Actuarial›Exam FM›General Cash Flows and Portfolios
Exam FM topic · 15–20% of exam

General Cash Flows and Portfolios

Valuing arbitrary cash flow streams, net present value, internal rate of return, dollar-weighted and time-weighted returns.

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Per-objective worked-example outlines

For each learning objective on General Cash Flows and Portfolios, here is the approach an exam item would test — the setup, the ordering of your reasoning, and the formula or identity you need to bring to the page. Approaches, not full solutions, by design. Verify against the current soa.org syllabus before your sitting.

Compute net present value and internal rate of return for a general cash flow stream

Setup

A project has irregular cash flows over several periods and you must compute NPV at a given rate or find the IRR.

Approach

Lay the cash flows on a timeline including signs; NPV = sum over t of CF_t · v^t at the given rate. For IRR, solve NPV(i) = 0 using the CF worksheet on the BA II Plus. Watch for multiple IRRs when sign changes are non-monotonic and check uniqueness via Descartes' rule of signs.

Key identity

NPV(i) = Σ CF_t / (1 + i)^t; IRR satisfies NPV = 0.

Calculate duration and convexity of cash flow streams and portfolios

Setup

A bond or stream of cash flows is given along with a yield, and you must compute Macaulay or modified duration and convexity.

Approach

Compute weighted average time using PV-weighted cash flows: Macaulay duration = Σ t · PV_t / P. Modified duration = Macaulay / (1 + i). Convexity = Σ t(t + 1) · PV_t / [P · (1 + i)^2]. For a portfolio, dollar-weight individual durations; in particular, modified duration is approximately the percentage price change per unit yield change.

Key identity

D_mod = D_Mac / (1 + i); ΔP/P ≈ -D_mod · Δy + (1/2) · Convexity · (Δy)^2.

Compute dollar-weighted and time-weighted rates of return for a portfolio

Setup

A portfolio has deposits and withdrawals at intermediate dates, and you must compute return for the period.

Approach

Dollar-weighted return is the IRR of all cash flows including the beginning and ending balances. Time-weighted return chains period returns between every cash flow: multiply (1 + r_k) across sub-periods, then subtract 1. Dollar-weighted weights deposits made early; time-weighted does not. Use time-weighted to evaluate manager skill, dollar-weighted to evaluate investor outcome.

Key identity

(1 + TW) = Π (V_after_k / V_before_k); DW solves NPV of all flows = 0.

Common exam traps on General Cash Flows and Portfolios

Recurring patterns where candidates lose points on General Cash Flows and Portfolios-style items. Each entry pairs the trap with the fix.

Trap

Confusing Macaulay and modified duration in the price-change approximation.

Fix

Always divide Macaulay by (1 + i) before plugging into ΔP/P ≈ -D · Δy.

Trap

Using time-weighted when the question asks for the investor return.

Fix

Dollar-weighted answers "how did the dollars perform"; time-weighted answers "how did the manager perform".

Trap

Reporting modified duration but in years when the yield is per period.

Fix

Match the units — if the yield is semiannual, modified duration is in semiannual units; multiply or divide accordingly.

Trap

Treating positive and negative cash flows interchangeably in IRR.

Fix

Signs matter: outflows are negative, inflows positive; multiple sign changes can mean multiple IRRs.

Where to find General Cash Flows and Portfolios in popular manuals

Pointers to where each major vendor covers this topic, so you can grab the right chapter without combing the full manual. We do not reproduce vendor content — just the location. Chapter and lesson numbers shift between editions; use these as a guide, not as a citation.

ASM

Cash flow, NPV/IRR, duration, and convexity chapters

ACTEX

Cash flows and portfolio metrics chapters

Coaching Actuaries

Learn modules on General Cash Flows and Portfolios; Adapt category "Cash Flows / Portfolios"

The Infinite Actuary

Video block on NPV/IRR and duration/convexity

6-day General Cash Flows and Portfolios micro plan

A focused 6-day sub-schedule for General Cash Flows and Portfolios specifically, at roughly 1.5–2.5 hours per day. Drop it inside your full Exam FM plan as a single coverage module.

Day 1

Read the NPV/IRR chapter; drill 10 calculator problems using the CF worksheet on the BA II Plus.

Day 2

Duration and convexity — 12 problems mixing Macaulay, modified, and approximation of price change.

Day 3

Time-weighted vs dollar-weighted returns — 10 portfolio problems with intermediate deposits.

Day 4

Portfolio metrics across multiple assets; 8 problems computing portfolio duration as a weighted average.

Day 5

Mixed 18-problem drill spanning NPV, IRR, duration, convexity, and returns.

Day 6

Re-do flagged problems and write a concise reference linking duration, convexity, and immunization.

How exclam.ai helps you master General Cash Flows and Portfolios

Flashcards from your manual

Upload your ACTEX Exam FM digital edition, scanned ASM pages, TIA handouts, or your own notes. exclam.ai extracts the General Cash Flows and Portfolios sections and generates flashcards automatically, tuned to the exam traps above.

Worked-example drilling

Each per-objective approach above maps to a quiz template. exclam.ai re-surfaces missed items until you can recall both the setup and the key identity from cold.

FSRS spaced repetition

Because General Cash Flows and Portfolios is 15–20% of your exam, losing it during review costs you. FSRS brings it back at the optimal moment.

General Cash Flows and Portfolios in the Exam FM context

SOA Exam FM has 8 topic areas. General Cash Flows and Portfolios is weighted at approximately 15–20% of the exam, here is where it sits relative to the other topics.

Topic areaWeight
Time Value of Money10–15%
Annuities15–20%
Loans10–15%
Bonds10–15%
→ General Cash Flows and Portfolios15–20%
Immunization10–15%
Interest Rate Swaps0–5%
Determinants of Interest Rates0–10%

Other Exam FM topics

Time Value of Money

10–15%

Interest rates, discount rates, present and future value, and the relationships between different interest measurement conventions.

Study this topic

Annuities

15–20%

Level and varying annuities paid annually or more frequently, annuities due and immediate, and deferred annuities.

Study this topic

Loans

10–15%

Loan repayment, amortization schedules, sinking funds, and varying loan payments.

Study this topic

Bonds

10–15%

Bond pricing, yield to maturity, premium and discount, and book value schedules.

Study this topic

Immunization

10–15%

Portfolio immunization strategies, Redington immunization, full immunization, and asset-liability matching.

Study this topic

Interest Rate Swaps

0–5%

Basic mechanics of interest rate swaps, including fixed and floating legs and swap rate determination.

Study this topic

Determinants of Interest Rates

0–10%

Economic and market factors that shape interest rates, including inflation, risk premiums, and the yield curve.

Study this topic

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