Poroflio part 5 Flashcards
What does Value at Risk (VaR) measure?
VaR measures downside risk: the loss size, probability of exceeding that loss, and a time frame.
What are the three components of VaR?
Loss size, probability, and time frame.
How is VaR typically expressed?
As a dollar loss, percentage loss, or confidence level (e.g., 95% confidence for 5% VaR).
What probabilities are common for VaR reporting?
1%, 5%, or 16% (one standard deviation below the mean for normal distribution).
What is the parametric (variance-covariance) method for VaR?
Assumes normal distribution; uses means, variances, and covariances to estimate VaR.
What is the formula for portfolio variance (two assets)?
σ²_portfolio = WA²σA² + WB²σB² + 2WAWB Cov_AB.
What is the lookback period in VaR estimation?
The historical time period used to estimate mean and variance for returns.
What are the weaknesses of the parametric method?
Relies heavily on normality assumption; not suitable for portfolios with options.
What is the historical simulation method for VaR?
Uses actual historical changes in portfolio value without assuming any distribution.
Strengths of historical simulation method?
No assumption of normality; captures non-linear risks like options.
Weaknesses of historical simulation method?
Depends heavily on the sample lookback period; may overestimate or underestimate VaR.
What is the Monte Carlo simulation method for VaR?
Simulates random values from assumed distributions for risk factors; calculates portfolio changes thousands of times.
Strengths of Monte Carlo simulation?
Flexible with distribution assumptions; handles complex portfolios and non-linearities.
Weaknesses of Monte Carlo simulation?
Dependent on assumptions about distributions and correlations; computationally intensive.
When would Monte Carlo and parametric methods produce identical results?
When the distribution and parameter assumptions are the same and sample size is large.
Example: In a portfolio of $10M, if 5% daily VaR = 2.06%, what is the loss amount?
206000
Example: In the same portfolio, if 5% annual VaR = 24.09%, what is the loss amount?
2409000
What are advantages of VaR?
Simple concept, compares risk across portfolios, used for performance evaluation, risk budgeting, accepted by regulators, and backtestable.
What are limitations of VaR?
Affected by assumptions, normality assumption underestimates tail risk, ignores liquidity risk, correlation spikes during stress, incomplete risk capture.
What is Conditional VaR (CVaR)?
The expected loss given that the loss is equal to or greater than the VaR (expected shortfall).
What is Incremental VaR (IVaR)?
Change in portfolio VaR resulting from a change in the portfolio allocation to a security.
What is Marginal VaR (MVaR)?
The slope of the VaR curve at the current weight; approximate change in VaR for a 1% increase in a security’s weight.
What is relative VaR (ex-ante tracking error)?
VaR of the difference between the portfolio return and benchmark return.
What does sensitivity analysis measure?
Effect on portfolio value of a small change in a single risk factor; complements VaR.
What does scenario analysis measure?
Effect on portfolio value of simultaneous significant changes in multiple risk factors.
What is historical scenario analysis?
Uses actual past events to model the effect of extreme risk factor changes on portfolio value.
What is hypothetical scenario analysis?
Models imagined extreme changes in risk factors that have not necessarily occurred before.
What is a stress test?
Examines portfolio value or solvency under extreme changes in risk factors.
What is beta in equities?
Measure of sensitivity of a security’s return to the market return.
Formula for expected return in CAPM?
E(Ri) = Rf + Beta_i × (E(RMKT) – Rf).
What measures fixed-income security risk?
Duration and convexity.
Formula for change in fixed-income price?
Change = –Duration × ΔY + ½ Convexity × (ΔY)^2.
What is delta in options?
Sensitivity of option value to changes in underlying asset price.
What is gamma in options?
Sensitivity of delta to changes in underlying asset price.
What is vega in options?
Sensitivity of option value to changes in expected volatility of the underlying asset.
Formula for change in call price?
Change = delta(ΔS) + ½ gamma(ΔS)^2 + vega(ΔV).
What are first-order and second-order effects?
First-order: duration (bonds), delta (options); Second-order: convexity (bonds), gamma (options).
What is the purpose of sensitivity risk measures?
To inform managers about portfolio exposure to various risk factors and facilitate risk management.
Why is risk exposure important in a portfolio?
Because eliminating all risk leads to returns no greater than the risk-free rate.
How are scenario analyses used in portfolios with options or embedded options?
Use pricing models to estimate changes in value under different risk factor scenarios.
Why are pricing models important for scenario analysis?
They accurately account for large changes in risk factors beyond simple sensitivities like duration and convexity.
What does scenario risk measure estimate?
Portfolio return resulting from a hypothetical or historical market event.
What is conservative scenario analysis?
Assumes instantaneous changes in risk factors without allowing manager actions like hedging or adjusting positions.
What is reverse stress testing?
Identify largest risk exposures, define an unacceptable outcome, and find risk scenarios that would cause that outcome.
How does scenario analysis complement sensitivity analysis?
Scenario analysis assesses vulnerabilities to large, simultaneous changes after sensitivity analysis identifies exposures.
Why is scenario analysis important for leveraged firms?
It helps assess how a single extreme risk factor movement could threaten firm survival.
How do VaR, sensitivity analysis, and scenario analysis complement each other?
VaR estimates probability of loss, sensitivity analysis shows exposures to individual risks, scenario analysis models multiple factor changes.
What is a limitation of sensitivity analysis?
Sensitivity measures like duration or delta assume small changes and ignore volatility differences across assets.
Example limitation of sensitivity analysis with bonds?
Two portfolios may have the same duration but different yield volatilities, leading to different risk profiles.
Example limitation of sensitivity analysis with options?
Option deltas may not account for different volatilities in underlying asset prices.
Does sensitivity or scenario analysis predict probabilities?
No, they estimate impact of changes but not the probability of the changes happening.
What is the role of stress tests in scenario analysis?
Evaluate firm solvency under extreme changes in a single risk factor.
What factors determine risk measures used by organizations?
Types of risks, regulations, and use of leverage.
What risk measures do banks commonly use?
Sensitivity measures, scenario analysis, stress testing, leverage risk measures, VaR, and economic capital estimates.
What is economic capital?
Amount of capital needed for a firm to survive severe losses.
What risk measures do traditional asset managers use?
Position sizes, sensitivity measures, scenario analysis, options risk, active share, and tracking error.
Difference between ex-post and ex-ante tracking error?
Ex-post: historical tracking error for performance attribution; Ex-ante: forward-looking risk estimation.
What risk measures are used by hedge funds?
Sensitivity analysis, leverage measures, scenario analysis, stress tests, VaR, and maximum drawdown.
What is maximum drawdown?
Largest decrease in value over a prior period; used when returns are non-normal.
What risk measures are used by defined benefit pension funds?
Surplus-at-risk, glidepath adjustments, and matching assets to liabilities.
What is surplus-at-risk?
VaR for plan assets minus liabilities.
What is a glidepath?
A multi-year plan to adjust pension fund contributions to correct overfunded or underfunded status.
What risk measures do P&C insurers use?
VaR, capital at risk, scenario analysis, and sensitivity analysis of investment portfolios.
How do P&C insurers reduce insurance risk?
By purchasing reinsurance and diversifying geographically.
What risk measures do life insurers use?
Sensitivity of investment portfolios and liabilities to market risk, and scenario analysis including market and nonmarket risks.
Why are life insurance liabilities sensitive to market risks?
Because annuities pay out over long periods, making their present value sensitive to discount rates.
How do life insurers manage asset-liability mismatches?
By matching the market risk of assets to liabilities as much as possible and using scenario analysis for residual risks.
What are the risks of improper constraint setting in risk management?
Too restrictive limits reduce profitability; too loose limits increase risk of financial stress or bankruptcy.
What is risk budgeting?
Determining the acceptable total risk for an organization and allocating that risk to activities or asset classes.
What is an example of risk budgeting?
Setting a maximum 5% VaR and allocating it across business units or portfolio deviations from a benchmark.
What are position limits?
Limits on allocations to individual securities, asset classes, countries, currencies, or net long/short positions to ensure diversification.
How can position limits be expressed?
As currency amounts, percentages of portfolio value, or based on liquidity measures like average daily trading volume.
What are scenario limits?
Limits on the expected loss under a specific risk scenario.
What are stop-loss limits?
Require reducing a risk exposure if losses exceed a specified amount over a given time period.
What is portfolio insurance?
Hedging a portfolio’s value with index puts as the value of securities or indices fall.
What are capital allocation decisions?
Deciding how a firm’s capital is allocated among business units or activities, considering both expected return and risk.
How can risk be incorporated into capital allocation?
By calculating a VaR for each business unit and allocating a maximum acceptable VaR across activities.
