Advising the Wealthy: formula sheet

Key formulas

Client profile to IPS mapping

Objectives = return objective + risk tolerance (ability and willingness); Constraints = liquidity, time horizon, taxes, legal/regulatory, unique circumstances

Use this as a checklist. Place each client fact under one heading and say what it implies.

Risk tolerance rule

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

Ability is financial capacity. Willingness is psychological comfort. The more conservative one governs.

Needs hierarchy for wealthy clients

Protect lifestyle first, then goals, then legacy and aspirational wealth

Core needs must be funded with low-risk assets before excess capital is taken to higher risk.

Overall risk tolerance

Overall risk tolerance = the lower of ability and willingness

Use this as the default rule. If willingness is below ability, you may try to educate the client, but the IPS should not assume more risk than the client will accept. If willingness is above ability, ability limits the risk.

Required nominal return (spending-based)

Required return ≈ (Spending ÷ Portfolio) + Inflation + Fees/taxes

Approximation. For precision use (1 + real return) × (1 + inflation) − 1, and add fees and taxes as stated in the question.

Real return

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

Use when the question gives a nominal return and asks for the inflation-adjusted figure.

After-tax return

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

Valid only when the full return is taxed at one rate. Check the question for different rates on income and gains.

IPS structure

Objectives: return, risk. Constraints: liquidity, time horizon, tax, legal and regulatory, unique circumstances

Use this as a checklist for every IPS question.

Tax cost of selling

Tax = (Sale price − Cost basis) × Capital gains tax rate × Number of shares

Compare this with the risk reduction gained. Use the after-tax proceeds to reinvest.

Zero-cost collar

Long protective put (strike X_put) + short covered call (strike X_call), with premiums offsetting

Floor at X_put, cap at X_call. The client keeps dividends and ownership but gives up gains above the cap.

Collar payoff range

Value at expiry = max(X_put, min(S_T, X_call)) per share

Ignores premium if the collar is zero-cost. Add or subtract any net premium.

Prepaid variable forward (PVF)

Upfront cash = a percentage of current value; at settlement deliver a variable number of shares depending on S_T relative to floor and cap prices

Works like a collar plus a loan. Client receives cash now and defers the sale.

Equity swap (hedge)

Client pays the stock total return, receives a fixed or floating rate

Gives economic exit without selling. Tax treatment may be treated as a constructive sale, depending on the jurisdiction.

Exchange fund idea

Contribute shares → receive a pro rata share of a diversified pool

Usually has a lock-up period and minimum holding. Defers the gain and diversifies.

After-tax return on a taxable account

r(after-tax) = r × (1 − t)

Use when all return is taxed at the same rate t each year. Different tax rates for income and gains need separate treatment.

After-tax future value, annual tax on return

FV = PV × [1 + r(1 − t)]^n

Used for assets taxed every year. This is the base case for comparing a gift with a bequest.

Future value of a gift versus a bequest

Gift FV = G × (1 − t_gift) × [1 + r(1 − t)]^n; Bequest FV = E × [1 + r(1 − t)]^n × (1 − t_estate)

G = amount gifted, E = amount held in the estate, t_gift = gift tax rate, t_estate = estate tax rate, t = annual tax rate on investment return, r = pre-tax return, n = years. Compare what the heir ends up with, and use the rates in the question.

Tax-free growth inside the estate versus outside

Estate growth is taxed at t_estate on the full value at death; a gift removes the growth from that base

This is why gifts of fast-growing assets can save tax. The saving depends on the tax-paying rules in the question.

Core capital test

Excess capital = Investable wealth − Core capital

Only excess capital is available for gifts, philanthropy or risky strategies without threatening the client's lifestyle.

Quick revision

• Profile first: objectives are return and risk; constraints are time horizon, liquidity, taxes, legal and regulatory, and unique circumstances.
• Risk tolerance combines willingness and ability; when they conflict, the lower one generally governs the risk taken.
• The IPS links client facts to the portfolio; every element should trace back to a stated fact.
• The wealth management process is cyclical: plan, implement, monitor and review, and update when circumstances change.
• Concentrated positions raise idiosyncratic risk; know the options for reducing it, such as selling, hedging with derivatives, or gifting.
• Compare concentration strategies by tax cost, risk reduction, liquidity and control retained.
• Tax and estate planning aims to keep more after-tax wealth for the client and heirs, within the law of the relevant jurisdiction.
• Use the rules given in the case; do not import tax rules from memory of a different country.
• Behavioral biases can be cognitive (belief errors) or emotional (feeling-driven); the fix differs for each.
• Match each bias to the client's actual behavior in the case before naming it.
• Read the command word: calculate, identify, justify, recommend and explain each need a different answer length.
• There is no penalty for wrong answers, so answer every question.

Common mistakes

• Treating a wealthy client like a retail investor and giving only an asset allocation. Fix: Check for tax, estate, business, concentration, family and liquidity needs before recommending anything.
• Assuming high wealth means high risk tolerance. Fix: Assess ability and willingness separately. If they conflict, the lower governs.
• Treating ability and willingness as the same thing Fix: Take ability from the financial facts and willingness from attitudes and behaviour. State them separately, then conclude.
• Choosing the higher of ability and willingness Fix: Default to the lower. A wealthy client who hates losses, or a risk-loving client with little cushion, should not be given an aggressive risk objective.
• Recommending a full sale without mentioning the tax cost. Fix: State the tax cost, then say why sale is still acceptable or why a staged sale or hedge is better.
• Saying a collar removes all risk. Fix: Say the collar limits loss only below the put strike and caps gains above the call strike. The client still bears loss down to the floor.
• Treating a revocable trust as removing assets from the taxable estate. Fix: Remember that if the settlor can revoke, the assets are generally still treated as the settlor's. Use irrevocable trusts for estate reduction, and say what control is lost.
• Giving away assets without checking core capital. Fix: Always test the client's lifestyle needs first. Only excess capital should be gifted.

Exam tips

• Command words are in bold. 'Identify' needs only a short statement. 'Justify' needs a reason tied to a vignette fact.
• Answer only the number of responses requested, in order.
• Link every need to a specific fact. Generic lists score poorly.
• When ability and willingness differ, say which governs and why.
• Show any calculation. A correct number alone can earn full credit, but showing work protects you if the number is wrong.
• Put every return calculation on its own line. A correct number typed on its own earns full credit for a calculation.
• Match the command word. 'Determine' needs a conclusion with a short reason. 'Justify' needs the reason linked to a client fact.
• Give only the number of responses requested, in the order asked, because extra responses are not evaluated.