Objective 3

Question 1

What is the difference in credit exposure in bonds and derivatives?

(VaR18)

Answer 1

• Bonds
  
  • Credit exposure = principal
  • Can vary before expiration if the market value of the bond fluctuates
• Derivatives
  
  • Credit exposure = netted payments (++ complex!)
  • Represents the positive value of the contract, which is much less than the notional account

Question 2

Relate the following against the four axioms of coherent risk measures:

• Maximum
• VaR
• CTE
• E(Loss)
• StdDev(Loss)
• E(Loss) + 2*StdDev(Loss)

Answer 2

Question 3

What are the three risk factors in credit risk?

(VaR18)

Answer 3

1. Default risk
   
   • Risk of default by the counterparty
   • Measured by the probability of default (PD)
2. Credit exposure
   
   • Risk of fluctuations in the market value of the claim on the counterparty
   • At default, this is known as exposure at default (EAD)
3. Recovery
   
   • Uncertainty in the fraction of the claim recovered after default
   • Recovery = 1 - loss given default (LGD)

Question 4

What are netting arrangements?

(VaR18)

Answer 4

• Important method to control credit risk exposures
• Allows the offsetting of oblications under the same agreement, resulting in one single net claim against the counterparty

Question 5

What are complementary tools for VaR?

(ERM102)

Answer 5

1. Alternatives to VaR
2. Stress testing
   
   • Strongly encouraged by regulators
3. Stressed VaR
   
   • Larger capital requirements than VaR
4. Sound judgment

Question 6

What are VaR’s shortcomings?

(ERM102)

Answer 6

1. VaR is not coherent (fails subadditivity property)
2. VaR does not consider tail risk (risk blindness)
3. The real distribution of returns is not normally distributed
4. Different companies use different methodologies to calculate VaR
   
   • e.g., Parametric (VarCovar), Historical simulation, Monte Carlo
5. Historical data and observation period
   
   • VaR reflect more historical than the present
6. Agency problems
   
   • Used to evaluate agents, traders, managers
7. Regulatory disclosure

Question 7

What is ECE?

(VaR18)

Answer 7

Expected Credit Exposure

= expected value of asset replacement value (if positive) on a target date

Question 8

What should the actuary perform in a data review?

(OR - ASOP23)

Answer 8

• Data definitions
  
  • Make a reasonable effort to determine the definition of each data element
• Identify questionable data values
  
  • Identify data values that are materially questionable
  • Consider further steps if questionable data could have a material impact
• Review of prior data
  
  • If similar review ahs been donde before, review current data for consistency with data previously used

Question 9

What is ECL?

(VaR18)

Answer 9

Expected Credit Loss

ECL_t = ECE_t x (1-f) x k_t

where

• k_t = (1-c_t-1) d_t *= default
• f* = recovery rate

Question 10

How is the probability of default (PD) assessed?

(VaR18)

Answer 10

1. Actuarial models
   
   • Similar to survivorship models where c_n is a cumulative default rate
   • k_i = (1-c_i-1)d_i
2. Market-based model
   
   1. Reduced form model
      
      • P* = 100 / (1 + y*)^T ~ y + π(1-f)
      • where probability of default is π
   2. Structural Model
      
      • See Merton model (~ Black-Scholes)

Question 11

What are alternatives to VaR?

(ERM102)

Answer 11

1. Expected shortfall (TVaR, CTE) - coherent
2. Conditional VaR (CVaR) - coherent, weighted average of VaR and ES
3. Modified VaR (mVaR) - considers skewness and kurtosis
4. CoVaR - conditional

Question 12

What should be documented by the actuary in terms of the data?

(OR - ASOP23)

Answer 12

1. The process the actuary followed to evaluate the data
2. A description of any material defects the actuary believes are in the data
3. A description of any adjustments or modifications made to the data, other than routine correction made by reference to such documents
4. Any other documentation necessary to comply with the disclosure requirements

Question 13

What are the limitations of an actuary’s responsibility with respect to data?

(OR - ASOP23)

Answer 13

1. The actuary is not required to determine whether the data or other information provided has been falsified or intentionally misleading
2. The actuary is not required to develop additional data compilations solely for the purpose of searching for questioanble or inconsistent data
3. The actuary is not required to audit the data

Question 14

According to ASOP23, what are some considerations in the selection of data?

(OR - ASOP23)

Answer 14

1. Appropriateness for the intended purpose of the analysis
2. Reasonableness and comprehensiveness of the necessary data elements
3. Any known, material limitations of the data
4. The cost and feasibility of obtaining alternative data
5. The benefit to be gained from an alternative data set or data source as balanced against its availability and the time and cost to collect and compile it
6. Sampling methods, if used to collect the data

Question 15

What is PVECL?

(VaR18)

Answer 15

Present value of expected credit loss

PVECL = Sum over t ( ECL_t x PV_t)

~ [(1/T) Σ ECE_t] (1-f) [Σk_t] [(1/T) Σ PV_t ]

= Avg exposure x LDG x Avg PD x Avg PV

Question 16

What are the four axious for coherent risk measures?

(ERM105)

Answer 16

1. Subadditivity
2. Monotonicity
3. Positive homogeneity
4. Translation invariance

Question 17

What are two approaches to calculate the Basel II capitals?

(VaR18)

Answer 17

1. Standardized approach
   
   • Risk weights are assigned to external credit ratings
2. Internal ratings-based (IRB) approach
   
   • Can be:
     
     1. Foundation IBR approach
        
        • Banks estimate PD
        • Supervisors supply other inputs
     2. Advanced IBR approach
        
        • Banks can supply other inputs as well

Question 18

Compare VAR with Credit Risk

(VAR18)

Answer 18

• Source of risk
  
  • Trad VAR - market risk
  • CR - market, default, recovery risks
• Unit to which risk limits apply
  
  • Trad VAR - trading organizations
  • CR - legal entity of counterparty
• Time horizon
  
  • Trad VAR - short term (days)
  • CR - long term (years)
• Portfolio
  
  • Trad VAR - static portfolio
  • CR - dynamic portfolio
• Mean reversion
  
  • Trad VAR - not important
  • CR - very important
• Legal issues
  
  • Trad VAR - not important
  • CR - very important