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Introduction to Value At Risk VaR

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Cash flow at Risk (CAR) ... VaR versus CAR. VaR. Total portfolio 'Value' ... CaR. Immediate cash flows are the item of interest. Limited financing capabilities ... – PowerPoint PPT presentation

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Title: Introduction to Value At Risk VaR


1
Introduction 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

2
Value-at-Risk (VaR)
  • Probabilistic worst case
  • Almost perfect storm
  • 1/100 year flood level

3
VaR Advantages
  • Risk -gt Single number
  • Firm wide summary
  • Handles futures, options, and other complications
  • Relatively model free
  • Easy to explain
  • Deviations from normal distributions

4
Value 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

5
Value at Risk Methods
  • Methods
  • Delta Normal
  • Historical
  • Monte-carlo
  • Bootstrap

6
Outline
  • Definitions
  • Parameters
  • Regulation
  • Limitations
  • Expected tail loss (ETL)
  • Cash flow at Risk (CAR)

7
Defining 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

8
Portfolio value today 100, Normal value (mean
100, std 10 per month), time horizon 1 month,
95 VaR 16.5
0.05 Percentile 83.5
9
VaR 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

10
Increasing 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

11
Choosing 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)

12
Outline
  • Definitions
  • Parameters
  • Regulation
  • Limitations
  • Expected tail loss (ETL)
  • Cash flow at Risk (CAR)

13
Regulation
  • 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

14
More 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?

15
Outline
  • Definitions
  • Parameters
  • Regulation
  • Limitations
  • Expected tail loss (ETL)
  • Cash flow at Risk (CAR)

16
VaR 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

17
Sub-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

18
Outline
  • Definitions
  • Parameters
  • Regulation
  • Limitations
  • Expected tail loss (ETL)
  • Cash flow at Risk (CAR)

19
Portfolio 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
20
Matlab and ETL
  • port vector of port values
  • z percentile(port,0.05)
  • var 100-z
  • etl 100-mean( port (portltz))

21
ETL 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

22
Outline
  • Definitions
  • Parameters
  • Regulation
  • Limitations
  • Expected tail loss (ETL)
  • Cash flow at Risk (CAR)

23
Cash 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

24
VaR 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)
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