Financial Risk Management
Regulatory Capital Standards with VaR Following P. Jorion, Value at Risk, McGraw-Hill Chapter 3
Daniel HERLEMONT
Why regulation?
Externalities Deposit insurance Moral hazard – less incentives to control risk Basel Accord 1988 measure of solvency = Cooke ratio
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Cooke ratio The Basel Accord requires capital to be at least 8% of the total risk-weighted assets of the bank. Capital definition is broad: Tier 1. Stocks, reserves (retained earnings) (≥ ≥50%) Tier 2. Perpetual securities, undisclosed reserves, subordinated debt >5 years.
Daniel HERLEMONT
Weights 0%
Asset Type
Cash Claims on OECD central government local currency claims on central banks
20%
Cash to be received OECD banks and regulated securities firms non-OECD banks below 1 year multilateral development banks foreign OECD public sector entities
50%
residential mortgage loans
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Weights Asset Type 100%
Claims on private sector (corp. debt, equity…) Claims on non-OECD banks above 1 year Real estate Plant and equipment
At national discretion 0-50%
Claims on domestic OECD public-sector entities
OECD (Organization for Economic Cooperation and Development): Austria, Belgium, Canada, Denmark, France, Germany, Greece, Iceland, Ireland, Italy, Luxembourg, The Netherlands, Norway, Portugal, Spain, Sweden, Switzerland, Turkey, UK, Japan, Finland, Australia, New Zealand, Mexico, Czech Republic, Hungary, Korea and Poland.
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Credit Risk Charge
CRC = 8% ⋅ ∑ wi ⋅ asseti i
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Activity Restrictions
Restrictions on large risks (over 10% of capital) must be reported over 25% prohibited total of large risks can not exceed 8*capital
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Criticism of 1988 Approach
Regulatory arbitrage (securitization) Credit derivatives Inadequate differentiation of credit risks Non-recognition of term structure effect Non-recognition of risk mitigation Non-recognition of diversification Non-recognition of market risk Daniel HERLEMONT
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Market Risk Amendment 1996
Trading book – financial instruments that intentionally held for short-term resale and are typically marked-to-market Banking book – other instruments, like loans. TRC = CRC + MRC Tier 3 capital: short-term subordinated debt (must be less than 2.5*Tier1) Daniel HERLEMONT
The Standardized Model
Maturity bands Partial netting Duration weights No diversification across risks
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The Internal Models Approach
Quantitative parameters for VaR 10 business days or 2 weeks 99% confidence level at least one year of historical data updated at least quarterly
Treatment of correlations – can be recognized
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k 60 MRCt = Max ∑ VaRt −i , VaRt −1 + SRCt 60 i =1 1 day can be scaled by square root of 10 Typically average times k is used. k initially is set to 3, but later it can be increased Specific Risk Charge SRC is added.
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Basel Rules MRC
Market Risk Charge = MRC SRC - specific risk charge, k ≥3.
k 60 MRCt = Max ∑ VaRt −i , VaRt −1 + SRCt 60 i =1 VaRt = VaRt (1d , 99%) × 10 Daniel HERLEMONT
Backtesting
Verification of Risk Management models. Comparison if the model’s forecast VaR with the actual outcome - P&L.
Exception occurs when actual loss exceeds VaR. After exception - explanation and action.
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Stress
Designed to estimate potential losses in abnormal markets. Extreme events Fat tails Central questions: How much we can lose in a certain scenario? What event could cause a big loss?
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Further development
Basel II Better treatment of credit risk Operational risk
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Non banks
Securities Firms Insurance companies Pension funds SEC reporting 7A in 10K
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FRM-99, Question 89
What is the correct interpretation of a $3 overnight VaR figure with 99% confidence level? A. expect to lose at most $3 in 1 out of next 100 days B. expect to lose at least $3 in 95 out of next 100 days C. expect to lose at least $3 in 1 out of next 100 days D. expect to lose at most $6 in 2 out of next 100 days
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Properties of Risk Measure
Monotonicity (XR(Y)) Translation invariance R(X+k) = R(X)-k Homogeneity R(aX) = a R(X) (liquidity??) Subadditivity R(X+Y) ≤ R(X) + R(Y) the last property is violated by VaR!
Daniel HERLEMONT
No subadditivity of VaR
Bond has a face value of $100,000, during the target period there is a probability of 0.75% that there will be a default (loss of $100,000). Note that VaR99% = 0 in this case. What is VaR99% of a position consisting of 2 independent bonds?
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FRM-98, Question 22
Consider arbitrary portfolios A and B and their combined portfolio C. Which of the following relationships always holds for VaRs of A, B, and C? A. VaRA+ VaRB = VaRC B. VaRA+ VaRB ≥ VaRC C. VaRA+ VaRB ≤ VaRC D. None of the above
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Confidence level
low confidence leads to an imprecise result. For example 99.99% and 10 business days will require history of 100*100*10 = 100,000 days in order to have only 1 point.
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Time horizon
long time horizon can lead to an imprecise result. 1% - 10 days means that we will see such a loss approximately once in 100*10 = 3 years. 5% and 1 day horizon means once in a month. Various subportfolios may require various horizons.
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Time horizon
When the distribution is stable one can translate VaR over different time periods.
VaR (T days ) = VaR (1 day ) T This formula is valid (in particular) for iid normally distributed returns.
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FRM-97, Question 7
To convert VaR from a one day holding period to a ten day holding period the VaR number is generally multiplied by: A. 2.33 B. 3.16 C. 7.25 D. 10
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