CH10 - Economic Capital and CVaR

Question 1

Difference between economic and regulatory capital

Answer 1

-EC: serves as a buffer against unexpected losses, and is not to be spent. Amount needs to be significant, and more needs to be allocated to riskier transactions. Once capital is allocated to the portfolio, it is allocated to individual transactions for pricing purposes, and to measure the reward performance (RAROC)
RC: regulators impose minimum capital requirements on FIs. Their mission is to protect the public’s deposits, and the fin system in general. They usually set high capital requirements so that these entities stay solvent. Banks still reluctant to measure profitability based on reg capital, prefer eco capital

Question 2

Default Risk vs Credit Risk

Answer 2

Two distinct views of credit losses: the default view and the MTM view.

• Default: even if cntrpty gets downgraded, the firm believes that they will repay. Its view of the exposure doesn’t change much - no losses are expected. Vast majority of industrial companies use this approach
• MTM: large FIs judge their performance on the economic value of the exposures they hold (not the # of defaults). They experience losses (gains) if the MV of their credit exposures falls (rises). (e.g. downgrade from rating agency)

Question 3

MTM continued

Answer 3

-The paper (MTM) loss would become a real loss if the firm decides to exit the position, yet no default has occurred.
Adv: based on market view, all available info
Disadv: can’t observe MV for companies that are not traded; changes in spreads encompass many factors, such as technical, macroeconomy etc.

Question 4

What is CVaR?

Answer 4

• The methodology firms use to size the amount of economic capital needed to support credit activities. It allows the firms to define the amount of losses it is prepared to withstand.
• Question: How much can my organisation lose from credit exposures?
• Three step actuarial framework:
  1. Over what time horizon are we concerned?
  2. What is the probability of losses of a certain size?
  3. How confident do we want to be in our ability to withstand losses?

Question 5

Determinants of CVaR: Time Horizon

Answer 5

See ratings matrix. An entity with a AA rating has a 90.24% chance to remain AA and 0.04% chance of defaulting on year later.
The same firm has a 74.99% chance of remaining an AA, and a larger chance of default after 3 years.
-CVaRs for longer time horizons will be larger
-Time horizon is also a measure of losses because it is a function of how quickly the firm is able to react to losses

Question 6

Determinants of CVaR: Loss Distribution

Answer 6

• Describes the relative frequency (probability) associated with all possible loss levels that a portfolio could experience within a given time horizon
• Shape: high probability of experiencing small losses, and a low probability of experiencing large losses (negative skew, fat tail)
• In the MTM view, we consider a loss distribution based on the probability of an obligor’s rating migration and MV, not its frequency and severity of default

Question 7

Determinants of CVaR: Confidence Level

Answer 7

-How certain do we want to be that the firm has enough capital to withstand a very large loss?
-A higher confidence level goes hand-in-hand with a lower risk appetite, and vice-versa
E.g. a firm chooses a CI at a point on the far right of the curve at 99.9%, with only 0.1% to the right. If this point represents losses of $100m, then the firm will hold capital to withstand losses up to this point.

Question 8

How is the Loss Distribution created?

Answer 8

We create a loss distribution through these three building blocks:

1. Probability of default for a single exposure: either using ratings for large companies, or internal ratings for small companies
2. Assessing the GE and expected recovery should the counterparty default.
3. Portfolio effects: joint probability distribution, which tells us the probability of all possible combinations of default/no default across the loans in the portfolio (correlations)