Poroflio part 5

Question 1

What does Value at Risk (VaR) measure?

Answer 1

VaR measures downside risk: the loss size, probability of exceeding that loss, and a time frame.

Question 2

What are the three components of VaR?

Answer 2

Loss size, probability, and time frame.

Question 3

How is VaR typically expressed?

Answer 3

As a dollar loss, percentage loss, or confidence level (e.g., 95% confidence for 5% VaR).

Question 4

What probabilities are common for VaR reporting?

Answer 4

1%, 5%, or 16% (one standard deviation below the mean for normal distribution).

Question 5

What is the parametric (variance-covariance) method for VaR?

Answer 5

Assumes normal distribution; uses means, variances, and covariances to estimate VaR.

Question 6

What is the formula for portfolio variance (two assets)?

Answer 6

σ²_portfolio = WA²σA² + WB²σB² + 2WAWB Cov_AB.

Question 7

What is the lookback period in VaR estimation?

Answer 7

The historical time period used to estimate mean and variance for returns.

Question 8

What are the weaknesses of the parametric method?

Answer 8

Relies heavily on normality assumption; not suitable for portfolios with options.

Question 9

What is the historical simulation method for VaR?

Answer 9

Uses actual historical changes in portfolio value without assuming any distribution.

Question 10

Strengths of historical simulation method?

Answer 10

No assumption of normality; captures non-linear risks like options.

Question 11

Weaknesses of historical simulation method?

Answer 11

Depends heavily on the sample lookback period; may overestimate or underestimate VaR.

Question 12

What is the Monte Carlo simulation method for VaR?

Answer 12

Simulates random values from assumed distributions for risk factors; calculates portfolio changes thousands of times.

Question 13

Strengths of Monte Carlo simulation?

Answer 13

Flexible with distribution assumptions; handles complex portfolios and non-linearities.

Question 14

Weaknesses of Monte Carlo simulation?

Answer 14

Dependent on assumptions about distributions and correlations; computationally intensive.

Question 15

When would Monte Carlo and parametric methods produce identical results?

Answer 15

When the distribution and parameter assumptions are the same and sample size is large.

Question 16

Example: In a portfolio of $10M, if 5% daily VaR = 2.06%, what is the loss amount?

Answer 16

206000

Question 17

Example: In the same portfolio, if 5% annual VaR = 24.09%, what is the loss amount?

Answer 17

2409000

Question 18

What are advantages of VaR?

Answer 18

Simple concept, compares risk across portfolios, used for performance evaluation, risk budgeting, accepted by regulators, and backtestable.

Question 19

What are limitations of VaR?

Answer 19

Affected by assumptions, normality assumption underestimates tail risk, ignores liquidity risk, correlation spikes during stress, incomplete risk capture.

Question 20

What is Conditional VaR (CVaR)?

Answer 20

The expected loss given that the loss is equal to or greater than the VaR (expected shortfall).

Question 21

What is Incremental VaR (IVaR)?

Answer 21

Change in portfolio VaR resulting from a change in the portfolio allocation to a security.

Question 22

What is Marginal VaR (MVaR)?

Answer 22

The slope of the VaR curve at the current weight; approximate change in VaR for a 1% increase in a security’s weight.

Question 23

What is relative VaR (ex-ante tracking error)?

Answer 23

VaR of the difference between the portfolio return and benchmark return.

Question 24

What does sensitivity analysis measure?

Answer 24

Effect on portfolio value of a small change in a single risk factor; complements VaR.

Question 25

What does scenario analysis measure?

Answer 25

Effect on portfolio value of simultaneous significant changes in multiple risk factors.

Question 26

What is historical scenario analysis?

Answer 26

Uses actual past events to model the effect of extreme risk factor changes on portfolio value.

Question 27

What is hypothetical scenario analysis?

Answer 27

Models imagined extreme changes in risk factors that have not necessarily occurred before.

Question 28

What is a stress test?

Answer 28

Examines portfolio value or solvency under extreme changes in risk factors.

Question 29

What is beta in equities?

Answer 29

Measure of sensitivity of a security's return to the market return.

Question 30

Formula for expected return in CAPM?

Answer 30

E(Ri) = Rf + Beta_i × (E(RMKT) – Rf).

Question 31

What measures fixed-income security risk?

Answer 31

Duration and convexity.

Question 32

Formula for change in fixed-income price?

Answer 32

Change = –Duration × ΔY + ½ Convexity × (ΔY)^2.

Question 33

What is delta in options?

Answer 33

Sensitivity of option value to changes in underlying asset price.

Question 34

What is gamma in options?

Answer 34

Sensitivity of delta to changes in underlying asset price.

Question 35

What is vega in options?

Answer 35

Sensitivity of option value to changes in expected volatility of the underlying asset.

Question 36

Formula for change in call price?

Answer 36

Change = delta(ΔS) + ½ gamma(ΔS)^2 + vega(ΔV).

Question 37

What are first-order and second-order effects?

Answer 37

First-order: duration (bonds), delta (options); Second-order: convexity (bonds), gamma (options).

Question 38

What is the purpose of sensitivity risk measures?

Answer 38

To inform managers about portfolio exposure to various risk factors and facilitate risk management.

Question 39

Why is risk exposure important in a portfolio?

Answer 39

Because eliminating all risk leads to returns no greater than the risk-free rate.

Question 40

How are scenario analyses used in portfolios with options or embedded options?

Answer 40

Use pricing models to estimate changes in value under different risk factor scenarios.

Question 41

Why are pricing models important for scenario analysis?

Answer 41

They accurately account for large changes in risk factors beyond simple sensitivities like duration and convexity.

Question 42

What does scenario risk measure estimate?

Answer 42

Portfolio return resulting from a hypothetical or historical market event.

Question 43

What is conservative scenario analysis?

Answer 43

Assumes instantaneous changes in risk factors without allowing manager actions like hedging or adjusting positions.

Question 44

What is reverse stress testing?

Answer 44

Identify largest risk exposures, define an unacceptable outcome, and find risk scenarios that would cause that outcome.

Question 45

How does scenario analysis complement sensitivity analysis?

Answer 45

Scenario analysis assesses vulnerabilities to large, simultaneous changes after sensitivity analysis identifies exposures.

Question 46

Why is scenario analysis important for leveraged firms?

Answer 46

It helps assess how a single extreme risk factor movement could threaten firm survival.

Question 47

How do VaR, sensitivity analysis, and scenario analysis complement each other?

Answer 47

VaR estimates probability of loss, sensitivity analysis shows exposures to individual risks, scenario analysis models multiple factor changes.

Question 48

What is a limitation of sensitivity analysis?

Answer 48

Sensitivity measures like duration or delta assume small changes and ignore volatility differences across assets.

Question 49

Example limitation of sensitivity analysis with bonds?

Answer 49

Two portfolios may have the same duration but different yield volatilities, leading to different risk profiles.

Question 50

Example limitation of sensitivity analysis with options?

Answer 50

Option deltas may not account for different volatilities in underlying asset prices.

Question 51

Does sensitivity or scenario analysis predict probabilities?

Answer 51

No, they estimate impact of changes but not the probability of the changes happening.

Question 52

What is the role of stress tests in scenario analysis?

Answer 52

Evaluate firm solvency under extreme changes in a single risk factor.

Question 53

What factors determine risk measures used by organizations?

Answer 53

Types of risks, regulations, and use of leverage.

Question 54

What risk measures do banks commonly use?

Answer 54

Sensitivity measures, scenario analysis, stress testing, leverage risk measures, VaR, and economic capital estimates.

Question 55

What is economic capital?

Answer 55

Amount of capital needed for a firm to survive severe losses.

Question 56

What risk measures do traditional asset managers use?

Answer 56

Position sizes, sensitivity measures, scenario analysis, options risk, active share, and tracking error.

Question 57

Difference between ex-post and ex-ante tracking error?

Answer 57

Ex-post: historical tracking error for performance attribution; Ex-ante: forward-looking risk estimation.

Question 58

What risk measures are used by hedge funds?

Answer 58

Sensitivity analysis, leverage measures, scenario analysis, stress tests, VaR, and maximum drawdown.

Question 59

What is maximum drawdown?

Answer 59

Largest decrease in value over a prior period; used when returns are non-normal.

Question 60

What risk measures are used by defined benefit pension funds?

Answer 60

Surplus-at-risk, glidepath adjustments, and matching assets to liabilities.

Question 61

What is surplus-at-risk?

Answer 61

VaR for plan assets minus liabilities.

Question 62

What is a glidepath?

Answer 62

A multi-year plan to adjust pension fund contributions to correct overfunded or underfunded status.

Question 63

What risk measures do P&C insurers use?

Answer 63

VaR, capital at risk, scenario analysis, and sensitivity analysis of investment portfolios.

Question 64

How do P&C insurers reduce insurance risk?

Answer 64

By purchasing reinsurance and diversifying geographically.

Question 65

What risk measures do life insurers use?

Answer 65

Sensitivity of investment portfolios and liabilities to market risk, and scenario analysis including market and nonmarket risks.

Question 66

Why are life insurance liabilities sensitive to market risks?

Answer 66

Because annuities pay out over long periods, making their present value sensitive to discount rates.

Question 67

How do life insurers manage asset-liability mismatches?

Answer 67

By matching the market risk of assets to liabilities as much as possible and using scenario analysis for residual risks.

Question 68

What are the risks of improper constraint setting in risk management?

Answer 68

Too restrictive limits reduce profitability; too loose limits increase risk of financial stress or bankruptcy.

Question 69

What is risk budgeting?

Answer 69

Determining the acceptable total risk for an organization and allocating that risk to activities or asset classes.

Question 70

What is an example of risk budgeting?

Answer 70

Setting a maximum 5% VaR and allocating it across business units or portfolio deviations from a benchmark.

Question 71

What are position limits?

Answer 71

Limits on allocations to individual securities, asset classes, countries, currencies, or net long/short positions to ensure diversification.

Question 72

How can position limits be expressed?

Answer 72

As currency amounts, percentages of portfolio value, or based on liquidity measures like average daily trading volume.

Question 73

What are scenario limits?

Answer 73

Limits on the expected loss under a specific risk scenario.

Question 74

What are stop-loss limits?

Answer 74

Require reducing a risk exposure if losses exceed a specified amount over a given time period.

Question 75

What is portfolio insurance?

Answer 75

Hedging a portfolio's value with index puts as the value of securities or indices fall.

Question 76

What are capital allocation decisions?

Answer 76

Deciding how a firm's capital is allocated among business units or activities, considering both expected return and risk.

Question 77

How can risk be incorporated into capital allocation?

Answer 77

By calculating a VaR for each business unit and allocating a maximum acceptable VaR across activities.