Tia Brehm C.2 Part 2

Front 1

What is a co-measure?

Back 1

Contribution of business unit to other risk measures

For a risk measure:ρ(Y) = Eh(Y) · L(Y)g(Y)

We have a co-measurer(Xj) = Eh(Xj) · L(Y)g(Y)

We require h() to be additive: h(x + y) = h(x) + h(y)

The co-measures sum to the risk measure

ρ(Y) = ∑j r(Xj)ERA

Front 2

Are co-measures marginal?

Back 2

Up to 1 co-measure will be marginal

Front 3

What makes an allocation a Marginal Method?

Back 3

A change in the company’s risk measure from a small change in a single business unit is attributed to that business unit

Front 4

What is a suitable allocation?

Are marginal allocations suitable?

Back 4

If a unit that has above average return on capital grows, then the return on capital for the entire firm will increase.

Yes. A marginal allocation will always be Suitable.

Front 5

What is a scalable risk measure?

Back 5

ρ(aY) = a · ρ(Y)

Front 6

How to directly calculate a marginal allocation from the risk measure?

Back 6

r(Xj) = lime→0 [ρ(Y + e · Xj) − ρ(Y) ] / e

Front 7

What is risk adjusted profit?

Back 7

Pj / r(Xj)

Pj = profit from unit j

r(Xj) is the allocated risk measure

For this to be true risk adjusted profit, need:r(Xj) ∝ Market Value of Risk

Front 8

Why would we use multiple risk measures to calculate risk adjusted profit?

Back 8

Pjr(Xj)

Pjis profit

r(Xj) is the allocated risk measure

• Need r(Xj) ∝ Market Value of Risk

• We don’t know Market Value, so we use several riskmeasures - and hope they indicate a consistent result

Front 9

How can we use a Stop-Loss to allocate cost of capital? (4)

Back 9

• The Market Price of a stop loss is the cost of capital

• Could use the Mean on Transformed probabilities

• Minimum Entropy Transform

• Mean + 30% Standard Deviation

Front 10

How can options be used to allocate cost of capital?Why aren’t Options considered a good solution?

Back 10

Use the Option Value of: The right of the business unit to callon the capital of the firmTiming is not fixed, thus they are difficult to value

Front 11

Why is allocating Capital considered Arbitrary and Artificial

Back 11

• Arbitrary - different risk measures give differentallocations, so the allocations are different• Artificial - each business unit has access to the capital ofthe entire firm, not just a portion of it

Front 12

Co-measure of VaR

Back 12

r(Xj) = E[Xj|F(Y) = α ]

The expected loss in unit j when the firm has a loss at the αthpercentile

h(Y) = Y ; L(Y) = 1 ; g(Y) = F(Y) = αE

Front 13

Co-measure of TVaR

Back 13

r(Xj) = E[Xj |F(Y) > α ]

The expected loss in unit j when the firm has a loss excess ofthe αth percentileh(Y) = Y ; L(Y) = 1 ; g(Y) = F(Y) > αE

Front 14

Co-measure of Standard Deviation

Back 14

r(Xj) =Cov(Xj,Y) / Stdev(Y)

This is the Marginal Co-measureh(Y) = Y − EY ; L(Y) = Y − EYStdev(Y); g(Y) = True

Front 15

What is the Co-measure of EPD?

Back 15

r(Xj) = (CoTVaRα − CoVaRα) · (1 − α)

This is analogous to the definition of EPD.

Front 16

List Advantages of Economic Capital (4)

Back 16

• Unifying Measure for all risks across anorganization

• More Meaningful than RBC or Capital AdequacyRatios

• Firm Quantifies Risks via ProbabilityDistributions

• Framework for setting acceptable risk levels

Front 17

What is the difference between Expected Policyholder Deficit and Value of Default Put at some percentile α

Back 17

EPD is the expected losses excess of VaRα

Value of Default Put is the Market Value of protecting against losses excess of VaRα

Front 18

What properties does a scalable risk measure have?

Back 18

It is both Marginal and Additive