If a capital allocation method allows negative allocations of capital, how does this impact its use?
It’s possible in many capital allocation methods for the capital to be negative, indicating a diversification benefit with other units. But negative capital is not helpful for calculating the RAROC, for pricing, or for performance measurement within the unit. It’s best used for aggregate risk management for the firm.
What is the purpose of holding capital?
- Maintain financial strength (reducing likelihood of insolvency)
- Absorb losses
- Support business growth opportunities and operations
- Meet regulations
- Achieve a target credit rating
Which capital allocation methods allow negative correlations? Which don’t? How does this impact choice of allocation method?
Discrete marginal, Shapley, Covariance, Co-VaR, and Co-TVaR all allow negative correlation. Proportional allocation doesn’t. Allocation methods that allow negative allocation are not useful for measuring manager performance.
What are the types of capital?
Available: The actual capital held. The excess of the MV of the assets over the MV of liabilities.
Regulatory: The amount required to hold to comply with regulations
Economic: The MV of capital required by the firm’s own assessment. The amount required to cover obligations with a given degree of confidence over a specific time horizon.
Why do regulators set capital requirements for banks and insurers?
Banks and insurers are heavily regulated because:
1. of the uncertain nature of the liabilities
2. the complexity of the operations (making it difficult for policyholders and depositers to assess the quality of the firm)
3. the importance of the continued solvency of the firms to the smooth running of the economy
Why should capital not be too high or too low?
- If capital held is too high, the cost of insurance could be too high (because the cost of capital is incorporated in product pricing) and returns could be lower (because capital needs to be quite liquid to absorb losses, so capital can’t be invested in very illiquid assets which tend to have higher returns).
- Capital shouldn’t be too low because the risk of insolvency would be high.
- Must strike a balance and hold sufficient capital to retain policyholder, investor, and counterparty confidence.
What are the sources of capital? And what are their perspectives when it comes to risk?
- Debt holders that expect a fixed return on the capital they provide. They will want the firm to minimize risk to reduce the likelihood that the firm will default.
- Shareholders that expect the remaining return after obligations are met. They will want the firm to take some risks to maximize returns.
What are the capital allocation methods?
Allocation methods based on a risk measure: Proportional, discrete marginal, Covariance, Co-Var, Co-TVaR, Euler, Shapley,
Allocation methods based on default cost: Myers-Read, Kim-Hardy, and Sherris
What is a fair allocation method?
- Full allocation. Total allocated capital should be equal to the firm-wide allocated capital.
- No undercut. The capital allocated to each unit should be less than or equal to the capital the units would require independently (because of diversification). BUs shouldn’t be seen as performing worse within the firm than if they were independent.
- Symmetry. If 2 units provide the same marginal increase in EC to all possible subsets of the firm’s units, they they should be allocated the same capital.
- Consistency. The capital allocation to 2 units shouldn’t be changed if they are combined into 1 unit.
Proportional capital allocation. How it works and pros and cons.
The firm-wide capital is allocated in proportion to the stand-alone capital of the individual units.
Pro: easy to calculate and explain.
Con: Not a fair allocation method
Discrete marginal capital allocation. How it works and pros and cons.
Start with one BU, adding one more BU at a time. The capital allocated to each BU is the difference between the capital required after vs before adding that BU to the group.
Pro: Accounts for the fact that some units hedge the losses of others.
Con: not a fair allocation method, the order that BUs are added makes a difference, and the capital allocated to a unit can be negative.
Shapley capital allocation. How it works and pros and cons.
Perform the discrete marginal allocation approach to all possible orderings of the BUs. The capital allocation is the average marginal capital allocation for each unit over all possible permutations.
Pro: If the risk measure is positive homogeneous, then doubling a unit’s loss results in double the allocated capital to that BU.
Con: Cumbersome to calculate as the number of BUs increases and not a fair allocation method.
Covariance capital allocation. How it works and pros and cons.
Can be used if standard deviation is the risk measure for the aggregate EC.
Pro: A fair allocation method
Con: Standard deviation is not a commonly used risk measure in risk management.
Co-VaR capital allocation. How it works and pros and cons.
Can be used if VaR is the risk measure for the aggregate EC.
Pro: Has a natural interpretation when the aggregate EC is determined through simulation.
Con: Not a fair allocation method
Co-TVaR capital allocation. How it works and pros and cons.
Can be used if TVaR is the risk measure for the aggregate EC.
Pro: A fair allocation method. Has a natural interpretation when the aggregate EC is determined through simulation.
Con: Not very tractable.
Myers-Read capital allocation. How it works and pros and cons.
Based on the value of a default option. A method used for pricing.
Con: Lack of connection between the aggregate economic capital (which is assumed given) and the allocation method. Allows negative capital allocations.
Sherris capital allocation. How it works and pros and cons.
Similar to Myers-Read, based on the value of a default option, but EC for the firm and BUs is adjusted to allow for the value of the default option before allocation of assets.
Con: Allows negative capital allocations.
Kim-Hardy capital allocation. How it works and pros and cons.
Can be decomposed into separate parts, depending on the purpose of the capital allocation. For example, allocates capital for (liability risk, reserve inadequacy risk, investment risk) or (line manager, investment manager, and risk manager).
What is ROC? How to calculate?
Return on capital. An effective measure of profitability.
Net income for the period / average actual capital for the period.
What is RAROC? How is it different from ROC?
Risk-adjusted return on capital. ROC that has been adjusted for risk. For example:
1) We can use expected income instead of actual income to smooth out business volatility.
2) We can reduce CFs by the cost of capital
How to calculate each type of RAROC
Prospective RAROC = expected net income / capital (available or economic)
Retrospective RAROC = actual net income / average capital over the period (available or economic)
How to decide on the way to calculate RAROC?
1) For measuring employee performance, make sure only factors in their control are reflected. Use a bottom-up approach.
2) For risk budgeting, use a top-down approach.
Purpose of RAROC
1) Help people understand how effectively the firm is using its capital
2) measure the performance of business units (retrospective)
3) make decisions for risk budgeting (prospective)
4) determine the cost of capital to incorporate in pricing
Why does using book values for ROC calcs cause issues?
1) Book value measures are inconsistent between and within firms due to their reliance on historical costs
2) Book values don’t take risk into consideration
