CFA Level III · Level III Core

An Overview of Private Wealth Management: formula sheet

Full chapter guide

Key formulas

Total wealth (economic balance sheet): Total wealth = Human capital + Financial capital; Human capital is the present value of expected future labor income. Financial capital is current investable and other assets.
Human capital (present value): Human capital = Σ [expected after-tax labor income in year t ÷ (1 + r)^t], for t = 1 to remaining working years; The discount rate r reflects the risk of the income stream. Riskier or more volatile income uses a higher rate.
Risk tolerance rule: Risk tolerance = lower of (ability to take risk, willingness to take risk); This is a prudent guideline used when the two conflict. State the reason, such as high ability but low willingness.
Human capital trend: Over time: human capital falls, financial capital rises (until retirement), then financial capital is drawn down; A general pattern, not an exact law. Illness, job loss or inheritance can change it.
Overall risk tolerance (reconciliation rule): Overall risk tolerance = lower of (willingness, ability) when they conflict; A rule of practice, not a mathematical law. If ability is low, the client cannot afford the risk even if willing. Use judgment when the shortfall is small.
Both high or both low: High + High = above average; Low + Low = below average; No conflict to resolve, so the overall level is the same as both.
High willingness, low ability: Overall = below average or low; Ability constrains. Risking money the client needs for essential goals is not appropriate.
Low willingness, high ability: Overall = below average, or educate and reassess; Do not simply impose more risk. Educate the client, then revisit. Until willingness changes, the portfolio should respect it.
IPS structure: IPS = Objectives (return, risk) + Constraints (liquidity, time horizon, tax, legal/regulatory, unique circumstances); Use these headings in this order. Each needs a conclusion, not just a description.
Overall risk tolerance (rule of thumb): Overall risk tolerance is generally set by the more conservative of ability and willingness; This is a guideline, not a strict equation. If ability is low, it limits the risk the client can take whatever their attitude. If ability is high but willingness is low, the adviser may also educate the client about risk, but the plan should still respect the client's attitude.
Required nominal return (approximate): Nominal ≈ real return + inflation; Exact form: (1 + real) × (1 + inflation) − 1. Use the exact form when the question gives numbers to compute.
After-tax return (fully taxable returns, taxed annually at one rate): After-tax return = pre-tax return × (1 − tax rate); Use this only when the whole return is taxed every year at a single rate. For a blended portfolio, compute each component's after-tax return using that component's own tax rate (for example interest, dividends and capital gains), then weight the results by portfolio weights.
Required return from a goal: r = (FV ÷ PV)^(1/n) − 1; Use when saving is a lump sum and no contributions are made. With contributions, solve using the annuity or financial calculator.
Net worth: Net worth = Total assets − Total liabilities; Use market values. Add human capital only when the question asks for an economic balance sheet.
Savings (surplus) from cash flow: Annual surplus = After-tax income − Living expenses − Debt service; A negative surplus means the client is drawing down assets. Check taxes are deducted first.
Liquidity ratio: Liquidity ratio = Liquid assets ÷ Monthly (or annual) essential expenses; Gives months of expenses covered. Compare to the emergency reserve the client needs.
Debt service ratio: Debt service ratio = Annual debt payments ÷ Gross (or after-tax) income; State which income base you use. Higher ratios signal less capacity for risk.
Goal priority rule: Fund needs first, then wants, using asset risk matched to goal importance; A rule of method, not a fixed formula. Essential goals suit low-risk assets; discretionary goals can bear more risk.
Economic balance sheet: Total economic wealth = Financial capital + Human capital + Pension and other assets (e.g., present value of social benefits); Liabilities include spending needs and debts. Use this to judge how much risk the whole client can take.
Human capital: Human capital = PV of expected future earnings (net of taxes); Discount rate reflects the riskiness of the earnings. Stable earnings use a lower rate.
Human capital and equity exposure: Bond-like human capital → higher equity in financial portfolio; equity-like or correlated human capital → lower equity; A rule of direction, not a fixed number. Check correlation with the portfolio.
Goals-based module structure: Personal risk (floor) + Market risk (core) + Aspirational risk (upside) = Total portfolio; Each module has its own time horizon, required return and target probability of success.
Funding a goal: Required capital for a goal ≈ PV of the goal's future cash needs at a risk-appropriate discount rate; Safer, higher-priority goals use lower discount rates, so they need more capital today.
Insurance role: Net economic wealth at risk = Human capital − Insurance protection available for that risk; Conceptual. Insurance transfers risk, which can support a more aggressive investment mix.

Quick revision

Private clients differ from institutions: goals are personal, constraints are varied and emotions matter.
Life cycle stage affects human capital, financial capital, time horizon and risk capacity.
Human capital is the present value of future earnings; stable earnings act like a bond-like asset, volatile earnings act more like equity.
Willingness to take risk is psychological; ability to take risk is financial and objective.
When willingness and ability conflict, the lower one usually limits the risk objective.
The IPS has return objective, risk objective and constraints: liquidity, time horizon, taxes, legal and regulatory, unique circumstances.
Return objectives must be stated in measurable terms, often needing a required return to meet goals.
Financial planning starts with understanding the client, then analysing facts, then recommending, implementing and monitoring.
Needs analysis separates essential goals from aspirational goals and ranks them by priority.
Asset allocation must follow from the IPS, not from market views alone.
Justify each recommendation with a specific client fact in as few words as possible.
Answer every question; wrong answers carry no penalty.

Common mistakes

Deciding risk level from age alone. Fix: Use age as a starting point, then adjust for income stability, wealth, dependents and attitude. Quote the case facts.
Treating human capital as always bond-like. Fix: Check the job. If income is tied to markets or a cyclical industry, treat human capital as equity-like and reduce correlated holdings.
Treating willingness and ability as the same concept. Fix: Tag every fact as either financial capacity (ability) or attitude (willingness) before concluding.
Using the higher of the two as overall risk tolerance. Fix: When they conflict, the lower generally governs. High willingness cannot create ability.
Treating willingness and ability to take risk as the same thing. Fix: Assess ability from finances (wealth, income stability, horizon, liabilities) and willingness from attitude and behaviour. Then take the lower.
Setting the return objective as the highest return possible. Fix: Set a required return from needs and goals, consistent with risk. Call out when desires push the target above what the risk level supports.
Jumping to an asset allocation before analysing the balance sheet and cash flows. Fix: State what the data show about liquidity, surplus and net worth first, then recommend.
Treating every stated goal as equally important. Fix: Rank goals as needs or wants by the harm of failure, and fund needs first.
Treating only financial assets as the client's wealth. Fix: Always sketch the economic balance sheet and name human capital, then say whether it is bond-like or equity-like.
Saying a young client should always hold mostly equities. Fix: Base the view on how stable and how correlated earnings are. A young client in a cyclical, equity-linked job may need less equity.

Exam tips

Match the command word: identify needs a short statement, justify needs a reason linked to the case.
Always say whether human capital is bond-like or equity-like and why, using the job described.
When ability and willingness differ, name both and say the lower governs. This is a frequent scoring point.
Check for traps: a young client with unstable income or large debts may have low ability to take risk despite a long horizon.
For calculations of human capital, show the discounting steps; a correct number alone earns credit, but your workings help you avoid errors.
Always label each fact as ability or willingness in your answer. Graders look for both parts.
In item sets, wrong options often raise risk to match high willingness. Check ability first.
In essays, name the rating for each part and then the overall rating. Do not write more than the command word needs.