Investment Planning: formula sheet

Key formulas

Components of an IPS

Objectives (return, risk) + Constraints (liquidity, time horizon, taxes, legal and regulatory, unique circumstances)

Cover every item, even if you write that a constraint is minimal for this client.

Overall risk tolerance

Overall risk tolerance = lower of ability and willingness (when they conflict)

Ability is based on facts. Willingness is based on attitude. Say which one is limiting.

Nominal required return (exact)

Required nominal return = (1 + spending rate + fees/taxes rate) × (1 + inflation) − 1

The spending rate, fees and taxes make up the required real return. Compound it with inflation. Use this when the question wants a precise figure.

Nominal required return (quick approximation)

Required return ≈ spending rate + fees/taxes rate + inflation

Spending rate = spending need ÷ portfolio value. The additive version slightly understates the exact result, because it leaves out the cross-term (real return × inflation). Use it only for a quick estimate or when the question allows it.

Real return from nominal

Real return = (1 + nominal) ÷ (1 + inflation) − 1

Use when a question gives a nominal return and asks for the real one.

Overall risk tolerance

Overall risk tolerance = lower of (ability to take risk, willingness to take risk)

This is the standard conservative rule. Use it when the two conflict, then explain and consider whether the gap can be narrowed.

Ability (risk capacity) drivers

Wealth vs goals, time horizon, liquidity needs, income stability, other support

Objective factors. A larger cushion over required spending and a longer horizon raise ability.

Willingness (risk attitude) drivers

Psychology, past reactions to losses, biases, questionnaire and interview answers

Subjective. Check for consistency and for the influence of recent market events.

Risk required vs risk tolerance

If risk required > risk tolerance, adjust the goals or plan, not the risk

Options: reduce return target, raise savings, extend horizon, cut spending.

Required nominal return (before tax, geometric)

(1 + real return) × (1 + inflation) − 1

Use this geometric form. The shortcut real + inflation is only an approximation.

Pre-tax return from after-tax return

Pre-tax return = After-tax return ÷ (1 − tax rate)

Applies when all return is taxed at one rate each year. If fees are not tax-deductible, treat them as a separate pre-tax drag and add them after the tax gross-up.

Required return from a capital need (lump sum)

r = (Future value needed ÷ Present value)^(1 ÷ n) − 1

Add expected contributions or withdrawals by using the annuity form or a financial calculator.

Spending rate

Spending rate = Annual spending ÷ Portfolio value

If the portfolio must keep its real value, required real return is at least spending rate plus fees and taxes.

IPS checklist

RRTTLLU = Return, Risk, Time horizon, Tax, Legal and regulatory, Liquidity, Unique

Use it to structure answers. Return and Risk are the objectives. The constraints are Time horizon, Tax, Legal and regulatory, Liquidity and Unique circumstances.

Human capital

HC = Σ [ expected after-tax labour income(t) ÷ (1 + r)^t ]

Discount rate reflects the risk of the income. Stable income gets a lower rate; volatile income gets a higher rate. Also account for the probability of survival and employment.

Economic net worth

Economic net worth = Human capital + Financial capital − Liabilities

Financial capital includes investable and other assets. Use it to see total resources, not just the investment portfolio.

Future value of a spending need

FV = PV × (1 + g)^n

g is the expected inflation or spending growth rate. Use a real rate if all flows are in real terms. Never mix real flows with nominal discount rates.

Present value of an annuity (capital needed)

PV = PMT × [1 − (1 + r)^−n] ÷ r

Use the annuity-due version (multiply by 1 + r) if payments start at the beginning of each period.

Real return

(1 + r real) = (1 + r nominal) ÷ (1 + inflation)

This is the exact form. Subtracting inflation is only an approximation.

Capital sufficiency

Surplus or shortfall = Financial capital available − PV of goals (needs and wants)

A shortfall means adjust savings, retirement age, spending or risk. Needs should be tested at higher confidence than wants.

Sub-portfolio funding order

Fund goals in priority order: essential (needs) → important → aspirational (wants/dreams)

Match assets to each goal's horizon and required success probability.

Total portfolio weight

Overall weight of asset class = Σ (sub-portfolio share of wealth × weight in that asset class)

Use this to check the aggregate allocation from a goals-based build.

Sub-portfolio share

Share of wealth = PV of the goal's funding need ÷ total investable wealth

Compare the sum of goal needs with total wealth to find excess or shortfall.

Excess capital

Excess capital = investable wealth − PV of core (essential) needs

Excess capital can go to aspirational goals, the legacy or higher-risk assets.

Planning cycle

Discovery → Analysis → IPS → Asset allocation and construction → Implementation → Monitoring, rebalancing, review → (repeat)

Know the order. Questions often ask which step comes next or which step was skipped.

Risk tolerance rule

Risk taken ≈ the lower of ability and willingness (when they conflict)

A rule of thumb in the usual treatment. Say why: a client unable to bear losses cannot take them, however willing.

Core IPS components

Objectives (return, risk) + Constraints (liquidity, time horizon, tax, legal and regulatory, unique circumstances)

Use this checklist to structure any recommendation.

Rebalancing trigger

Rebalance if weight drifts outside a set range, or at set calendar dates, net of costs and taxes

Wider ranges mean fewer trades, lower costs, but more drift.

Ethical duty checklist

Loyalty, prudence and care; suitability; fair dealing; disclosure of conflicts; confidentiality; documentation

Match the facts in the vignette to one or more of these duties.

Quick revision

• The IPS records objectives (return and risk) and constraints, and guides all later decisions.
• Risk tolerance has two parts: ability (capacity, based on facts) and willingness (attitude).
• If ability and willingness conflict, the lower one usually sets the overall risk tolerance.
• Constraints are liquidity, time horizon, tax, legal and regulatory, and unique circumstances.
• Return objectives may be absolute or relative, and may be stated before or after tax and inflation.
• Capital needs analysis compares the present value of needs with the resources available.
• A longer time horizon and stable income generally raise risk ability.
• Spending needs, emergency reserves and liabilities shape liquidity constraints.
• Allocation should follow from the IPS, not from past returns or market views alone.
• Review the IPS when client circumstances, goals or markets change materially.
• A correct number typed on its own earns full credit for a calculation. Showing steps is good practice for accuracy but is not required. Make sure the number answers what was asked.
• Put the client's interest first and keep advice suitable and documented.

Common mistakes

• Treating willingness and ability as the same thing. Fix: Sort each fact: finances and horizon go to ability, attitudes and past behaviour go to willingness. Then state the lower as the binding one.
• Stating a return objective without a number or a measure. Fix: Convert the goal into a required return using spending, inflation and the portfolio value. Say whether it is real or nominal.
• Treating willingness as the same as ability Fix: Ask separately: can the client afford a loss (ability), and does the client want to accept risk (willingness)?
• Averaging the two instead of taking the lower Fix: Use the conservative rule. Overall risk tolerance is the lower of the two when they conflict.
• Treating desired return as the required return. Fix: Required return funds needs only. Quote the desired return separately and note it is subject to risk tolerance.
• Adding real return and inflation instead of compounding. Fix: Use (1 + real) × (1 + inflation) − 1 unless the question says to add.
• Mixing real cash flows with a nominal discount rate Fix: Decide first: all real or all nominal. Convert the return to real using the exact formula if flows are in today's money.
• Treating human capital as risk-free for every client Fix: Judge income stability and correlation with markets. A commission-based or cyclical earner has equity-like human capital, which lowers ability to take portfolio risk.
• Saying goals-based allocation and mental accounting are the same thing. Fix: Say that mental accounting is an unplanned bias that ignores correlations, while goals-based allocation is a structured process with priorities and a total-portfolio check.
• Putting the same risky mix in every goal bucket. Fix: Match the risk of each bucket to the goal's priority, horizon and required probability of success.

Exam tips

• Match the command word. 'Determine' wants a conclusion, 'justify' wants the reason using a case fact.
• Always state ability and willingness separately before the overall conclusion.
• In calculations, show the number clearly. A correct number on its own earns full credit.
• Check that your return objective is consistent with the risk you concluded. Examiners reward flagging a conflict.
• In item sets, read the answer options against the constraint categories: liquidity, horizon, tax, legal, unique.
• Always give both levels and the overall conclusion. Examiners award points for each part.
• When asked to justify, tie each level to a specific fact from the vignette, not a general statement.
• Use the exact command word. A determine question needs a conclusion, and a justify question needs a reason.