Risk The change in total portfolio VaR if a single position is added or removed, measuring the marginal risk contribution of that holding.

Market Risk Market risk is the exposure of an investment portfolio to broad movements in asset prices, interest rates, or indices driven by macroeconomic conditions or sentiment shifts. It affects most assets in the same direction at the same time.

Maximum Drawdown The largest percentage decline from a portfolio's peak value to its lowest subsequent value, capturing the worst case loss between highs.

Maximum Drawdown as a Risk Measure Understand maximum drawdown as a risk metric: how it measures peak-to-trough losses, what it reveals about downside risk that volatility misses, and how investors use it for position sizing.

Maximum Drawdown Calculation With Example Maximum drawdown measures the steepest decline from peak to trough in a portfolio or asset return series. A worked example shows how to calculate it step by step.

Maximum Drawdown vs Value at Risk Compare maximum drawdown and value at risk—two downside metrics—to understand when each reveals the true risk in a portfolio.

Migration Risk The risk that a borrower's credit rating will deteriorate, reducing bond value and increasing future borrowing costs before default occurs.

Model Error The risk that a financial model's assumptions or calculations are fundamentally wrong, producing unreliable valuations or forecasts.

Model Risk Model risk is the danger that a financial model is wrong — due to faulty assumptions, incorrect inputs, incomplete data, or misuse — leading to misdecision, mispricing, or catastrophic losses.

Model Risk in Finance The danger of relying on flawed or misapplied quantitative models for pricing and risk measurement, and how firms manage it.

Model Risk in VaR Estimation Understand model risk in VaR: distributional assumptions, correlation estimates, and calibration errors that cause VaR to underestimate tail losses.

Model Risk Management and the SR 11-7 Guidance SR 11-7 supervisory letter outlines Federal Reserve requirements for model risk management, validation, and ongoing monitoring.

Modified Value at Risk Adjusts Value at Risk estimates for non-normal distribution features like skewness and kurtosis using Cornish-Fisher expansion.

Monte Carlo VaR Monte Carlo value-at-risk is a method of estimating portfolio loss by simulating thousands or millions of possible future scenarios using probabilistic models, then calculating loss percentiles from the simulated outcomes.

Moral Hazard and Excessive Financial Risk-Taking Moral hazard arises when implicit guarantees or asymmetric compensation encourage banks and traders to take excessive risk. A primer on the incentive problem.

MREL vs TLAC: Key Differences Explained Explore the MREL vs TLAC difference: how the EU's minimum requirement for own funds and eligible liabilities differs from the global total loss-absorbing capacity standard.

Natural Hedging Reducing exposure to price or currency fluctuations by matching operational revenues and costs in the same currency or commodity, without using derivatives.

Net Investment Hedge Derivative strategy that hedges the translation risk on a parent company's equity stake in a foreign-currency subsidiary.

Net Stable Funding Ratio: How It Works The NSFR ensures banks can survive a one-year funding crisis using stable funding sources. Learn how available and required stable funding are calculated.

Omega Ratio as a Risk-Reward Measure The Omega ratio captures the full distribution of returns above and below a threshold, offering a more complete picture of risk-reward than Sharpe.

Operational Hedge vs Financial Hedge Operational hedges reduce risk through business structure and geography; financial hedges use derivatives. Each suits different risk profiles and time horizons.

Operational Resilience Regulatory Requirements for Banks Operational resilience rules require banks to identify critical services, set tolerance thresholds, and test their ability to recover within those limits.

Operational Risk Operational risk is the potential for loss stemming from failed or inadequate internal processes, people, systems, or external events such as fraud, legal action, or natural disaster.

Operational Risk Capital Charge: The Standardised Approach The standardised operational risk capital charge under Basel III: how the BI and ICs drive required capital without model complexity.