Measuring and Managing Market Risk

Market risk measures are how firms decide how much risk to take, where to take it and when to cut it. This module covers the three ways to estimate value at risk, what VaR leaves out and the measures that fill the gaps (conditional, incremental and relative VaR), sensitivity measures and stress tests, and how risk budgets, limits and capital allocation turn these numbers into decisions. It ends by comparing the measures that banks, asset managers, pension funds and insurers care about most. Level II item sets mix VaR arithmetic with judgment about its limitations, so both are practised here.

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What you will learn

1. Estimate value at risk with the parametric, historical simulation and Monte Carlo methods, and interpret the result.

VaR = minimum loss expected over a horizon with a stated probability (5% VaR is exceeded on 5% of occasions).
Parametric VaR = (z x sigma - expected return) x portfolio value; z = 1.645 at 5% and 2.326 at 1%.
Scale the mean by T and the standard deviation by the square root of T when changing horizon.
Historical simulation uses actual past changes applied to today's positions; no distribution assumption.
Monte Carlo uses chosen distributions and many random scenarios; best for options and fat tails.

2. Evaluate the strengths and limitations of VaR and explain conditional, incremental, marginal and relative VaR.

VaR is simple, comparable and widely accepted, but depends on subjective choices.
VaR ignores the size of tail losses and, under normality, understates their frequency.
VaR ignores liquidity and can fail when correlations and volatility change in a crisis.
CVaR (expected shortfall) = average loss beyond VaR; banks now use 97.5% expected shortfall for market risk capital.
Incremental VaR = change in VaR from a position change; marginal VaR = per-unit sensitivity; relative VaR = ex ante tracking error.

3. Use sensitivity measures such as beta, duration, convexity and the option Greeks, together with scenario analysis and stress tests, to complement VaR.

Sensitivities (beta, duration, convexity, delta, gamma, vega) measure exposure to one factor at a time.
Bond price change = -modified duration x yield change + 0.5 x convexity x (yield change) squared.
Option value change = delta x price change + 0.5 x gamma x (price change) squared.
Historical scenarios replay real events; hypothetical scenarios imagine new ones; reverse stress tests start from the loss.
Scenario results carry no probability, so they complement VaR rather than replace it.

4. Apply risk budgets and position, scenario and stop-loss limits, and use risk measures to allocate capital.

Risk budgeting allocates total risk appetite top-down to units according to expected return per unit of risk.
Position limits cap size; scenario limits cap stress losses; stop-loss limits force cuts after losses; VaR limits cap statistical risk.
Because of diversification, unit VaR limits can sum to more than the firm-wide limit.
Return on risk capital = expected profit / risk capital; compare activities on this ratio, not on profit.
A limit that is raised whenever it is breached gives no protection.

5. Compare the risk measures emphasised by banks, asset managers, pension funds and insurers, and relate them to each organisation's liabilities.

Banks: liquidity gaps, leverage, balance-sheet rate sensitivity, VaR/expected shortfall, stress tests, capital.
Long-only managers: tracking error, active share, position and liquidity limits; hedge funds add VaR, leverage and drawdown.
DB pension funds: funded ratio, surplus at risk and the asset-liability duration gap.
P&C insurers: catastrophe scenarios; life insurers: asset-liability matching and surplus volatility.
Choose the risk measure that captures how the organisation could fail its obligations.

Module at a glance

VaR is a minimum loss with a probability and horizon; it is a threshold, not a worst case.
Parametric VaR = (z x sigma - mean) x value; scale the mean by T and volatility by the square root of T.
Historical simulation reuses past moves; Monte Carlo uses chosen distributions and suits options and fat tails.
CVaR averages losses beyond VaR; incremental VaR measures a position's effect; relative VaR is ex ante tracking error.
Duration-convexity, beta and delta-gamma estimates feed scenario analysis and stress tests that VaR cannot replace.
Risk budgets allocate risk appetite; position, scenario, stop-loss and VaR limits enforce it; compare activities on return per unit of risk capital.
Banks watch liquidity, leverage and capital; asset managers tracking error or drawdown; pension funds surplus at risk; insurers asset-liability and catastrophe risk.

This free module has 5 lessons, 16 practice questions with full explanations.

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