CFA® Level I Portfolio Management

The 6 learning modules

1. 01 Portfolio Risk and Return: Part I

   The building blocks of portfolio theory. You review the historical return and risk of the major asset classes, including skewness, kurtosis and liquidity, then model risk aversion with a utility function and indifference curves. The core is the risk of a portfolio of two or more assets and how correlation drives diversification, leading to the minimum-variance frontier, the efficient frontier, the capital allocation line and the choice of an optimal portfolio for a given investor.

   8 lessons · 6 videos in the Academy →

2. 02 Portfolio Risk and Return: Part II

   Capital market theory. When all investors share the same expectations, the optimal risky portfolio becomes the market portfolio and the capital allocation line becomes the capital market line, including the case where borrowing costs more than lending. You split total risk into systematic and nonsystematic risk, estimate beta, and use the CAPM and the security market line to find expected returns. The module ends with the CAPM's assumptions and limitations, the Sharpe ratio, Treynor ratio, M² and Jensen's alpha, and using the security market line to decide whether a security is undervalued or overvalued.

   7 lessons · 7 videos in the Academy →

3. 03 Portfolio Management: An Overview

   Why a portfolio perspective matters, including the limit of diversification in a crisis, when correlations tend to rise. You learn the three steps of the portfolio management process (planning, execution and feedback) and the needs of different investors: individuals, defined benefit and defined contribution pension plans, endowments, foundations, banks, insurers and sovereign wealth funds. The rest covers the asset management industry, active versus passive management and recent trends, and pooled products such as mutual funds, ETFs, hedge funds and private equity funds, with their fee structures.

   7 lessons · 1 video in the Academy →

4. 04 Basics of Portfolio Planning and Construction

   How an investment policy statement is built. You set risk objectives (absolute or relative to a benchmark), separate a client's ability to take risk from their willingness, and set return objectives, including required returns after spending, inflation, costs and taxes. The constraints are liquidity, time horizon, taxes, legal and regulatory factors and unique circumstances. The module then covers capital market expectations, strategic asset allocation, how to define asset classes, rebalancing ranges, tactical deviations, and ESG approaches such as exclusionary screening, best-in-class selection, engagement and impact investing.

   8 lessons · 3 videos in the Academy →

5. 05 The Behavioral Biases of Individuals

   The difference between cognitive errors, which come from faulty reasoning, and emotional biases, which come from feelings. Cognitive errors split into belief perseverance biases (conservatism, confirmation, representativeness, illusion of control, hindsight) and processing errors (anchoring, mental accounting, framing, availability). The emotional biases are loss aversion, overconfidence, self-control, status quo, endowment and regret aversion. Questions give a short scenario and ask you to name the bias or its consequence, and the module ends with how biases may explain momentum, bubbles and crashes, and the value effect.

   8 lessons · 3 videos in the Academy →

6. 06 Introduction to Risk Management

   Risk management as a process for choosing which risks to take, not for avoiding risk altogether. It covers the risk management framework, risk governance from the board down, risk tolerance and risk budgeting. You classify risks as financial (market, credit, liquidity) or non-financial (operational, legal, model, tax, solvency and others), see how risks interact, and measure them with standard deviation, beta, duration, delta, gamma, vega, value at risk and stress tests. Finally, you choose between prevention and avoidance, acceptance, transfer (insurance) and shifting (derivatives).

   8 lessons · 2 videos in the Academy →

What the questions cover

• Return and risk of asset classes, risk aversion, utility and indifference curves
• Two-asset portfolio risk, correlation and the power of diversification
• The efficient frontier, the capital allocation line and the capital market line
• Systematic risk, beta, the CAPM and the security market line
• Performance measures: Sharpe ratio, Treynor ratio, M² and Jensen's alpha
• Investment policy statements: risk and return objectives, constraints and asset allocation
• Behavioural biases, and the risk management framework, metrics and ways of modifying risk

Key formulas

Two-asset portfolio variance

$\displaystyle \sigma_P^2 = w_1^2\sigma_1^2 + w_2^2\sigma_2^2 + 2w_1w_2\rho_{12}\sigma_1\sigma_2$The last term is the covariance term. The lower the correlation, the lower the portfolio risk.

Utility of an investment

$\displaystyle U = E(r) - \frac{1}{2}A\sigma^2$A is the risk-aversion coefficient: positive for a risk-averse investor, zero for risk-neutral. Use decimals, not percentages.

Capital allocation line / capital market line

$\displaystyle E(R_P) = R_f + \frac{E(R_M) - R_f}{\sigma_M}\,\sigma_P$The slope is the Sharpe ratio of the risky portfolio. With the market portfolio as the risky portfolio, the line is the CML.

Beta

$\displaystyle \beta_i = \frac{\text{Cov}(R_i, R_m)}{\sigma_m^2} = \rho_{i,m}\frac{\sigma_i}{\sigma_m}$Beta measures systematic risk only. The market has a beta of 1 and the risk-free asset a beta of 0.Learn it: Return-generating models, the market model and beta →

CAPM / security market line

$\displaystyle E(R_i) = R_f + \beta_i\,[E(R_m) - R_f]$A security whose forecast return lies above the SML is undervalued; below it, overvalued.Learn it: The CAPM: assumptions, the SML and its limits →

Sharpe ratio

$\displaystyle \frac{R_p - R_f}{\sigma_p}$Excess return per unit of total risk.Learn it: Sharpe ratio, Treynor ratio, M² and Jensen's alpha →

Treynor ratio

$\displaystyle \frac{R_p - R_f}{\beta_p}$Excess return per unit of systematic risk. Suitable only for well-diversified portfolios.Learn it: Sharpe ratio, Treynor ratio, M² and Jensen's alpha →

M² (risk-adjusted performance)

$\displaystyle M^2 = (R_p - R_f)\frac{\sigma_m}{\sigma_p} + R_f$The portfolio's return if it were scaled to the market's total risk. M² alpha is M² minus the market return; the ranking always matches the Sharpe ratio.

Jensen's alpha

$\displaystyle \alpha_p = R_p - [R_f + \beta_p(R_m - R_f)]$Actual return minus the return the CAPM predicts for the portfolio's beta.Learn it: Sharpe ratio, Treynor ratio, M² and Jensen's alpha →

The Portfolio Management formula sheet: the key formulas explained

Common mistakes

• Putting percentages into the utility function. With E(r) = 10% and σ = 20%, U = 0.10 − 0.5 × A × 0.04, not 10 − 0.5 × A × 400.
• Forgetting the 2 in the covariance term of portfolio variance, or dropping the term altogether, which is only correct when the correlation is zero.
• Dividing covariance by the market's standard deviation instead of its variance when calculating beta.
• Confusing the CML with the SML. The CML plots expected return against total risk and only efficient portfolios lie on it; the SML plots it against beta and every correctly priced security lies on it.
• Classifying overconfidence as a cognitive error. It has features of both, but the curriculum places it among the emotional biases. Remember too that cognitive errors are usually moderated, while strong emotional biases are usually adapted to.
• Adding spending, inflation and costs to get a required return when the question asks for a compounded figure, or grossing up an after-tax return by multiplying by (1 + t) instead of dividing by (1 − t).
• Reading a 5% value at risk as the most the portfolio can lose. It is the minimum loss expected in the worst 5% of outcomes, and with a normal distribution it is measured from the expected return, not from zero.

How to study it

• Match the performance measure to the situation: Sharpe and M² for a portfolio that is the investor's whole risky position, Treynor and Jensen's alpha for one that is well diversified.
• Classify biases by type (cognitive or emotional) before anything else. Many questions test the classification, or what follows from it: whether the adviser should moderate the bias or adapt to it.
• Keep returns in decimals whenever you square something. The utility function and portfolio variance both give nonsense answers if you mix percentages and decimals.
• Practise the two-asset variance calculation until you can do it on your calculator without writing out every term. It is the longest calculation in the topic and comes up in several forms.
• For the descriptive modules, learn short lists: the three steps of the process, the IPS constraints, the ways to modify risk. Questions usually give a scenario and ask which item on the list it is.

Try 3 Portfolio Management questions

Practise and prove Portfolio Management

The question bank and the mock exams are the practice half of CheapMocks Academy. Try the free sample questions, see the topic weights for the whole exam and the latest Level I pass rates.

Portfolio Management FAQ