Measuring and Managing Market Risk

Question 1

An advantage of statistical factor models

Answer 1

They make minimal assumptions.

However, the interpretation of statistical factors is generally more difficult than the interpretation of macroeconomic and fundamental factor models.

Question 2

Assumption of CAPM

Answer 2

• Perfect competition - Frictionless and can borrow a the RfR
• Rational, mean-variance optimizer
• Perfect information (same variance and covariance matrix)

Question 3

What is the purpose of VaR

Answer 3

Value at Risk is to capture market risk.

Equity prices
Commodity prices
Forex
Interest rates

Does not tell about about average loss

Question 4

How to interpret a one day 95% VaR

Answer 4

95% confidence that we will NOT lose more than … per day

with 95% probability, we will experience a maximum loss of …

Question 5

How to interpret 5% VaR

Answer 5

The 5% minimum loss of a portfolio over a 1 day period

or…

A expected loss of … to occure every 20 days (depend on duration)

Question 6

3 different ways to estimate VaR

Answer 6

Parametric method
Historical simulation method
Monte Carlo Simulation

Question 7

Explain Parametric Method

Answer 7

Variance - Covariance method
Begins with risk decomposition of the portfolio holdings
Assumes return distribution for risk factor is normal distributed
We need expected returns and standard deviation of portfolio

Question 8

Calculate VaR for parametric method

Answer 8

[Expected return - Z* Portfolio standard dev]*(-1) * Pv

Z = Standard deviation number

Question 9

Pros and Cons of parametric method

Answer 9

Pro: Simple and straightforward

Con: VaR is very sensitive to expected returns and standard deviation
Difficult to use of portfolio contains options since it threatens normality. Options have a non normal payoff function.

Question 10

Historical simulation method

Answer 10

We set / construct a portfolio with fixed weights
We measure portfolio return over the observed period
We then rank the portfolio returns from smallest to largest
We then use percentile to find 1,5,10 % VaR

• I we have 500 observation, and we want to find 5% VaR, the 25th observation os our 5% VaR

.

Question 11

Brief characteristics of historical simulation method

Answer 11

Not constrained by normality assumption
Estimates VaR based on what actually happened
Can handle any kind of financial instruments

Question 12

Monte Carlo Simulation

Answer 12

Not constrained by any distribution - We can define the distribution

Avoids complexity of parametric method when portfolio has many risk factors

Calculating VaR is the same as historical method

Question 13

Conditional VaR - CVaR

Answer 13

Relies on a particular VaR measure - Average loss greater than our particular VaR measure.

average loss on the condition that VaR > Cut off

Informs us about average loss

Typically obtained by backtesting

Also known as Expected tail loss or expected shortfall

Question 14

Incramental VaR - IVaR

Answer 14

How VaR will change if a position size changes relative to the remaining position.

example:
SPY - 80 % weight - > 90% weight
LWC - 20 % weight -> 10% Weight

VaR 2,407,503 -> 2,733,722

IVaR = 2,733,722 - 2,407,503 = 326,192

Question 15

Marginal VaR - MVaR

Answer 15

Conceptually the same to IVaR, but reflects the effects of a very small change in a position - 1 unit change in position.

Question 16

Relative VaR - Ex Ante tracking error

Answer 16

The degree to which the performance of a given portfolio might deviate from a benchmark.

Portfolio vs Benchmark

Question 17

What is Sensitivity risk measure

Answer 17

Examines how performance responds to a single change in an underlying risk factor.

Remember; How SENSITIVE a FACTOR is to a change

Question 18

What is scenario risk measure

Answer 18

Estimates the portfolio returns that would result from a hypothetical change in the market or historical events.

Scenario = What if something was different

Scenario = What if something was different

Question 19

Sensitivity and Scenario vs VaR

Answer 19

VaR: measure of loss and probability of large loss

SS: Change in the value of an asset in response tp a change in something else

VaR: Uses market returns from a look back period

SS: Uses market returns from a specific unrepresentative time period

Question 20

Constraints in measuring and managing market risk

Answer 20

Risk Budgeting
Position Limits
Scenario Limits
Stop-loss Limits

Question 21

Explain the following constraint - Risk Budgeting

Answer 21

Total risk appetite allocated to sub activities

Question 22

Explain the following constraint - Position Limits

Answer 22

A control on overconcentration

Question 23

Explain the following constraint - Scenario Limits

Answer 23

A limit on the estimated loss for a gain scenario

Question 24

Explain the following constraint - Stop-loss Limits

Answer 24

When a loss of a particular size occurs in a specific period - reduce or liquidate portfolio position.

Question 25

Name the 3 factors that influence the types of risk measuers

Answer 25

1. Degree of leverage
2. Mix of risk factor exposure
3. Accounting / Regulatory requirement

Question 26

surplus at risk in regards to VaR

Answer 26

How assets might underperform to their liabilities.

Surplus at risk is an application of VaR; it estimates how much the assets might underperform the liabilities with a given confidence level, usually over a year

Question 27

Liquidity Gap

Answer 27

Relevant to the banks.
Liquidity between the assets and liabilities.
How quickly can I get cash for my assets to pay my liabilities?

Question 28

Is credit spread a market risk sensitivity measure?

Answer 28

No it is not!!!

Question 29

Risky financial assets tend to display

Answer 29

High returns when the marginal value of consumption is low.

and

Low returns when the marginal value of consumption is high.

Question 30

What is the difference between the nominal and risk free interest rate?

Answer 30

Break-even inflation rate

Question 31

The component of the discount rate that is most viable between asset class and another is the ..

Answer 31

Risk preimiums related to cash flow uncertainity.

The size of the risk premiums will vary among asset classes and the variation is largely resposnible for the distinction between one asset class and another.

Question 32

Amount of standard deviation 1% VaR

Answer 32

2.33 Sdv

Question 33

Amount of standard deviation 5% VaR

Answer 33

1.65 Sdv

Question 34

VaR at 1 Standard deviation

Answer 34

16% VaR