R40: Measuring and Managing Market Risk Flashcards
Value at Risk (VaR)
- the minimum loss that would be expected a certain percentage of the time over a certain time period, given assumed market conditions
- meant to capture market risk for equity prices, interest rates, exchange rates, and commodity prices.
VaR at 1%
2.33 sd
VaR at 1sd
16% VaR
VaR at 5%
1.65 sd
parametric method
- generally assumes distribution of returns on risk factors is normal
- simple & straightforward
- VaR sensitive to E(R) and sd
- difficult to use if the portfolio contains options as that threatens normality
historical simulation method process
- for certain time period (ie 2 years), weight the portfolio every day, calculate a daily return for each day
- 500 hundred observations, calculate the day to day losses and rank them
- then take percentiles (5% VaR), that’s the VaR
historical simulation method notes
- what if you a bond today that didn’t exist 2 years ago,
- a lot of modifications, use of proxies
- not constrained by assumption of normality
- estimation of VaR using what actually happened (while keeping in mind that the past may not repeat itself)
monte carlo simulation
- same method of ranking losses
- not constrained by any distribution
- avoids complexity of the parametric method when the portfolio has many risk factors
Conditional VaR
- relies on a particular VaR
- it is the average loss if the VaR loss is exceeded
- best derived using historical simulation and monte carlo
Incremental VaR
- how a VaR will change if a position size is changed relative to the remaining position
- before vs after calculation
Marginal VaR
- conceptually the same as incremental VaR, but for very small change in position
- change in VaR given a $1 or 1% change
Relative VaR
- ex-ante tracking error
- the degree to which the performance of a given portfolio might deviate from its benchmark
- (portfolio holdings - benchmark holdings): active positions
Sensitivity Risk Measures
- examines how performance responds to a single change in an underlying risk factor
- equities: factor sensitivities
- fixed income: duration and convexity
- options: delta, gamma, and vega
Scenario risk measures
- estimates the portfolio return that would result from a hypothetical change in markets or a repeat of a historical event.
- multiple factor movements (i.e vega, delta is at a point in time)
Historical Scenario Measures
- portfolio values are re-measured
- equities using historical prices to model behavior
- fixed income- re-priced based on conditions that pre-vailed at the time, using the inputs to a valuation model that existed at that time (interest rates, credit spreads, etc)
- scenario is run as if total price action across the scenario period happened instantaneously.
Output to historical scenario measures
- total return
- total return vs benchmark
- extra collateral/cash requirements (effects of margin calls and the cascading effects)
Modified approach to hist. scenario measures
-staggered scenario which allows expected management action
Hypothetical scenarios
- imagined scenarios
- those that have never been experienced historically
- justification: the past doesn’t repeat itself exactly
- reverse stress test: start with exposure, and then determine an event that causes exposure
- design rare, but not impossible scenario (earthquake, war)
- goal is to understand risk, not eliminate them
Limits placed on risk measurements
- risk budgeting
- position limits
- scenario limits
- stop-loss limits
Risk budgeting
- total risk allocated to sub-activities
- VaR 4 million: budget 2m to market risk, 1.5m to credit risk, 0.5m to operational risk
Position limits
-control on over-concentration
Scenarion limits
-a limit on the loss for a given scenario
stop loss limit
-if a certain threshold for losses is breached during a specific period, liquidate or reduce position
3 factors that influence the types of risk measures
1) degree of leverage
2) mix of risk factor exposures
3) accounting/reg requirements
economic capital
the amount of capital a firm needs to hold if it is to survive severe losses from the risks of its business
What do we want to do with duration if the yield curve rises
We want to reduce duration.
-duration is a bond’s price sensitivity to changes in the interest rates, if interest rates rise, bond prices go down, so we want a lower duration
