R. 48 Measuring and Managing Market Risk

Question 1

VaR

• Definition

Answer 1

Three explicit elements of a VaR statement—the frequency of losses of a given minimum magnitude expressed either in currency or percentage terms.

Consider the statement: The 5% VaR of a portfolio is €2.2 million over a one-day period.

• frequency: In this example, that period of time is one day. If VaR is measured on a daily basis, and a typical month has 20–22 business days, then 5% of the days equates to about one day per month.
• minimum loss: VaR is a minimum! Most you can lose for unlevered portfolio is everything!
• currency or %: In this example, if the portfolio value is €400 million, the VaR expressed in percentage terms would be 0.55% (€2.2 million/€400 million = 0.0055).

Thus, the VaR statement can be rephrased as follows: A loss of at least €2.2 million would be expected to occur about once every month. A 5% VaR is often expressed as its complement—a 95% level of confidence: We are 95% certain loss will be less than €2.2M, and 5% certain it will be greater than €2.2M.

Question 2

Methods of Estimating VaR

Answer 2

3 Steps (same regardless of method)

1. Risk decomposition
   
   • (break out various risks: equity/bond, currency, interest rate, etc.)
2. Gather historical data for each risk factor
3. Use data to estimate VaR

Question 3

VaR

• Advantages and Disadvantages
• Extensions

Answer 3

Question 4

Sensitivity Risk Measures

• Equity exposure
• Fixed Income exposure
• Options

Answer 4

Question 5

How VaR is complemented by sensitivity scenario risk measures

Sensitivity and Scenario Risk Measures complement VaR

• Comparisons w/ VaR
• Advantages and Limitations of Sensitivity Risk Measures and Scenario Risk Measures

Historical risk measures

Answer 5

VaR

• Measure of the probability of large losses.
• Incorporates the probability of movements in the risk factors, but will not be accurate if correlations or market volatility has changed
• Best to complement with Sensitivity and Scenario Risk Measures

Sensitivity risk analysis

• Estimates the change in a security or portfolio value to an incremental change in a risk factor.
• Sensitivity Complements VaR b/c:

1. Addresses shortcomings of position size measures
2. Does not rely on history

Scenario risk analysis

• Estimates effect on portfolio value of a specific set of changes in relevant risk factors. Can be historical or hypothetical.
• Scenario Complements VaR b/c

1. Overcomes any assumption of normal distributions
2. Can stress test most concentrated positions in portfolio

Question 6

Application of Risk Measures

• 3 general types
• Measures for
  
  • Banks
  • Asset Managers
  • Hedge funds
  • Pension funds
  • Insurers

Answer 6

Types of risks

1. Degree of leverage
2. Mix of risk factor exposures for a business
3. Accounting or regulatory requirements

Banks

• Liquidity gap between assets and liabilities
• VaR for the fair value portion of the balance sheet
• Leverage calculated by giving more weight to riskier assets
• Sensitivities for the held-for-sale portion of the balance sheet
• Economic capital for market, credit, and operational risk
• Scenario analysis, including stress testing, to determine if capital is sufficient

Asset Managers

Position limits on country, currency, sector, and asset class. They are common and easy to understand.
• Sensitivities, such as duration for fixed-income securities and the Greeks for options.
• Beta sensitivity for equity accounts.
• Liquidity, such as how long it would take to liquidate a security.
• Scenario analysis to examine response to stressed markets.
• Active share, which is the percentage of the portfolio that differs from the benchmark.
• Redemption risk, which measures what percentage of the portfolio could be redeemed at peak times.
• Ex post versus ex ante tracking error. Ex post tracking error measures the historical return deviations, which is useful to assess the manager’s skill. Ex ante tracking error measures the risk in the current portfolio.
• VaR is used by some traditional asset managers, but it is not as common as ex ante tracking error.

Hedge funds

• Sensitivities
• Gross exposure, which is the sum of the absolute value of long plus short positions.
• Leverage. Unfortunately, there are many different ways to incorporate leverage in the calculations.
• VaR, generally focuses on high confidence intervals and short holding periods.
• Scenarios for specific risks.
• Maximum drawdown, which could be defined as the worst-returning month or worst peak-to-trough decline. This is an important measure for non-normal return distributions.

Pension funds

• Interest rate and curve risk
Expected cash flows are grouped by maturity and currency. The liability payments can be expressed as negative cash flows.
• Surplus at risk
This method uses VaR to compute how much the assets might underperform the liabilities. Surplus risk will be greater when the assets are more volatile or less correlated with the liabilities.
• Glide path
A glide path gradually moves the overfunded or underfunded pension plan to its target funding level.
• Liability hedging exposures versus generating exposures
A portion of the assets can be used to hedge the liabilities, while another portion can be used to generate excess returns.

Insurers

1. Property and casualty

• Sensitivities and exposures
  Insurers design asset allocations to stay within specified exposure limits.
• Economic capital and VaR
  Premiums are established to cover expected payouts, but adverse deviations can occur, which necessitates the need for capital.
• Scenario analysis
  Market risk and insurance risks can be stressed in the same scenario.​

2. Life insurance companies

• Sensitivities
  
  • The exposures are measured and monitored.
• Asset and liability matching
  
  • A perfect match is not required, but much closer than that for property and casualty lines of business.
• Scenario analysis
  
  • Scenarios jointly stress market and non-market sources of cash flow risk. For example, liability cash flows could increase when asset market values are down.

Question 7

Constraints in Risk Mgmt

Answer 7

Risk Budgeting

• first sets limits for the entire firm, then allocates to the sub-activities. It is often based on VaR or ex ante tracking error. The sub-activities could be based on business units or risk types

Position Limits

• can be imposed based on the market value of securities or notional principal of derivatives. They are good controls against overconcentration. Limits could be placed on factors such as issuer, country, or investment strategy.

Scenario Limits

• place limits on the loss in a given scenario. This can be used to address shortcomings in VaR. If results are not within the limits, corrective action should be taken

Stop-Loss Limits

• require changes if losses over a given magnitude occur in a specified period. This can catch trending losses that are staying just below the VaR daily limits. Rather than liquidating positions, hedges could be required if losses are excessive. This approach is called a drawdown control or portfolio insurance.