IAI CM1 study guide

IAI CM1 · Work through your exam, one topic at a time.

CM1 is one of the early subjects in the Institute of Actuaries of India (IAI) actuarial examination series, and the IAI's own site describes the Institute as "a statutory body established under The Actuaries Act 2006 (35 of 2006) for regulation of profession of Actuaries in India." The exam is split evenly between two halves: Actuarial Mathematics and Statistics. The mathematics half builds the core life-contingent toolkit - survival models, life tables, assurance and annuity functions, premiums, reserves and multiple-decrement ideas. The statistics half covers probability distributions, sampling, estimation theory, hypothesis testing, regression and correlation, and the foundations of risk modelling. CM1 suits candidates who have completed the earlier foundation subjects and are comfortable with calculus, probability and algebra; it is normally attempted alongside or just before CM2. Topics on this exam: Actuarial Mathematics and Statistics. The IAI CM1 study guide has 2 sections and about 768 words.

CM1 Actuarial Mathematics: Theory of Interest and Contingencies

The Actuarial Mathematics domain of CM1 tests two linked skills: valuing deterministic cash flows through the theory of interest, and valuing payments that depend on survival or other decrements through contingencies. Most marks come from setting up a correct equation of value and solving it, so precision about timing and basis matters more than formula recall. v = 1/(1+i), d = i/(1+i), δ = ln(1+i); ä n = (1−v^n)/d, a n = (1−v^n)/i, s n = a n(1+i)^n. Equation of value: choose one comparison date; earlier amounts accumulate, later ones discount.

382 words, about 2 min 02

CM1 Statistics: Returns, Dependence and Simple Stochastic Models

The Statistics domain tests the descriptive and probabilistic tools CM1 applies to investment returns and mortality: moments, dependence between variables, return distributions, and simple stochastic models used to represent interest rates and decrements. Sample variance divides by n − 1; population variance divides by n. Covariance σ xy = Σ(x−x̄)(y−ȳ)/(n−1); correlation ρ = σ xy/(σ x σ y), and ρ = 0 does not imply independence. Two-asset portfolio: E = w μ 1 + (1−w) μ 2; Var = w²σ 1² + (1−w)²σ 2² + 2w(1−w)ρσ 1σ 2.

386 words, about 2 min