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)