CFA Level I · CFA Level I Exam

Portfolio Management: An Overview: formula sheet

Full chapter guide

Key formulas

Portfolio expected return: E(Rp) = Σ wᵢ × E(Rᵢ); A weighted average of asset expected returns. Weights sum to 1. Diversification does not reduce this.
Two-asset portfolio variance: σp² = w₁²σ₁² + w₂²σ₂² + 2 w₁ w₂ ρ₁₂ σ₁ σ₂; Standard deviation is the square root. The correlation term ρ₁₂ drives the diversification benefit.
Perfect positive correlation case: σp = w₁σ₁ + w₂σ₂ when ρ₁₂ = +1; Risk is just the weighted average of the risks. No diversification benefit.
Total risk decomposition: Total risk = Systematic risk + Unsystematic risk; Diversification removes unsystematic risk. Systematic risk remains.
Three stages of the process: Planning → Execution → Feedback; Planning: client needs, IPS, capital market expectations. Execution: strategic asset allocation, security selection, trading. Feedback: monitoring, rebalancing, performance evaluation.
IPS core content: IPS = Objectives (return, risk) + Constraints (liquidity, time horizon, tax, legal/regulatory, unique circumstances); Remember it as objectives plus constraints. The IPS is a written document and is reviewed when the client's situation changes.
Drift from target weight: Drift = Current weight − Target weight; Current weight = asset value ÷ total portfolio value. Rebalancing is the action taken to reduce this drift.
Endowment/foundation return objective: Required return ≈ spending rate + inflation + investment costs; This is a rule of thumb for preserving real value. Use it when the question asks for the return needed to sustain spending forever.
Funded status of a DB plan: Funded status = plan assets − present value of pension liabilities; A surplus means more ability to take risk. A deficit means less ability, especially if the sponsor is weak.
Bank profitability driver: Net interest spread = yield on assets − cost of funds; Banks need positive spread, so asset-liability matching and liquidity matter.
Risk tolerance rule: Overall risk tolerance = lower of ability and willingness; If ability is low but willingness is high, treat risk tolerance as below average.
Net asset value per share: NAV per share = (Fund assets − Fund liabilities) ÷ Shares outstanding; Open-end funds transact at NAV, calculated at the end of the day. Closed-end funds and ETFs trade at market prices that can differ from NAV.
Premium or discount to NAV: Premium/(Discount) = (Market price − NAV) ÷ NAV; Positive means premium, negative means discount. Mainly relevant for closed-end funds and, to a small degree, ETFs.
Active return: Active return = Portfolio return − Benchmark return; Active management aims for a positive active return after fees.
Rule: buy-side vs sell-side: Buy-side = invests capital; Sell-side = sells securities and services; Asset managers, pension funds and hedge funds are buy-side. Brokers, investment banks and market makers are sell-side.
IPS structure (RRTTLLU): IPS = Objectives (return, risk) + Constraints (time horizon, tax, liquidity, legal and regulatory, unique); Return and risk are objectives. The other five are constraints. Exam questions often test this split.
Overall risk tolerance: Risk tolerance = lower of (ability to take risk, willingness to take risk); When the two conflict, the more conservative one generally drives the risk objective. This is a guideline, not an exact calculation.
Required nominal return (approximate): Required nominal return ≈ real return needed + expected inflation; Use the exact form (1 + real) × (1 + inflation) − 1 when the question asks for precision.
Ability vs willingness: Ability = objective (wealth, income, horizon, liquidity); Willingness = subjective (attitude, psychology); Use this to classify each fact in a case.
Current weight of an asset: Weight = Market value of asset ÷ Total portfolio market value; Compute after prices move. Compare with the target weight to find the drift.
Drift from target: Drift = Current weight − Target weight; Positive drift means overweight, so sell. Negative drift means underweight, so buy.
Trade amount to rebalance: Trade = (Target weight × Total portfolio value) − Current market value of asset; Positive means buy, negative means sell. Trades across all assets sum to zero if there is no cash flow in or out.
Active return: Active return = Portfolio return − Benchmark return; The basic feedback measure of manager performance against the benchmark.
Rebalancing trigger types: Calendar | Percentage-of-portfolio (corridor) | Combination; Calendar rebalances at fixed dates. A corridor rebalances when a weight leaves its allowed range. A combination checks on dates and trades only if a corridor is breached.

Quick revision

Diversification reduces portfolio risk when assets are not perfectly positively correlated.
The portfolio approach judges each asset by its effect on the whole portfolio, not on its own.
The process has three stages: planning, execution, and feedback (monitoring and rebalancing).
The IPS is written in the planning step and guides all later decisions.
Risk tolerance combines willingness (attitude) and ability (capacity) to take risk. When the two conflict, the more conservative one governs the risk objective.
Ability to take risk depends on factors such as wealth, time horizon and income stability.
Constraints in an IPS are liquidity, time horizon, tax, legal and regulatory, and unique circumstances.
Strategic asset allocation sets long-term target weights; tactical allocation makes short-term deviations to exploit views.
Passive management aims to match a benchmark; active management aims to beat it, usually at higher cost.
Pooled products include mutual funds, ETFs, hedge funds and private equity funds. The diversification and cost-sharing benefits apply mainly to mutual funds and ETFs.
Rebalancing returns the portfolio to target weights after market moves or after a change in the client's needs.
Performance feedback compares results with the benchmark and the IPS objectives, and may lead to revising the IPS.

Common mistakes

Saying diversification reduces expected return. Fix: Expected portfolio return is the weighted average of asset returns. Diversification lowers risk without changing that average.
Believing diversification can remove all risk. Fix: Only unsystematic risk can be diversified away. Systematic risk stays, because every asset is exposed to it.
Placing strategic asset allocation in the planning stage. Fix: Treat SAA as the first step of execution. Planning produces the IPS and expectations; SAA applies them.
Saying the IPS only lists the client's return goal. Fix: The IPS covers both objectives (return and risk) and constraints (liquidity, time horizon, tax, legal and regulatory, unique circumstances).
Saying the employee bears investment risk in a DB plan. Fix: In a DB plan the sponsor carries the risk because the benefit is promised. In a DC plan the employee carries it.
Treating a foundation's or endowment's horizon as short because it makes annual payouts. Fix: The institution is intended to last indefinitely, so the horizon is long even though some liquidity is needed for spending.
Treating closed-end funds like open-end funds and assuming they always trade at NAV. Fix: Remember that only open-end funds transact with the fund at NAV. Closed-end fund shares trade in the market and can sit at a premium or discount.
Labelling an asset manager or hedge fund as sell-side. Fix: Sell-side sells securities and services to investors, such as brokers and investment banks. Anyone who invests capital is buy-side.
Treating risk tolerance as only the client's attitude. Fix: Remember risk tolerance combines ability and willingness. Ability is objective; willingness is subjective.
Averaging ability and willingness when they conflict. Fix: Take the lower of the two as the overall risk tolerance, so the portfolio stays within what the client can both afford and stomach.

Exam tips

Read the question for 'return' versus 'risk'. Many traps swap the two.
If a numerical risk answer exceeds the weighted average of standard deviations and correlation is below 1, it is wrong.
Use your calculator memory to store variance terms, then press √ last.
Words like 'eliminates all risk' or 'guarantees' usually signal a wrong option.
With three options, sort each risk example into market-wide or firm-specific, then eliminate fast.
Questions often list a task and ask for its stage. Learn one task per stage cold: IPS (planning), SAA (execution), rebalancing (feedback).
Expect an IPS content question. Know that it holds objectives and constraints, and that it should be reviewed as circumstances change.
Watch for order traps. The IPS comes before asset allocation, and asset allocation comes before security selection.