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CAS Exam 9 Study Notes: Risk Measures and Capital Allocation
2019-04-27
I've uploaded my notes on risk measures and capital allocation. These cover learning objectives C6 through C9 of the syllabus. Four readings comprise these learning objectives: Capital Allocation by Percentile Layer by N. M. Bodoff, Solvency Measurement for Property-Liability Risk-Based Capital Applications by R. P. Butsic, Allocation of Captial in the Insurance Industry by J. D. Cummins, and Risk-Adjusted Performance Measurement for P and C Insurers by R. Goldfarb. The notes explain various methods for determining an overall capital requirement for an insurance company, methods for allocating the cost of capital among lines of business, and how to use this allocation to assess lines of business on a risk-adjusted basis and determine appropriate risk loadings for the rates.
Keywords: Actuarial Science, Study Note, Exam 9
CAS Exam 9 Study Notes: Insurance Profitability
2019-04-25
I've uploaded my notes on insurance company profitability, based on two readings by Ira Robbin: The Underwriting Profit Provision and IRR, ROE, and PVI/PVE. These readings provide an overview of seven methods for assessing the profitability of an insurance company and determining a fair premium, and correspond to learning objectives D4 and D5 on the syllabus.
Keywords: Actuarial Science, Study Note, Exam 9
CAS Exam 9 Study Notes: Catastrophe Insurance Risk Loads
2019-04-16
I've uploaded my notes on Donal Mango's paper An Application of Game Theory: Property Catastrophe Risk Loads. The paper addresses the problem of determining a fair risk load for a catastrophe insurance account based on its degree of correlation with other accounts in the portfolio. Marginal methods have the problem that they are not renewal additive; that is, when the accounts renew, the total risk load does not equal the indicated risk load for the aggregate portfolio. Mango introduces a game-theoretic approach for allocating contributions to covariance among the various accounts in a manner that is renewal additive.
Keywords: Actuarial Science, Study Note, Exam 9
CAS Exam 9 Study Notes: Managing Interest Rate Risk
2019-04-16
I've uploaded my notes on managing interest rate risk, based on Chapters 16 and 23 from the textbook Investments by Bodie, Kane, and Marcus. The notes explain how duration and convexity can be used to assess the sensitivity of an asset or liability to changes in the interest rate, and give an overview of strategies for managing interest rate risk.
Keywords: Actuarial Science, Study Note, Exam 9
CAS Exam 9 Study Notes: Riskiness Leverage Models
2019-04-13
My notes on Rodney Kreps' paper on Riskiness Leverage Models are now available. The paper establishes a general framework for determining a capital requirement for a firm based on a riskiness leverage function that reflects attitudes toward risk. Moreover, the framework provides a method for allocating the capital to different sources of risk that contribute to the aggregate result. Many common co-measures, such as covariance and co-TVaR, are shown to be special cases of this general framework. The ideas are illustrated simulated data; the paper is accompanies by a spreadsheet that performs these simulations, and the notebook above illustrates how to perform these simulations in R.
Keywords: Actuarial Science, Study Note, Exam 9
CAS Exam 9 Study Notes: Credit Risk and Credit Derivatives
2019-04-09
My notes on credit risk and credit derivatives are now available. These notes are based chapters 14 and 16 of the textbook Investments by Bodie, Kane, and Marcus, and the paper The Economics of Structured Finance by Joshua Coval, Jakub Jurek, and Erik Stafford. The notes describe the basic ideas of the bond rating system and methods of securitizing debt, with most of the attention given to Collateralized Debt Obligations. Methods for determining the default probability and expected loss of a CDO are described, and the sensitivity of these methods to the assumptions about the default probability and correlation of the underlying debts is assessed through simulations. The numerous problems associated with CDOs are discussed, and their role in the 2008 financial crisis is explained.
Keywords: Actuarial Science, Study Note, Exam 9
CAS Exam 9 Study Notes: Bond Pricing and Interest Rates
2019-04-07
My notes on bond prices and interest rates are now available. These notes are based chapters 14 and 15 of the textbook Investments by Bodie, Kane, and Marcus. The notes explain how to determine prices and yields to maturity of bonds. Yields of bonds of various maturities are used to determine the yield curve, followed by a discussion of reasons that the yield curve is typically non-flat.
Keywords: Actuarial Science, Study Note, Exam 9
CAS Exam 9 Study Notes: Franchise Value
2019-04-03
My notes on franchise value are now available. These notes are based on the paper Managing Interest Rate Risk: ALM, Franchise Value, and Strategy by William H. Panning. This reading demonstrates how to calculate the franchise value of an insurance company, which is the present value of future renewals. In essence, it is able to assign a dollar value to the company's ability to retain customers. Panning calculates the sensitivity of franchise value to changes in the interest rate, and proposes a strategy for managing interest rate risk by varying premium as the interest rate changes.
Keywords: Actuarial Science, Study Note, Exam 9
CAS Exam 9 Study Notes: Behavioural Finance
2019-04-02
My notes on behavioural finance are now available. These notes correspond to Chapter 12 of the textbook Investments by Bodie, Kane, and Marcus, and objective A10 on the syllabus. The notes explain how market inefficiencies can arise as a result of information processing errors and behavioural biases, and introduce some technical tests that attempt to detect evidence of these biases in market trends.
Keywords: Actuarial Science, Study Note, Exam 9
CAS Exam 9 Study Notes: Arbitrage Pricing Theory
2019-03-30
My notes on Arbitrage Pricing Theory are now available. These notes correspond to Chapter 10 of the textbook Investments by Bodie, Kane, and Marcus. The notes describe how a benchmark expected return for a well-diversified portfolio of stocks can be calculated based on the assumption that the return on the portfolio should not permit arbitrage. The benchmark is based on the correlation of the portfolio return with various macroeconomic factors. These notes correspond to objective A8 on the syllabus.
Keywords: Actuarial Science, Study Note, Exam 9
CAS Exam 9 Study Notes: Efficient Market Hypothesis
2019-03-30
My notes on the Efficient Market Hypothesis are now available. These notes correspond to Chapter 11 of the textbook Investments by Bodie, Kane, and Marcus. Market efficiency is the idea that information about a security is reflected in its price: three types of efficiency are described, depending on what type of information is reflected. Empirical studies providing evidence of inefficiencies in the market are also summarized. These notes correspond to objective A9 on the syllabus.
Keywords: Actuarial Science, Study Note, Exam 9
CAS Exam 9 Study Notes: Securitization of Catastrophe Risk
2019-03-26
My notes on securitization of catastrophe risk are now available. These notes are based on the paper CAT Bond and Other Risk-Linked Securities: State of Market and Recent Developments by J. D. Cummins. The reading describes various instruments that are used to transfer catastrophic insurance risk to financial markets, the reasons for doing so, and impediments to growth of the catastrophe securities market. These notes correspond to objective C5 on the syllabus.
Keywords: Actuarial Science, Study Note, Exam 9
CAS Exam 9 Study Notes: The Capital Asset Pricing Model
2019-03-24
I've uploaded my notes on the Capital Asset Pricing Model, based on Chapter 9 of the Investments textbook by Bodie, Kane, and Marcus. These notes correspond to learning objectives A6 and A7 on the Exam 9 syllabus. The notes explain the assumptions behind the Capital Asset Pricing Model, illustrate how it can be used to establish a benchmark price for a security based on its correlation with the market, and summarize variations on the CAPM that relax some of its assumptions.
Keywords: Actuarial Science, Study Note, Exam 9
CAS Exam 9 Study Notes: Single Index Models
2019-03-17
I've uploaded my notes on single index models, based on Chapter 8 of the Investments textbook by Bodie, Kane, and Marcus. These notes correspond to learning objective A5 on the Exam 9 syllabus, and explain how a linear regression of returns of an individual security against market returns leads to a portfolio optimization model that is considerably simpler than the full Markowitz model.
Keywords: Actuarial Science, Study Note, Exam 9
CAS Exam 9 Study Notes: Optimal Risky Portfolio
2019-03-12
I've uploaded my notes on construction of an optimal risky portfolio, based on Chapter 7 of the Investments textbook by Bodie, Kane, and Marcus. These notes correspond to learning objectives A2 - A4 on the Exam 9 syllabus. The notes explain how to select weights for risky assets that maximize the Sharpe ratio, in both the bivariate case (using an explicit formula) and the multi-variate case (using quadratic programming). The notes also illustrate how correlation between assets reduces the benefits of diversification due to systematic risk.
Keywords: Actuarial Science, Study Note, Exam 9
CAS Exam 9 Study Notes: Insurance Profitability
2019-02-24
I've uploaded my notes on insurance profitability, based on the Exam 9 syllabus reading Insurance Profitability by Charles L. McClenahan. The reading makes the case that, from a regulatory perspective, the relevant metric for assessing an insurer's profitability is return on sales, rather than return on equity.
Keywords: Actuarial Science, Study Note, Exam 9
CAS Exam 9 Study Notes: Optimal Capital Allocation
2019-02-24
My study notes on optimal capital allocation are now available. These notes address how a mathematical formulation of an investor's risk tolerance can be translated into an optimal allocation of capital between a risky portfolio and a risk-free asset can be determined. (The topic of how to determine the components of the risky portfolio are a separate note.) These notes are based on Chapter 6 of the textbook Investments by Bodie, Kane, and Marcus, and correspond to learning objective A1 on the CAS Exam 9 syllabus.
Keywords: Actuarial Science, Study Note, Exam 9
CAS Exam 9 Study Notes: Internal Rate of Return
2019-02-21
My study notes the internal rate of return model are now available. These notes are based on Sholom Feldblum's paper Pricing Insurance Policies: The Internal Rate of Return Model, and relate to learning objective D1 on the CAS Exam 9 syllabus.
Keywords: Actuarial Science, Study Note, Exam 9
CAS Exam 9 Study Notes: Insurance Leverage
2019-02-21
I've posted my study notes on insurance leverage, based on a paper by J. Robert Ferrari and a discussion by R. J. Balcarek. These papers illustrate how loss reserves can be viewed as playing a role analogous to debt capital, and provide leverage as a result. These notes correspond to objective D2 on CAS Exam 9.
Keywords: Actuarial Science, Study Note, Exam 9
CAS Exam 7 Study Notes: Risk Margins, Stochastic Reserve Models, and Enterprise Risk Management
2018-05-13
I've uploaded the last three of my Exam 7 Study Note files, covering the following topics:
- Assessment of Risk Margins, based on a paper by Karl Marshall, Scott Collings, Matt Hodson, and Conor O'Dowd.
- Stochastic Loss Reserving, based on three readings: Obtaining Predictive Distributions for Reserves Which Incorporate Expert Opinion by R.J. Verrall, Using the ODP Bootstrap Model: A Practitioner's Guide by M. Shapland, and Stochastic Loss Reserving Using Bayesian MCMC Models by G. Meyers.
- Enterprise Risk Management, based on a reading by Brehm, Gluck, Kreps, Major, Mango, Shaw, Venter, White, and Witcraft.
Keywords: Actuarial Science, Exam 7, Study Note
CAS Exam 7 Study Notes: Unpaid Claims by Layer
2018-04-17
My notes on unpaid claims by layer of loss are now available. These notes synthesize the ideas in two syllabus readings. The first, A Model for Reserving Workers Compensation High Deductibles by Jerome Siewert, describes how to relate unlimited development loss development factors to limited and excess development factors. The second, Claims Development by Layer: The Relationship Between Claims Development Patterns, Trend, and Claim Size Models by Rajesh Sahasrabuddhe, generalizes these ideas to include adjustments for accident year and calendar year trends.
Keywords: Actuarial Science, Exam 7, Study Note
CAS Exam 7 Study Notes: Premium Asset for Retro Policies
2018-04-12
I've uploaded my notes on premium estimation for retrospectively rated policies, which are based on a paper by Michael Teng and Miriam Perkins, and includes a discussion by Sholom Feldblum. The notes demonstrate how to estimate future premium on retrospectively-rated policies through the calculation of premium development to loss development (PDLD) ratios.
Keywords: Actuarial Science, Exam 7, Study Note
CAS Exam 7 Study Notes: Loss Reserving for Reinsurance
2018-04-10
I've uploaded my notes on loss reserving for reinsurance, which are based on a section on reinsurance loss reserving that appears in Foundations of Casualty Actuarial Science by G. S. Patrik. The notes describe some concerns that are specific to reinsurance reserving, and provide details on the Stanard-Buhlmann method, which is often used for long-tailed lines of reinsurance.
Keywords: Actuarial Science, Exam 7, Study Note
CAS Exam 7 Study Notes: Benktander Method and Optimal Credibility
2018-04-09
I've uploaded my notes on the Benktander method and optimal credibility. These notes are based on two papers from the syllabus. The first, Credible Claims Reserves: The Benktander Method by Thomas Mack illustrates how to apply the methods to a single accident year. The second, Credible Loss Ratio Claims Reserves: The Benktander, Neuhaus, and Mack Methods Revisited, addresses the question of how to apply the methods to an entire development triangle, by taking credibility-weighted averages of the individual loss ratio claims reserve and the collective loss ratio claims reserve.
Keywords: Actuarial Science, Exam 7, Study Note
CAS Exam 7 Study Notes: Testing Assumption of the Chain Ladder Method
2018-04-08
I've uploaded my study notes on the topic of testing assumption underlying the chain ladder method. These notes are based on a combination of two closely-related papers, Measuring the Variability of Chain Ladder Reserve Estimates by Thomas Mack, and Testing the Assumptions of Age-to-Age Factors by Gary Venter. The topics addressed include testing the variance assumption underlying the method, testing for calendar year or accident year correlations, and comparing the "direct linear relationship" assumption of the chain ladder method against alternative emergence patterns, such as a linear-plus-constant pattern or a Bornhuetter-Ferguson or Cape Cod emergence pattern.
Keywords: Actuarial Science, Exam 7, Study Note
CAS Exam 7 Study Notes: Maximum Likelihood Approaches in Reserving
2018-03-28
I've uploaded my study notes based on LDF Curve-fitting and Stochastic Reserving: A Maximum Likelihood Approach by David Clark. This paper describes how to fit a smooth curve to the historical loss emergence pattern, under both the Loss Development Factor and Cape Cod reserving methods, and how to obtain estimates for the variance of the reserves resulting from use of this method. In the notes, I demonstrate how to use R to maximize the likelihood functions corresponding to Clark's models and replicate the examples from his paper.
Keywords: Actuarial Science, Exam 7, Study Note
CAS Exam 7 Study Notes: Loss Development Using Credibility
2018-02-28
I've uploaded my notes on Loss Development Using Credibility, a paper by Eric Brosius. The paper explains how to use linear regression to predict ultimate claim values based on the amount reported as of a given date, and demonstrates that the result has an equivalent interpretation as a credibility-weighted average of the ultimate loss estimates from the link ratio and budgeted loss methods. The notebook illustrates how to replicate the examples from the paper using R. Of particular interest, it shows how to use R to simulate the results of a Poisson process as a means to generate data to illustrate the methodology.
Keywords: Actuarial Science, Exam 7, Study Note
CAS Exam 7 Study Notes: P&C Insurance Company Valuation
2018-02-21
As part of my preparation for Exam 7 of the Casualty Actuarial Society, I'm writing my study notes in R notebooks, using R code to illustrate the concepts in the readings. As a result, the notes will sometimes address more than the bare minimum that is needed to pass an exam, but will contain additional information that can be used to put the ideas into practice using contemporary statistical software. Some of the notebooks may be of interest, independent of the subject matter, of illustrations of R techniques.
The first instalment is P&C Company Valuation, based on a reading by Richard Goldfarb. It addresses learning objectives B1-B3 on the exam, explaining several methods for determining the value of an insurance company. Of particular interest is that it shows how R can be used to quickly perform sensitivity testing over a range of assumptions, and visualize the results.
Keywords: Actuarial Science, Exam 7, Study Note