ERA 2 TIA Flashcards
What are the major differences in the 1st and 2nd
evolutionary step in Decision Analysis?
- Use of Distributions for the inputs instead of
fixed amounts - Output is also a Distribution
What is the major difference between the 2nd and 3rd
evolutionary step in Decision Analysis?
Use a Risk Preference (Utility) function to value
the possible outcomes
What is the argument that the 3rd evolutionary step
in Decision Analysis is Unnecessary
Firms only compensate owners for systemic risk,
since the firm-specific risk is averaged out.
therefore, no need for formulations of corporate risk preferences; only systemic risk should be managed
Name some reasons why companies should pay
attention to firm-specific risk (3)
- Management cannot easily separate firm-specific
vs. systemic risk - Some risks are instantaneous, and can’t be
managed through discounting - market based information is too noisy to use for
cost-benefit analysis
Owners and Management want corporate policy that
makes risk management decisions more (4):
- Objective
- Consistent
- Repeatable
- Transparent
Spetzler parameterizes a Utility function for
management. What are the benefits of using a Utility function to
make decisons? (3)
- Transparent
- Objective
- Mathematical
Walls identifies an efficient set of portfolios for the
firm to invest in. Why is this not sufficient to select the best portfolio?
We need the company risk preference to select the
optimal portfolio along the efficient frontier
According to Mango what 3 questions does Walls ask?
- How much risk are we willing to tolerate
- How much reward are we willing to give up for a given
reduction in risk - Are the risk-reward tradeoffs along the efficient frontier
acceptable to us?
The first two come from the parameterized utility function
It’s possible there are no options on the efficient frontier that
are acceptable
Why is allocating capital considered irrelevant? (2)
- All of the company’s capital supports each policy
- Allocating cost of capital is preferred
What risk sources should capital be allocated to?
- Risk taking sources (eg. products)
- Non Risk taking sources (eg. credit risk)
What is RORAC?
Return On Risk Adjusted Capital
1. Allocate Capital on a risk adjusted basis
2. Apply a company wide hurdle rate to determine
the cost of capital in $
3. This is a form of cost of capital
How do Merton & Perold define the cost of capital?
Amount to purchase a guarantee that the firm will
meet its obligations
How do we use Cost of Capital to determine if a
course of action is suitable?
EVA = NPV − [Cost of Capital] > 0
Economic Value Added
Under Capital Allocation, how do we determine if a
course of action is suitable?
for example a purchase of additional reinsurance
NPV > Cost of Capital
[Net Reinsurance Cost] < −∆ Capital · [Hurdle Rate]
~~~
That is the benefit to cost of capital should be greater than
the reinsurance cost
~~~
Reinsurance Premium 30m Expected Reinsurance Benefit 20m Net Reinsurance Cost 10m ~~~
∆ Capital -100m
Hurdle Rate 12%
~~~
```
10m < 12m
Cost < Benefit
~~~
What is Value at Risk VaRα?
The loss at the αth percentile.
VaRα = E[Y|F(Y) = α]
What is Tail Value at Risk TVaRα?
The average loss excess of the percentile α
TVaRα = E[Y|F(Y) > α]
What is Excess Tail Value at Risk XTVaRα?
Conceptually, the expected losses are funded by premium.
The excess is funded by capital - This is what XTVaR
represents.
XTVaRα = E[Y | F(Y) > α] − E[Y]
= TVaRα - Mean
What is Expected Policyholder Deficit EPD?
If capital is set as VaRα then EPD is the expected loss given default, times the probability of default.
EPD = (TVaRα − VaRα) · (1 − α)
Why does Venter not recommend VaR as a risk
measure for insurance companies?
It is too simplistic for insurers, which tend to use a number of
risk measures, many of which are more informative than VaR
Why shouldn’t we use a 1-in-3000 year risk metric? (3)
- Not able to accurately measure the losses so deep in the tail
- Selection of 1-in-3000 is arbitrary
- Better to choose probability levels that are less remote, but still impact the company
What features does the following risk measure have? (2)
E[Y · e^(cY/EY)]
- Captures all the moments
- Usually only exists if there is a maximum loss
What is the Value of the Default Put Option?
The market cost of purchasing insurance to cover any losses, when in default.
If VaRα is the capital level, then EPD is the expected unconditional loss, and the Default Put is the Market Value.
What is a Probability Transform?
How can we use it to calculate risk measures?
- A probability transform changes the density function -
usually increasing the the density of worse losses - A risk measure (such as mean) can be calculated on the
transformed probabilities
What is the Esscher Transform?
f^*(y) = k · e^y/c · f(y)
What is a Complete Market?
A market where any risk can be sold
What Probability Transforms are favored in
incomplete markets? (2)
- Minimum Martingale Transform (MMT)
- Minimum Entropy martingale Transform (MET)
- They give reasonable approximations for reinsurance
prices
What transform can be used to model prices for
bonds and catastrophe bonds?
The Mean under the Wang transform closely approximates
the market value for bonds and catastrophe bonds
How to calculate Blurred VaRα?
Uses η(p) to weigh the losses, with the most weight at Y = F^−1(α), and the weight decreasing to either side.
E[Y · η(F(Y))] η(p) = e^[−θ(p−α)^2]
Large θ makes it tight around α
What market considerations should an insurer take
into account when setting capital?
- Some customers want a well capitalized insurer, others
want a better price - A company with 80% renewal business could afford to lose 20% of capital - this would be a meaningful risk metric
Why is TVaR a better risk measure than VaR at a
given percentile for setting capital levels?
VaR is the minimum loss excess of a percentile
TVaR is the average loss excess of a percentile
What is a co-measure?
For a risk measure:ρ(Y) = E[h(Y) · L(Y)|g(Y)]
We have a co-measurer(Xj) = E[h(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) = ∑ r(Xj)
Are co-measures marginal?
Up to 1 co-measure will be marginal
Co-measure of VaR
r(Xj) = E[Xj | F(Y) = α]
The expected loss in unit j when the firm has a loss at the αth percentile
h(Y) = Y ; L(Y) = 1 ; g(Y) = F(Y) = α
Co-measure of TVaR
r(Xj) = E[Xj | F(Y) > α]
The expected loss in unit j when the firm has a loss excess of
the αth percentile
h(Y) = Y ; L(Y) = 1 ; g(Y) = F(Y) > α
Co-measure of Standard Deviation
r(Xj) = Cov(Xj,Y) / Stdev(Y)
This is the Marginal Co-measure
h(Y) = Y − EY ; L(Y) = (Y − EY) / Stdev(Y); g(Y) = True
What is the Co-measure of EPD?
r(Xj) = (CoTVaRα − CoVaRα) · (1 − α)
This is analogous to the definition of EPD.
What makes an allocation a Marginal Method?
An allocation is marginal if the change to the company’s risk measure from a small change in a single business unit is attributed to that business unit.
What is a suitable allocation?
Are marginal allocations suitable?
An allocation is suitable if a small increase to a unit that has a higher return on capital than the company (average), leads to an increase in the return on capital for the company.
Yes. A marginal allocation will always be Suitable
What is the Marginal Decomposition of E[Y · e^cy/EY]?
List the first 4 methods used to quantify Stability
Methods 13 & 14 to quantify stability use Financial
Ratios
Method 15 to quantify stability can compare many
reinsurance programs at once
