Title: Introduction to Value At Risk VaR
1Introduction to Value At Risk VaR
- FIN285 Lecture 7
- Fall 2006
- Readings Dowd Chapter 2,
- Stulz 4.1-4.1.2, box 4.1, 4.1.3-4.1.4
2Value-at-Risk (VaR)
- Probabilistic worst case
- Almost perfect storm
- 1/100 year flood level
3VaR Advantages
- Risk -gt Single number
- Firm wide summary
- Handles futures, options, and other complications
- Relatively model free
- Easy to explain
- Deviations from normal distributions
4Value at Risk (VaR)History
- Financial firms in the late 80s used it for
their trading portfolios - JP Morgan, 1990s
- 415 and VaR
- RiskMetrics, 1994
- Currently becoming
- Wide spread risk summary
- Regulatory
5Value at Risk Methods
- Methods
- Delta Normal
- Historical
- Monte-carlo
- Bootstrap
6Outline
- Definitions
- Parameters
- Regulation
- Limitations
- Expected tail loss (ETL)
- Cash flow at Risk (CAR)
7Defining VaR
- Mark to market (value portfolio)
- 100
- Identify and measure risk (future value)
- Normal mean 100, std. 10 over 1 month
- Set time horizon of interest
- 1 month
- Set confidence level 95
8Portfolio value today 100, Normal value (mean
100, std 10 per month), time horizon 1 month,
95 VaR 16.5
0.05 Percentile 83.5
9VaR Definitions in Words
- Measure initial portfolio value (100)
- For 95 confidence level, find 5th percentile
level of future portfolio values (83.5) - The amount of this loss (16.5) is the VaR
- What does this say?
- With probability 0.95 your losses will be less
than 16.5
10Increasing the Confidence Level
- Increase level to 99
- Portfolio value 76.5
- VaR 100-76.5 23.5
- With probability 0.99, your losses will be less
than 23.5 - Increasing confidence level, increases VaR
11Choosing VaR Parameters
- Holding period
- Risk environment (depends)
- Portfolio constancy/liquidity (short)
- Data quantity (short)
- Confidence level
- Estimate of extreme tails (high)
- Min return
- Data quantity (low)
12Outline
- Definitions
- Parameters
- Regulation
- Limitations
- Expected tail loss (ETL)
- Cash flow at Risk (CAR)
13Regulation
- International bank capital requirements
- Basle accord (1996 amendment)
- Internal models
- Capital requirement k(Average VaR over the
last 60 days)k is between 3 and 4Depends on
past accuracy - VaR parameters
- 99 confidence
- 10 day holding period
14More Thoughts on Regulation and VaR (see box 2.2)
- Somewhat consistent approach (but arbitrary)
- Variability across firms (trusting banks to get
risk management right) - Might banks be able to figure out how to get
around this regulation? - Does this make capital markets more or less
stable?
15Outline
- Definitions
- Parameters
- Regulation
- Limitations
- Expected tail loss (ETL)
- Cash flow at Risk (CAR)
16VaR Limitations
- Uninformative about extreme tails
- Bad portfolio decisions
- Might add high expected return, but high loss
with low probability securities - VaR/Expected return, calculations still not well
understood - VaR is not Sub-additive
17Sub-additive Risk Measures
- A sub-additive risk measure is
- Sum of risks is conservative (overestimate)
- VaR not sub-additive
- Temptation to split up accounts or firms
18Outline
- Definitions
- Parameters
- Regulation
- Limitations
- Expected tail loss (ETL)
- Cash flow at Risk (CAR)
19Portfolio value today 100, Normal returns (mean
100, std 10 per month), time horizon 1
month, 95 VaR 16.5, Expected Tail 79.2,
ETL 20.8
0.05 Percentile 83.5
20Matlab and ETL
- port vector of port values
- z percentile(port,0.05)
- var 100-z
- etl 100-mean( port (portltz))
21ETL versus VaR
- Advantages
- Better information on possible tail losses
- Some better properties (sub-additive)
- Disadvantages
- Sensitive to outliers
- Difficult to estimate (for high confidence
numbers) - More difficult to explain
22Outline
- Definitions
- Parameters
- Regulation
- Limitations
- Expected tail loss (ETL)
- Cash flow at Risk (CAR)
23Cash Flow at RiskStulz 4.1.3-4.1.4
- Cash flow short falls
- EC-C (actual - expected)
- Distribution of this random variable
- Prob( EC-C gt CAR) confidence
- 95 CAR 10 million,
- Prob(Cashflow shortfall lt 10) 0.95
- Prob(EC-C lt 10) 0.95
- 95 confident your cashflow losses are less than
10 million
24VaR versus CAR
- VaR
- Total portfolio Value
- Good for firms with many financial assets
- Actual cash flows not a problem
- CaR
- Immediate cash flows are the item of interest
- Limited financing capabilities
- Can this get blurry?
- Yes, highly leveraged financials can have cash
flow problems (LTCM) - Might still have strong net asset values
- Futures trader (margin calls)