Measuring and Managing Market Risk Flashcards
An advantage of statistical factor models
They make minimal assumptions.
However, the interpretation of statistical factors is generally more difficult than the interpretation of macroeconomic and fundamental factor models.
Assumption of CAPM
- Perfect competition - Frictionless and can borrow a the RfR
- Rational, mean-variance optimizer
- Perfect information (same variance and covariance matrix)
What is the purpose of VaR
Value at Risk is to capture market risk.
Equity prices
Commodity prices
Forex
Interest rates
Does not tell about about average loss
How to interpret a one day 95% VaR
95% confidence that we will NOT lose more than … per day
with 95% probability, we will experience a maximum loss of …
How to interpret 5% VaR
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)
3 different ways to estimate VaR
Parametric method
Historical simulation method
Monte Carlo Simulation
Explain Parametric Method
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
Calculate VaR for parametric method
[Expected return - Z* Portfolio standard dev]*(-1) * Pv
Z = Standard deviation number
Pros and Cons of parametric method
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.
Historical simulation method
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
.
Brief characteristics of historical simulation method
Not constrained by normality assumption
Estimates VaR based on what actually happened
Can handle any kind of financial instruments
Monte Carlo Simulation
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
Conditional VaR - CVaR
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
Incramental VaR - IVaR
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
Marginal VaR - MVaR
Conceptually the same to IVaR, but reflects the effects of a very small change in a position - 1 unit change in position.
Relative VaR - Ex Ante tracking error
The degree to which the performance of a given portfolio might deviate from a benchmark.
Portfolio vs Benchmark
What is Sensitivity risk measure
Examines how performance responds to a single change in an underlying risk factor.
Remember; How SENSITIVE a FACTOR is to a change
What is scenario risk measure
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
Sensitivity and Scenario vs VaR
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
Constraints in measuring and managing market risk
Risk Budgeting
Position Limits
Scenario Limits
Stop-loss Limits
Explain the following constraint - Risk Budgeting
Total risk appetite allocated to sub activities
Explain the following constraint - Position Limits
A control on overconcentration
Explain the following constraint - Scenario Limits
A limit on the estimated loss for a gain scenario
Explain the following constraint - Stop-loss Limits
When a loss of a particular size occurs in a specific period - reduce or liquidate portfolio position.
Name the 3 factors that influence the types of risk measuers
- Degree of leverage
- Mix of risk factor exposure
- Accounting / Regulatory requirement
surplus at risk in regards to VaR
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
Liquidity Gap
Relevant to the banks.
Liquidity between the assets and liabilities.
How quickly can I get cash for my assets to pay my liabilities?
Is credit spread a market risk sensitivity measure?
No it is not!!!
Risky financial assets tend to display
High returns when the marginal value of consumption is low.
and
Low returns when the marginal value of consumption is high.
What is the difference between the nominal and risk free interest rate?
Break-even inflation rate
The component of the discount rate that is most viable between asset class and another is the ..
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.
Amount of standard deviation 1% VaR
2.33 Sdv
Amount of standard deviation 5% VaR
1.65 Sdv
VaR at 1 Standard deviation
16% VaR
