I don’t go to Giant Eagle much because Aldi and Kroger are usually a lot cheaper. It’s just for when I’m too lazy to drive more than 3 minutes 
For the p-p plot in Meyers, does anyone have a more intuitive explanation for why the S shape means a light tailed model? Does the “predicted” in histogram become the y-axis in p-p?
Yes, if you look at the plot on the y axis, that makes the histograms. If you have a lot of actual points in the tail ends then it’s a light tailed model since the 10th/90th percentiles of the model should actually be lower/higher, respectively.
Yeah okay, that would make sense. The x axis is labeled Expected which makes one think “actual” is on the y axis, but I think it really is x axis
Yeah the axis labels aren’t really intuitive. I think the idea is if you have 10 points then the “expected” percentiles of those 10 points are 1/11, 2/11, …, 10/11, so I think that’s what’s on the “expected” axis.
Taylor:
This paper was only added to the syllabus in 2019 so very little of it has been tested. I honestly don’t know what they’ll ask but here are the things that seem most likely to me.
- For the Exponential Dispersion Family:
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- Theta is the location parameter, related to the mean
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- Phi is the dispersion parameter
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- b(theta) is the cumulant function, it determines the shape of the distribution
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- c(y,phi) is the normalizing constant
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- mu = b’(theta)
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- Var(Y)=a(phi)*b’'(theta)
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- Variance function V(mu) = b’'(theta)
- When V(mu) = mu^p, for p <= 0 or p >= 1, it’s a Tweedie distribution. Large p gives a heavier tail.
- p = 0 is normal, p = 1 is ODP, p = 2 is Gamma, p = 3 is inverse Gaussian
- For the ODP, know the loglikelihood formula, how to calculate phi and the deviance
- Heteroscedasticity Adjustment: weights are inversely proportional to variance of the Pearson residuals.
- The Pearson residuals can be very skewed and not even close to normal. Standardized deviance residuals may be better to use since they should be normal. Know how to calculate these deviance residuals.
- Know the cross-classified model and how to calculate the alpha and betas for it. Also know it gives the same result as chain ladder given the distribution is ODP.
- Again, like Shapland, there’s a lot more detail here that could be tested but I’m just focusing on the above and spending my time knowing other papers better. Having some extra background knowledge on GLMs definitely couldn’t hurt though
Meyers:
- How to do the K-S test
- Know how to interpret the histograms and what they would look like for light/heavy tails and biased high or low models
- Be able to interpret p-p plots and identify light/heavy tails and low/high biased models
- Know for incurred losses Correlated Chain Ladder was able to pass the K-S test with the data used
- Know for paid losses, it was harder to find a working model, and the CSR (changing settlement rate) model was able to do the trick
- Know that for both paid/incurred all models failed the Anderson-Darling test, which is a more strict test on the tail behavior
- Calculation of the mean for correlated chain ladder has been asked before
- Skew Normal or Mixed Lognormal-Normal calculations also could come up as well as detailed calculations with any of the models. I’m skipping all this since I think the point of the paper isn’t the details of the models themselves but more the process and the K-S test + histograms/p-p plots.
- Know that this paper was based on data from 1997 and these results found in this paper may not be true in general if we looked at more recent data.
Verrall:
- Know the variance of the losses at C_i,j for ODP, Negative Binomial, and Normal
- Know that the negative binomial has a parameterization that has chain ladder LDFs so it is intuitively linked to chain ladder
- Understand the basic idea behind Bayesian MCMC - we have a prior guess for our parameters, then create a posterior distribution for them based on a mix of our prior guess and the actual data
- Understand the relationship between the prior distribution and the model result. i.e. priors with smaller variance mean we’re more confident in them, so the result should be less driven by the data and vice versa
- The stochastic row parameter model (which is often tested) weights the chain ladder and B-F reserves with a credibility based on the prior and percent paid. Know this formula.
- Know how to calculate the mean/variance of a gamma distribution in terms of alpha and beta.
- The stochastic column and row parameter model first models column parameters using a separate parameterization of chain ladder. I was feeling lazy and like this wouldn’t come up since it’s never been tested so I skipped it.
Siewart:
- Know the basics of the 6 different methods discussed: Loss Ratio Method, Implied Development, Direct Development, Cred-Wtd Techniques/B-F, Development Model, Distributional Model
- Know formulas for the limited and excess LDFs in terms of the unlimited LDF and the severity relativities. Know these formulas are assuming claim counts are already fully developed.
- Know the formulas for calculating incremental limited/excess LDFs as well.
- You can understand the basics of table M as well (easier if you’ve taken exam 8), but I doubt this will come up.
Sahasrabuddhe:
- Know how to create the trend triangle and adjust unlimited severities at the most recent AY to older values based on trend
- Be able to adjust a triangle at limit L to a triangle at basic limit B
- Be able to adjust an LDF in the most recent accident year for basic limit B to an LDF for any other accident year for limit X. Also be able to do this for XSLDFs
- Know this paper applies trend (including CY trend) to cumulative losses, which is a huge weakness.
- There’s a bit more detail here on bounds to severity relativities but they’ve never been tested so I’m skipping them.
Marshall:
- Know how to calculate overall independent risk CoV based on the independent risk CoV for each line
- Calculation of CoV for internal systemic risk and external system risk based on weights and correlation. I like to do this calculation in matrix form, so I don’t have to remember the summation indices.
- Internal systemic risk components: Specification error, Parameter Selection Error, Data Error. Know examples and definitions of these.
- External systemic risk components: Economic/Social Risks, Legislative Political and Claims Inflation Risks, Claims Managemenet Process Change Risk, Expense Risk, Event Risk, Latent Claim Risk, Recovery Risk. Again, know these definitions.
- Know internal benchmarking for short vs long tail lines and OCL vs PL CoVs.
- Know how to combine CoV for 3 categories into total CoV and calculate a risk margin (usually 75th percentile of normal distribution). Note 75th percentile of normal distribution actually gives a higher risk margin than 75th percentile of lognormal.
Teng & Perkins:
- Calculation of PDLD1, and PDLD_n for n > 1.
- Calculation of CPDLDs
- Calculation of premium asset.
- Know Feldblum’s discussion of why PDLD1 isn’t quite right (there’s a component that’s fixed and based off the expected losses.)
- Know the differences between the formula driven PDLD approach and the empirical approach.
- Know how the PDLD method is an improvement of Fitzgibbon’s linear regression (it had a constant PDLD for all development periods which isn’t accurate)
- Also know why PDLDs are expected to decrease with age (Loss development for claims above the occurrence cap and loss development above the aggregate cap happen more at later periods)
Goldfarb:
- Know how to calculate discount rate due to CAPM.
- Know the DDM calculations and why it isn’t ideal sometimes (highly leveraged, companies don’t have to pay out dividends)
- Know the equation for FCFE and how to calculate the company value with the FCFE model.
- Know the weaknesses of FCFE and its strengths over the FCFF model
- When beta/ROE are higher, discount rate should be higher since company is likely taking on more risk.
- Calculation of company value with abnormal earnings model.
- Know it’s hard to maintain abnormal earnings indefinitely due to competition and that the AE model is less leveraged than DDM/FCFE (at least when you pick a decreasing AE after the forecast horizon).
- Know the formulas for both P/E ratio and P/BV ratio.
- Multiples (P/E and P/BV) can be used to estimate the company value or it can be used as a check when using another method. Look at peer companies to see what the multiples used for a check should be.
- Know why transaction multiples are good/bad to use (knowledgable parties involved, but IPOs usually underpriced and M&A usually overpriced)
- Know the different real options (abandonment, expansion, contraction, option to defer, option to extend) and why these aren’t usually used (hard to estimate black-scholes parameters, unclear how to treat policyholders’ liabilities expiration date)
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Taking another break, ERM stuff to come either later today or early tomorrow depending on how lazy I feel this afternoon.
This will benefit future generations to come (provided this site doesn’t shut down like AO)
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Really I’m just out here trying to go over everything again in a bit of detail so I have something else to look over before I sit Thursday, but if it helps others that’s definitely not a bad thing.
I’d like to put a big disclaimer here for all of Brehm and the ERM material. Usually my exam strategy is to focus on the quantitative problems and knock them out of the park, and take the qualitative stuff a bit less seriously. I’ve tried to do a somewhat thorough job with Brehm, but there’s just so much here that I’m basing my notes mainly off past problems.
Brehm Ch1:
- Know risk categories for an insurer (Financial, Operational, Strategic, Insurance Hazard)
- Know 5 traditional methods of risk management (Avoidance, Reduction of chance of occurrence, Mitigation of the effect, Transfer of the consequences, Retention)
- Know sources of underwriting risk (loss distributions, pricing risk, parameter risk, CAT modeling uncertainty)
- Know that ERM is an on-going process and that only material risks should be focused on. Also know both upside and downside risks should be analyzed.
Ch2:
- 3 evolutionary steps in corporate decision analysis: Deterministic, Risk Analysis (gives a distribution of outcomes), Certainty Equivalent (run outcomes through risk preference function)
- Know calculation of RORAC, NPV, and EVA
- Benefits/Downsides to different risk meausures for required capital including VaR, TVaR, EPD, WTVaR, XTVaR, moment-based measures. Know how to calculate these given simulations as well.
- You may want to learn about marginal and scalable risk measures but I didn’t really bother.
- Know that allocating capital is arbitrary and artificial since each business unit has access to the entire capital of the firm
- 3 paradigms for the value of reinsurance: Provides stability, frees up capital, adds to the market value of the firm
- There are a ton of graphs and calculations related to reinsurance in this chapter but I’m not really going into detail. I find that the past questions have been fairly easy and are able to be figured out given the information provided and some reasoning.
- I do want to reiterate my disclaimer above though and add onto it that chapter 2 is probably my weakest section within Brehm as well.
Ch3:
- Know basics of an Internal Risk Model including purpose, input/output, scope, staffing, parameter estimation issues, correlation assessment issues, and validation issues.
- For modeling parameters 3 types of risk: Projection risk, estimation risk, model risk. Know these definitions and examples.
- Know that for larger firms the process risk is reduced due to the size, so parameter risk becomes much more important. Systematic risk from trend does not go away with large company size.
- Know the definition of a Copula and its purpose.
- Know the Frank, Gumbel, HRT, and Normal copulas and how they look
- Know the left tail and right tail concentration functions (these are the only quantitative questions that have been asked on copulas historically).
Ch4:
- Know the definition of Operational risk vs Strategic risk
- 7 Types of Operational Risk: Internal Fraud, External Fraud, Employment Practices and Workplace Safety, Clients Products and Business Practices, Damage to Physical Assets, Business Disruption and System Failures, Execution Delivery and Process Management
- 7 Types of Strategic Risk: Industry, Technology, Brand, Competitor, Customer, Project, Stagnation
- Understand the Bridging Model and how it can be dangerous to use when older years’ expected loss ratios are too low.
- 4 aspects of effective cycle management: Intellectual Property, Underwriter Incentives, Market Overreaction, Owner Education
- Understand Agency Theory
- Things like Control Self-Assessment, Key Risk Indicators, and Six Sigma are very possible topics that haven’t been tested often
- 5 steps for managing Operational Risk
- Understand scenario planning
Ch5:
- 4 theories to the UW Cycle: Institutional Factors, Competition, Capital, Economic Linkages
- Soft vs Technical approaches
- Soft approaches: Detailed Scenarios, Delphi Method, Formal Competitor Analysis
- Technical approaches: Auto-regressive model, Factor model
- Behavior (Econometric) Modeling has structural insight of a soft approach and statistical validity of technical approach.
- Understand supply and demand curves, how they relate and how capital/economic factors impact them
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At this point I’m done studying and am just going to relax the rest of the day before sitting tomorrow morning. I’ll make a very brief post tomorrow about whether I thought the exam difficulty was about expected, hard, or easy and whether I think I passed.
Good luck with the studying everyone!
hey amp (or anyone else),
What do you make of 2019 #10b? I can’t find anything in the Shapland text that tells you to use one simulated outcome on the fitted triangle, and then the second on the sample triangle.
I even downloaded the linked Excel files, and I can’t find it.
I don’t think it was necessarily in Shapland but since you already found the sample triangle and were given the fitted triangle, it was a pretty straightforward calculation.
I think that question was more just to test whether you understand the process for the stochastic BF than something that you would actually do in practice.
My intuition was to use both simulated ultimate loss levels on the sample triangle, but the examiner’s report said that was an incorrect approach. To be deducted points for using a method that the source text doesn’t explicitly endorse or prohibit seems crazy to me.
EDIT: Nevermind, it was explicitly stated in the problem to do it that way. Ugh…
I completely agree if they didn’t say explicitly to use one simulated result on the fitted and one on the sample that you should use both on the sample.
Yeah, one of the things I noticed on 2018 and 2019 is the question wording got a bit trickier, so it’ll be a good idea to make sure we read everything carefully.
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I have a question regarding change in capital for FCFE model when there are multiple constraints. Do we first find the most constraining capital measure for each period, then calculate the change? Or do we calculate changes in capital for each measure, then take the largest one? I’m guessing it’s the former.
Use the most constraining since it will give you the actual change in capital.
I’m not sure I see the difference in the two, but I think it’s the former. For example, if beginning equity is 100, and:
Standard / Requirement end of this year / Requirement end of next year/
RBC / 110 / 140
Management / 120 / 135
Then you would choose the management’s required level for the end of this year, and RBC’s required level for end of next year.
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This is right assuming the company meets all capital goals. It’s possible in the first year they could decide to just hit the RBC threshold and say screw the capital needed to maintain their rating or something. But assuming they want to meet all thresholds this is the way to do it.
I do really like how this website automatically updates without refreshing so I can just keep this thread on my second monitor while I chill and play games. I have hope for this place to be an adequate replacement to the AO long term.