Portfolio Management Process: formula sheet

Key formulas

Discretionary service

Manager decides + manager executes

Done independently on the client's behalf, as per the agreement and the client's objectives.

Non-discretionary service

Manager suggests + client approves + manager executes

Each transaction needs client consent. Execution is still by the manager.

Advisory service

Manager advises + client decides + client executes

No authority to transact on the client's account.

Core objective

Best return for the risk the client can accept

Objectives are set by the client's goals, risk tolerance, horizon, liquidity needs and constraints.

Overall risk level

Risk the portfolio can take = lower of (risk tolerance, risk capacity)

If willingness and ability differ, follow the lower one. Do not average them in exam answers.

Objectives

Objectives = Return objective + Risk objective

Both must be set. A return target without a risk limit is incomplete.

Constraints (memory list)

Time horizon, Liquidity, Taxes, Legal/regulatory, Unique circumstances

Constraints limit how objectives can be pursued. They are not objectives themselves.

Tolerance vs capacity

Tolerance = willingness (psychological); Capacity = ability (financial)

Capacity depends on wealth, income stability, liabilities, dependants and horizon.

Objectives of an IPS

Objectives = Return objective + Risk objective

Risk objective covers both willingness to take risk and ability to take risk. The lower of the two should guide the portfolio.

Constraints of an IPS

Constraints = Time horizon + Liquidity + Taxes + Legal/regulatory + Unique circumstances

Remember as the five constraints. Return and risk are objectives, not constraints.

Guidelines in an IPS

Guidelines = Asset allocation ranges + Permitted/prohibited instruments + Benchmark + Review and rebalancing + Reporting

These convert objectives and constraints into working rules for the manager.

Risk tolerance rule

Overall risk tolerance = lower of (willingness, ability)

Use this when willingness and ability to take risk conflict.

Portfolio weight of an asset class

Weight = Value of the asset class ÷ Total portfolio value × 100

Use current market values. Weights of all classes add up to 100%.

Expected portfolio return

E(Rp) = Σ (wᵢ × E(Rᵢ))

Weighted average of each class's expected return. Weights must add up to 1.

Strategic vs tactical vs dynamic

Strategic = long-term fixed targets; Tactical = short-term view-based tilts; Dynamic = ongoing adjustment to market or situation

Match the time horizon and trigger given in the question.

Rebalancing amount

Amount to move = (Current weight − Target weight) × Total portfolio value

A positive result means you sell that class; a negative result means you buy.

Top-down sequence

Economy → Sector/Industry → Company

Moves from broad to narrow. The exam may ask you to put the steps in order.

Bottom-up sequence

Company → (Sector and economy are secondary)

Stock selection drives the portfolio. Macro views matter less.

Active return

Active return = Portfolio return − Benchmark return

Positive means the manager beat the benchmark. Passive aims for active return near zero.

Price-to-earnings ratio

P/E = Market price per share ÷ Earnings per share

Growth stocks usually show high P/E. Value stocks usually show low P/E.

Price-to-book ratio

P/B = Market price per share ÷ Book value per share

A low P/B is a common value screen. It is not proof of a bargain.

Current weight of an asset class

Weight = Value of asset class ÷ Total portfolio value × 100

Calculate this for every asset class before comparing with the target.

Drift

Drift = Current weight − Target weight

Positive drift means overweight (sell). Negative drift means underweight (buy).

Rebalancing amount

Trade value = (Target weight × Total portfolio value) − Current value

Positive means buy. Negative means sell. Trades across classes net to zero if there is no new cash and no costs.

Active return vs benchmark

Active return = Portfolio return − Benchmark return

Compare over the same period and on the same basis (for example both total return).

Constant mix response

Market rises → sell the rising asset; market falls → buy the falling asset

Buy and hold does no trading. CPPI does the opposite of constant mix: it buys the rising asset and sells the falling one.

Absolute return

(Ending value − Beginning value + Income) ÷ Beginning value × 100

Ignores time. Use for periods up to a year.

CAGR

(Ending value ÷ Beginning value)^(1/n) − 1

n is the number of years. Assumes no interim cash flows.

Holding period return for a sub-period

(End value − Begin value − Cash flow added) ÷ Begin value

Value is measured just before each cash flow.

Time-weighted return

[(1 + r₁) × (1 + r₂) × … × (1 + rₙ)] − 1

Geometric linking of sub-period returns. Not affected by flow size or timing.

Money-weighted return

Rate r at which PV of inflows = PV of outflows (IRR / XIRR)

Affected by size and timing of flows.

Sharpe ratio

(Rp − Rf) ÷ σp

Uses total risk (standard deviation).

Treynor ratio

(Rp − Rf) ÷ βp

Uses systematic risk (beta).

CAPM expected return

Rf + β × (Rm − Rf)

Required return for the portfolio's beta.

Jensen's alpha

Rp − [Rf + β × (Rm − Rf)]

Positive means outperformance after adjusting for beta.

Tracking error

Standard deviation of (Rp − Rbenchmark)

Measures how closely the portfolio follows its benchmark.

Quick revision

• The process runs in order: know the client, write the IPS, set allocation, construct, monitor and rebalance, then evaluate.
• Risk tolerance is willingness to take risk; risk capacity is ability to bear loss. The lower of the two should guide the plan.
• Investor objectives cover return and risk. Constraints include time horizon, liquidity needs, taxes, legal limits and special circumstances.
• The investment policy statement is a written document that records objectives, constraints and guidelines for managing the portfolio.
• Strategic asset allocation sets long-term target weights; tactical allocation makes short-term deviations to use market views.
• Asset allocation is a major driver of portfolio risk and return, more than individual security picks.
• Active management tries to beat a benchmark; passive management aims to track it.
• Growth style focuses on companies with high earnings growth; value style focuses on stocks priced low relative to fundamentals.
• Rebalancing brings weights back to target after market moves or when the client's needs change.
• Monitoring covers both the market and the client's circumstances, because a life change can alter the IPS.
• Evaluate performance against the client's objectives and a suitable benchmark, and look at returns in relation to risk taken.

Common mistakes

• Treating non-discretionary as the same as advisory Fix: In non-discretionary, the manager still executes after approval. In advisory, the client executes.
• Thinking discretionary means the manager can ignore the client's wishes Fix: Discretion works within the agreement, the client's objectives and any restrictions set by the client.
• Treating risk tolerance and risk capacity as the same thing. Fix: Tolerance is willingness (mind). Capacity is ability (money). Ask which one the fact describes.
• Choosing the higher of the two when they differ. Fix: The portfolio should follow the lower of tolerance and capacity.
• Treating risk tolerance as a constraint. Fix: Remember that return and risk are the two objectives. Constraints are time horizon, liquidity, taxes, legal and regulatory, and unique circumstances.
• Using willingness to take risk alone. Fix: Also test ability, based on income, wealth, horizon and dependents. The lower of the two sets the overall risk tolerance.
• Treating tactical and dynamic allocation as the same thing. Fix: Tactical is a view-based, temporary tilt around a base mix. Dynamic is a continuing adjustment, often rule based.
• Thinking strategic allocation is never changed. Fix: It is reviewed when the client's goals, horizon or risk capacity change. It is not changed for short-term market moves.
• Saying active management always beats passive. Fix: Active management aims to beat the benchmark but can lag it, especially after higher costs.
• Mixing up top-down and bottom-up. Fix: Top-down starts at the economy. Bottom-up starts at the single company.

Exam tips

• Always apply the decide-and-execute test before reading the options.
• Reject options that use words like guaranteed, assured or risk-free.
• Expect scenario questions where a client approves or does not approve each trade. Look for the approval step.
• Remember that objectives are personal to the client. Two clients can have very different portfolios.
• If an option names risk and return together, it is often the stronger choice.
• Questions are usually short client stories. Tag each fact as tolerance or capacity before reading the options.
• Be alert to options that follow the client's wish over their ability. These are common trap options.
• Know the constraint list cold: time horizon, liquidity, taxes, legal and regulatory, unique circumstances.