18. Risk-Adjusted Measures of Profit and Capital Allocation Flashcards
What is the formula for return on capital?
(Net Income)/(BV of Equity+BV of Debt)
What is the formula for return on equity?
(Net Income)/(BV of Equity)
What are 2 problems with accounting measures like ROE?
- Considers book value instead of market value. Two firms having the same assets might have a different book value of assets.
- Does not take risk into account.
To solve the issues of looking at book value and not considering risk, what do risk-adjusted measures of performance do?
- Use market value
- Use expected income and economic capital to integrate risk.
What are the downsides of using RAROC?
There are multiple definitions of the RAROC: prospective, retrospective, using actual net income, expected net income.
It also introduces subjectivity with the expected income.
Name 4 desirable characteristics for an allocation procedure to have.
- Full allocation
- No undercut (a business unit should not be allocated more capital than if it were alone)
- Symmetry (same marginal increase)
- Consistency (combining units)
Describe proportional allocation
o Based on the stand-alone capital of individual units
o Full allocation, no undercut, symmetry, not consistent
Describe marginal allocation
o Adding the capital needed, unit by unit (in sequence)
o Dependent on the order
o Full allocation, no undercut, symmetry, not consistent
Describe Shapley allocation
o Average of all order of discrete marginal allocation
o Full allocation, no undercut, symmetry, not consistent
Describe Covariance allocation
o Using Cov(Xi, X)/sqrt(V(x)) as proportion
o Full allocation, no undercut, symmetry, consistent
o Can only be used when std is used: not very common
Describe Co-VaR allocation
o Uses EV knowing X is VaR(X)
o Full allocation, undercut, symmetry, consistent
o Can only be used with VaR
o Lack of stability in the allocation
Describe Co-CTE allocation
o Uses expected value of X knowing that the total allocated capital is greater than the quantile.
o Full allocation, no undercut, symmetry, consistent
o Much more stable than Co-VaR
Describe Euler allocation methods
If insead of using a “in or out” method (like discrete marginal or Shapley) we use a continuous marginal approach, we are using a Euler allocation for a certain risk measure. co-VaR and co-CTE are examples of Euler allocation methods.
What is the difference with capital allocation based on default cost compared with other methods?
Capital allocation based on default cost differs from other allocation methods because it directly ties the allocated capital to the cost of potential default, rather than focusing on risk contributions in a purely statistical sense.
Describe the Myers-Read Allocation
o Based on the value of a default option (if Assets < Liabilities)
o Allocates capital based on the contribution to the default
o Captures the advantages of Euler Allocation
o Drawback: lack of connection between aggregate economic capital and allocation method. Allocated capital might also be negative.
Describe the Sherris Allocation
o Similar to Myers-Read but focuses on the impact of each unit on the firm’s expected default cost rather than default probability alone.
o Economic capital for the firm and individual lines is determined taking the default option into account, explicitly, before allocating capital.
Describe the Kim-Hardy Allocation
o Same starting point as Sherris, but considers it as a real-word risk measure
o Advantage: can be decomposed into separate parts
o Can split the diversification benefit, great for evaluating management perf.
(Concept: Allocates capital based on the conditional tail expectation of each business unit’s loss contribution, ensuring that capital is distributed in a way that accounts for extreme tail risk. Instead of focusing purely on expected default costs, it considers the conditional expectation of losses in severe loss scenarios, making it a tail-sensitive method.)
Why would an allocation of capital made for pricing purposes might not be fit for budgeting or assessing the performance of managers?
- Negative capital allocation might not be fit for any use.
- You might not want to use a capital allocation that would encourage a manager to take more risk, but this method could be perfectly appropriate for pricing purposes : to consider risk.
What are disadvantages of the allocation methods broadly centered on the aggregate risk measure for the firm.
- Allocated capital can be negative (can be useful for assessing risk)
- If used for pricing, may give rise to arbitrage. Value of insurance should not depend on the structure of the firm writing it.
- May not always recognize very different types of risk involved
