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Study guide · Session 2

Portfolio Construction

8-12% of the exam · session 2 · 6 learning modules

This topic covers how investors combine assets into portfolios: digital assets as a new asset class, the mathematics of risk, return and diversification, the CAPM and risk-adjusted performance measures, the investors and products of the asset management industry, the investment policy statement and the behavioural biases that shape decisions. Level I questions mix short calculations (portfolio standard deviation, CAPM, Sharpe and Treynor ratios) with recall and application of definitions.

A study feature written by ExamDragon, not part of the real exam. Each heading is one of this topic's 6 learning modules in the 2027 curriculum, named in our own words.

At a glance

Session 2
8-12%

of the exam, as CFA Institute weights it for 2027

Weight
8-12%
Modules
6
Key terms
9

What this guide covers, module by module

  1. PC.1Diversification, utility and efficient frontiers
  2. PC.2CAPM, beta and risk-adjusted ratios
  3. PC.3Investor types, pensions and pooled funds
  4. PC.4Writing an IPS and allocating assets
  5. PC.5Cognitive errors and emotional biases
  6. PC.6Risk frameworks, governance and budgets

PC.1Diversification, utility and efficient frontiers

  • Over long periods, small-company stocks have had the highest average returns and risk, then large-company stocks, then bonds, then Treasury bills; higher return has come with higher risk.
  • A risk-averse investor needs a higher expected return to accept more risk; utility can be written U = E(r) - 0.5 x A x variance, where A is the risk-aversion coefficient (higher A means more risk averse; A = 0 is risk neutral).
  • Sample variance = sum of squared deviations from the mean / (n - 1); covariance measures how two returns move together, and correlation = covariance / (sigma1 x sigma2), between -1 and +1.
  • Two-asset portfolio variance = w1^2 x s1^2 + w2^2 x s2^2 + 2 x w1 x w2 x rho x s1 x s2; the portfolio standard deviation is below the weighted average of the two whenever rho is below +1.
  • The lower the correlation, the larger the diversification benefit; with rho = -1 a zero-risk portfolio of the two assets exists.
  • The minimum-variance frontier shows the lowest risk for each expected return; its leftmost point is the global minimum-variance portfolio, and the part above it is the efficient frontier.
  • The optimal portfolio is where the investor's highest attainable indifference curve touches the capital allocation line.
  1. The situationA portfolio is 50% in asset A (standard deviation 18%) and 50% in asset B (standard deviation 12%), with correlation 0.2.
  2. Step 1Variance = 0.25 x 0.0324 + 0.25 x 0.0144 + 2 x 0.5 x 0.5 x 0.2 x 0.18 x 0.12.
  3. Step 2= 0.0081 + 0.0036 + 0.00216 = 0.01386.
  4. Step 3Standard deviation = square root of 0.01386 = 11.8%, against a weighted average of 15.0%.
  5. Where questions turnForgetting to square the weights and standard deviations, or using the weighted average of standard deviations, which is correct only when the correlation is +1.
  6. The takeawayCorrelation below 1 cuts portfolio risk below the weighted average of the assets' risks.
Practise PC.1

PC.2CAPM, beta and risk-adjusted ratios

  • Combining a risk-free asset with a risky portfolio gives a straight capital allocation line: E(Rp) = Rf + [(E(Ri) - Rf) / sigma_i] x sigma_p; when the risky portfolio is the market, the line is the capital market line.
  • Total risk = systematic (market) risk + nonsystematic (firm-specific) risk; nonsystematic risk can be diversified away at little cost, so the market rewards only systematic risk.
  • Beta = covariance(i, m) / variance(m) = correlation x sigma_i / sigma_m; the market model is Ri = alpha + beta x Rm + error.
  • CAPM: E(Ri) = Rf + beta x [E(Rm) - Rf]; plotted against beta it is the security market line. An asset whose forecast return is above the SML is undervalued, below it overvalued.
  • Sharpe ratio = (Rp - Rf) / sigma_p; Treynor ratio = (Rp - Rf) / beta_p; M-squared = Rf + Sharpe ratio x sigma_m (compare with Rm); Jensen's alpha = Rp - [Rf + beta_p x (Rm - Rf)].
  • Sharpe and M-squared use total risk and suit a whole portfolio; Treynor and Jensen's alpha use systematic risk and suit a well-diversified portfolio that is part of a larger one.
  1. The situationA fund returned 9% with standard deviation 15% and beta 0.9; the risk-free rate was 3% and the market returned 8% with standard deviation 12%.
  2. Step 1Sharpe = (9 - 3) / 15 = 0.40, against the market's (8 - 3) / 12 = 0.42.
  3. Step 2Treynor = (9 - 3) / 0.9 = 6.67%, against the market's 5.00%.
  4. Step 3Jensen's alpha = 9 - [3 + 0.9 x 5] = 1.5%; M-squared = 3 + 0.40 x 12 = 7.8%, 0.2% below the market.
  5. Where questions turnUsing total risk (standard deviation) where beta belongs, as in the CAPM, or forgetting to subtract the risk-free rate.
  6. The takeawayThe fund beat the market on systematic risk but not on total risk, so it carries unrewarded nonsystematic risk.
Practise PC.2

PC.3Investor types, pensions and pooled funds

  • The portfolio approach judges each investment by its effect on the whole portfolio's risk and return; diversification lowers risk without necessarily lowering expected return, though it may fail in severe crises when correlations rise.
  • The process has three steps: planning (understand the client, write the investment policy statement), execution (asset allocation, security analysis, portfolio construction) and feedback (monitoring, rebalancing and performance evaluation).
  • Investors differ: individuals (varied horizons and needs), defined benefit plans, endowments and foundations (long horizons, spending needs), banks (short horizon, liquidity, matching deposits), insurers (life: longer horizon; property and casualty: shorter, more liquidity), sovereign wealth funds.
  • In a defined benefit plan the employer promises a retirement benefit and bears the investment risk; in a defined contribution plan contributions are set and the employee bears the investment risk and chooses the investments.
  • Asset managers can be active or passive, and traditional or alternative; passive management has gained share, and the industry has consolidated.
  • Open-end mutual funds issue and redeem shares at net asset value; closed-end funds have a fixed number of shares that trade on an exchange, often away from NAV; exchange-traded funds trade intraday, usually close to NAV because authorised participants create and redeem units.
  1. The situationTwo employees retire with the same salary history: one in a defined benefit plan promising 1.5% of final salary per year of service, the other in a defined contribution plan whose account fell 20% in the last year.
  2. Step 1The defined benefit pension is set by the formula; the investment loss falls on the sponsor, which may need to contribute more.
  3. Step 2The defined contribution account balance is what the employee has; the 20% loss falls on the employee.
  4. Step 3So investment risk sits with the sponsor in one case and with the participant in the other.
  5. Where questions turnMixing up open-end and closed-end funds: only closed-end fund shares trade at prices that can sit well away from NAV for long periods.
  6. The takeawayWho bears investment risk is the key difference between the two plan types.
Practise PC.3

PC.4Writing an IPS and allocating assets

  • An investment policy statement (IPS) is a written agreement that sets out the client's objectives and constraints and the rules for managing the portfolio; it gives discipline and continuity if the adviser changes.
  • Major components: introduction, statement of purpose, duties and responsibilities, procedures for updating, investment objectives, constraints, guidelines, evaluation and review, and often appendices on strategic asset allocation and rebalancing.
  • Return objectives can be absolute (a required return) or relative to a benchmark; a required real return combines with inflation as (1 + real) x (1 + inflation) - 1.
  • Risk tolerance has two parts: ability (capacity), set by horizon, wealth and spending needs relative to assets, and willingness, a psychological attitude; when they conflict, the adviser usually follows the lower and discusses the gap with the client.
  • Constraints: liquidity, time horizon, tax concerns, legal and regulatory factors, and unique circumstances (including ethical or ESG preferences).
  • Asset classes should be internally similar, distinct from each other with low correlations, and together cover the investable universe; strategic asset allocation is the long-term mix, tactical allocation a short-term deviation.
  • ESG can be integrated by negative or positive screening, ESG integration in analysis, thematic investing, impact investing and active ownership (engagement and proxy voting).
  1. The situationA retired client with USD 2,000,000 needs USD 70,000 a year from the portfolio and wants to keep its purchasing power with expected inflation of 2.5%.
  2. Step 1Real return needed = 70,000 / 2,000,000 = 3.5%.
  3. Step 2Nominal return = (1.035 x 1.025) - 1 = 6.09%, about 6.1%.
  4. Step 3The additive shortcut 3.5% + 2.5% = 6.0% slightly understates it.
  5. Where questions turnAssuming a client who says they love risk can take it: ability to take risk can be low (short horizon, large spending needs) even when willingness is high.
  6. The takeawayReturn objectives are built from spending needs and inflation, compounded rather than added.
Practise PC.4

PC.5Cognitive errors and emotional biases

  • Cognitive errors come from faulty reasoning or information processing and can often be corrected with better information and education; emotional biases come from feelings and intuition and are harder to correct, so advisers often adapt to them.
  • Belief perseverance errors: conservatism (slow to update on new information), confirmation (seeking support for existing views), representativeness (judging by resemblance or a small sample), illusion of control and hindsight.
  • Processing errors: anchoring and adjustment, mental accounting (treating money differently by its source or purpose), framing (choices change with how the question is posed) and availability (overweighting easily recalled events).
  • Emotional biases: loss aversion (losses hurt more than equal gains please, leading to holding losers too long and selling winners early), overconfidence, self-control, status quo, endowment and regret aversion.
  • Biases can help explain market patterns that traditional finance struggles with, such as momentum, bubbles and crashes, and the value effect.
  1. The situationAn investor keeps a stock that has fallen 40% because selling would 'make the loss real', while selling another that rose 15% to 'lock in the gain'.
  2. Step 1The pain of realising a loss outweighs the pleasure of an equal gain.
  3. Step 2This is loss aversion, an emotional bias, which shows up as the disposition effect.
  4. Step 3An adviser might moderate it with rules set in advance, such as a review trigger after a set decline.
  5. Where questions turnClassifying overconfidence or loss aversion as cognitive errors, or confusing anchoring (sticking to an initial number) with conservatism (slow updating of beliefs).
  6. The takeawayEmotional biases are usually managed by adapting the process rather than by more information.
Practise PC.5

PC.6Risk frameworks, governance and budgets

  • Risk management is the process of setting the level of risk an organisation is willing to take, measuring the risk it actually takes and adjusting the two to match; the aim is the right risk, not the least risk.
  • Risk governance is the top-down layer: the board sets risk tolerance and oversight, and management carries it out through policies, limits and reporting.
  • Risk tolerance is how much risk the organisation will accept in pursuit of its goals; it should be set before a crisis, not during one.
  • Risk budgeting allocates the total risk the organisation will bear across activities or asset classes, for example by volatility, factor exposure or value at risk.
  • Financial risks include market, credit and liquidity risk; non-financial risks include operational, legal, compliance, model, settlement, tax and reputational risk, and the two kinds often interact, especially in stress.
  • Ways to modify risk: avoid it, accept it (self-insure or diversify), transfer it (insurance) or shift it (derivatives such as forwards, futures, swaps and options).
  1. The situationA pension fund's board sets a maximum annual volatility of 10% for the whole portfolio and splits it between equities (7 percentage points of contribution to total volatility) and bonds (3 percentage points).
  2. Step 1The 10% ceiling is a statement of risk tolerance made by the governing body.
  3. Step 2Dividing that ceiling between asset classes is risk budgeting.
  4. Step 3Measuring each manager against its share and acting on breaches is risk monitoring and modification.
  5. Where questions turnConfusing transferring risk (paying an insurer to bear the loss) with shifting risk (changing the payoff profile with a derivative), or treating risk management as risk minimisation.
  6. The takeawayGovernance sets the limit, budgeting allocates it, and management measures and adjusts against it.
Practise PC.6

Key terms

Consensus mechanism
The rule a distributed ledger uses to agree which transactions are valid.
Stablecoin
A digital asset designed to keep a stable value, usually against a fiat currency.
Risk-aversion coefficient (A)
The parameter in the utility function that measures how much an investor dislikes variance.
Global minimum-variance portfolio
The portfolio of risky assets with the lowest possible variance.
Capital market line
The capital allocation line that uses the market portfolio as the risky portfolio.
Beta
Covariance of an asset with the market divided by the market's variance; a measure of systematic risk.
Security market line
The CAPM plotted as expected return against beta.
Investment policy statement
The written document setting a client's objectives, constraints and portfolio rules.
Loss aversion
Feeling the pain of a loss more strongly than the pleasure of an equal gain.

After this guide: After this guide you should be able to compute portfolio risk, CAPM returns and the four performance ratios, place an investor and an IPS component correctly, and classify a behavioural bias.

Practise Portfolio Construction

Built to the topics and weights CFA Institute publishes for the 2027 Level I curriculum. The module names, explanations, worked examples and traps are ExamDragon's own. Every source this path is built on.