Brehm Ch 2 Flashcards
Define decision analysis
using simulation to drive corporate decision making
Describe 3 evolutionary steps of decision analysis process
- Deterministic project analysis
Uses a single deterministic forecast for project CFs to produce an objective function like PV or internal RoR.
This analysis may demonstrate some sensitivities to critical variables. - Risk analysis
Forecasts of distributions of critical variables are input into a MC simulation process to produce a distribution of the PV of CFs. - Certainty equivalent
Expands upon risk analysis by quantifying the intuitive risk judgment using a utility function (corporate risk preference).
Describe how uncertainty is handled in each step of decision analysis process.
- Deterministic project analysis: uncertainty is handled judgmentally rather than stochastically.
- Risk analysis: risk judgment is still applied intuitively.
- Certainty equivalent: utility function does not replace judgment. Instead, it formalizes judgment to that it can be consistently applied.
Explain how efficient market theory removes need for certainty.
Since investors can diversify away firm-specific risk, it does not have a risk premium and should be ignored.
The goal of firm managers is to maximize shareholder value, so they should ignore firm-specific risk as well.
This is why certainty equivalent approach is not appropriate for public companies.
Provide 2 counter arguments to the belief that market theory removes need for certainty.
- It is difficult to determine which risks are firm-specific and which risks are systematic.
Attempts have been made to determine which corporate decisions affect the stock price and which do not, but results are inconclusive. - Market-based risk signals (such as risk-adjusted rate) often lack the refinement needed for manages to mitigate or hedge the risk.
- Risk-adjusted discount rate (market-based risk signal) reflects risk only if there is a time lag. For many kinds of risks, time aspect is unimportant since risk is instantaneous (jump risk).
List the 5 major elements involved in internal risk modelling.
- Data classification and organizational scheme
- Capture exposures and loss history
- Estimate event frequency and severity distribution, Corporate hedging, Correlation and shock scenarios
- Develop aggregate loss distributions
- Corporate risk tolerance, CoC allocated, Cost benefit analysis on mitigation and hedging
List the 4 objectives of Internal Risk Model (IRM) mechanism
- Starts with an aggregate loss distribution, with many sources of risk (such as LOBs)
- Quantifies the impact of the possible aggregate loss outcomes on the corporation
- Assigns a cost to each amount of impact
- Attributes cost back to the risk sources
Define Corporate Risk Tolerance
Refers to the organization’s:
1. size
2. financial resources
3. ability
4. willingness
to tolerate volatility.
Explain how an efficient frontier can be used to select an insurance portfolio.
In order to translate impacts to costs, corporations must define explicit risk preferences.
For example, suppose a firm has identified an efficient frontier of possible insurance portfolios (portfolios that minimize risk for a given RoR).
The firm can plot these portfolios on a standard efficient frontier graph where y-axis is risk and x-axis is return.
The firm can then plot its current portfolio and see how it compares with efficient frontier.
If current portfolio has same return but more risk, then it is suboptimal.
List 3 questions a firm should try to answer when selecting one of the efficient portfolios.
- How much risk is the firm willing to tolerate?
- How much reward is the firm willing to give up for a given reduction in risk?
- Are the risk-reward tradeoffs available along the efficient frontier acceptable to the firm?
The 1st question requires an answer to the firm’s risk tolerance.
The second question requires the firm to express its risk preferences explicitely.
Describe how RORAC is determined.
Financial firms should rely on allocating the cost of capital (rather than the capital itself).
One way to do so is by allocating risk capital first and then using it to assign the cost of that risk capital to portfolio elements.
The cost is the product of the risk-adjusted capital and a hurdle rate.
This product is known as the Return on Risk-Adjusted Capital (RORAC).
Under RORAC, risk capital for financial intermediary is the amount needed to guarantee the performance of contractual obligations at default-free level.
Briefly describe an alternative to RORAC.
The cost of risk capital can be determined directly without allocating risk capital first.
Describe how RORAC can be used to determine if an activity is worth pursuing.
Once we have the Cost of Capital, a good way to determine if an activity is worth pursuing is by calculating the economic value added (EVA).
EVA = NPV Return - CoC
Activities with positive EVA should be pursued.
Explain how cost-benefit analysis (CBA) can be used to select risk mitigation strategies.
Once capital allocation is complete, a cost-benefit analysis can be used to determine which mitigation strategies should be pursued.
If we are using EVA approach where the CoC is determined directly, we would implement strategies that produce positive incremental EVA.
If we are using capital allocation approach where we have allocated risk capital, we would pursue activities where the benefit exceeds the costs of implementation.
Define economic capital.
Typically, economic capital refers to the VaR (value at risk).
Identify 4 advantages of using economic capital for ERM analysis.
- Provides a unifying measure for all risks across an organization.
- More meaningful to management than risk-based capital or capital adequacy ratios.
- Forces the firm to quantify the risks it faces and combine them into a probability distribution.
- Provides a framework for setting acceptable risk levels for the organization as a whole AND for individual business units.
Briefly describe why calculating VaR for all risks combined and then allocated down to individual units is beneficial.
Because it provides a consistent measurement of risk across units.
Briefly explain why a rounded number is usually selected for the target level.
Ex: 1-in-3333 VaR instead of 1-in-3467 VaR
The target level is often selected so that the economic capital is slightly less than the actual capital being held.
Define Moment-Based Measures and provide 2 examples of such measures.
Use the moment of a random variable, such as the change in capital over an accounting period.
Ex:
1. variance
2. standard deviation
Identify 2 disadvantages of using variance or standard deviation as risk measure.
For each, provide an alternative.
- Favorable deviations are treated the same as unfavourable ones.
Use semi-standard deviation since it only uses unfavourable deviations. - As quadratic measures, they may not adequately capture market attitudes to risk (understated).
Use skewness since uses higher moment, thus might better capture market attitude.
OR
Use exponential moments since they capture the effect of large losses on risk exponentially, the they might better capture market attitude.
Describe tail-based measures.
Tail-based measures emphasize large losses only.
Describe the 5 types of tail-based measures
- VaR: percentile of the probability distribution
- TVaR: expected loss at a specified probability level and beyond
- XTVaR: calculated as TVaR - mean.
When mean is financed by other funding, then capital is only needed for losses above the mean. - EPD: calculated by multiplying (TVaR - VaR) by the complement of the specified probability level.
Ex: EPD@96% = (TVaR - VaR)*(1-96%) - Value of default put option: when capital and/or reinsurance is exhausted, firm has the right to default on its obligations and put the claims to the policyholders.
The market value of this risk is the value of the default put option.
It is usually estimated using options pricing methods.
Provide an advantage and disadvantage of using VaR as tail-based risk measure.
Advantage: emphasizes large losses
Disadvantage: only looks at one point in the distribution
Provide an advantage and disadvantage of using TVaR as tail-based risk measure.
Advantage: reflects losses that exceed VaR
Disadvantage: losses are reflected linearly in the tail and does not reflect the fact that a risk that is twice as large is more than twice as bad.
Define probability transforms
Probability transforms measure risk by shifting the probability towards the unfavourable outcomes and then computing a risk measure with the transformed probabilities.
Provide 1 example of probability transforms
- Expected loss under transformed probabilities (ex: CAPM and Black-Scholes)
- Minimum martingale transform
- Minimum entropy martingale transform
- Wang transform
Provide 3 reasons why probability transforms are useful.
- Transformed means are useful because they often provide the market value of the risk being measured.
- Martingale transforms approximate the market prices of reinsurance from application to compound poisson process.
- Wang transform approximates market prices of standard bonds and CAT bonds.
Describe the TVaR criticism and how transformed probabilities can overcome this.
TVaR is often criticized because it is linear in the tail (a loss twice as large is considered twice as bad).
Under transformed probabilities, TVaR becomes WTVaR (weighted TVaR).
This is NOT linear in the tail and considers a loss that is twice as large to be more than twice as bad.
Describe Generalized Moments.
Expectations of a random variable that are NOT simply powers of that variable.
For example. TVaR at prob level a can be written as E(Y given F(Y) greater than a).
A generalized moment can be used to add weight to losses in the loss distribution around VaR percentile (blurred VaR).
How do we determine which measure to use?
If we want to get closer to the market value then a risk measure like WTVaR, minimum entropy transform and exponential moment may be a better decision.
However, these should be weighted against the practicality and simplicity of standard risk measures such VaR and TVaR.
The amount of capital an insurance company holds is a function of which 3 things.
- Customer reaction
- Capital requirements of rating agencies
- Comparative profitability of new and renewal business
Describe how customer reaction affects amount of capital held. How can it be tracked?
Some customers care deeply about the amount of capital being held by insurers and/or the financial rating of an insurer.
Oftentimes, declines in financial ratings can lead to declines in business.
To assess capital needs from this POV requires keeping in touch with customers.
Describe how capital requirements of rating agencies affects amount of capital held.
Different rating agencies require different amounts of capital to be held by an insurer.
Modelling may help convince an agency of the adequacy of capital.
Describe how comparative profitability of new and renewal business affects the amount of capital held.
Renewal business tends to be more profitable due to more informed pricing and underwriting.
Thus, it is important to retain renewal business.
List 2 purposes of capital allocation.
- Capital allocation shows the contribution of each business unit to overall risk.
- Capital allocation can be used for calculating risk-adjusted profitability and setting capacity controls by LOBs.
Provide the 2 methods for risk allocation.
- Proportional Capital Allocation
Allocate the overall risk to individual business units based on their proportion to risk. - Risk decomposition
Estimate contributions of individual business units to overall risk.
Define risk measure as an average of company results under certain conditions.
The contributions from each business units is the average of the business unit’s results under same conditions (co-measures).
Define co-measures.
In order to create a co-measure, we must express rho(Y) as a conditional expected value:
rho(Y) = E(h(Y)L(Y) given g(Y))
g is dome condition about Y
h is an additive function h(V+W) = h(V)+h(W)
L is any function for which this conditional expected value exists.
Then, the co-measure for such a risk measure is:
r(Xj) = E(h(Xj)L(Y) given g(Y))
