CFA Level I 2025 Portfolio Management: Risk-Return Basics & Common Errors

Portfolio management is central to the CFA® Level I curriculum, representing 8–12 percent of exam questions. Its Risk-Return Basics section teaches candidates to quantify and balance potential gains against volatility, forming the bedrock of investment decision-making. Mastery of these concepts not only ensures passing exam performance but also equips future analysts to construct resilient portfolios in today’s dynamic markets.

Deriving Portfolio Variance from Fundamentals

The variance of a portfolio measures the dispersion of returns and is derived from individual asset variances and covariances. For two assets, the formula is:

σₚ² = w₁²σ₁² + w₂²σ₂² + 2w₁w₂Cov(R₁, R₂)

Where:

σₚ² = portfolio variance
w₁, w₂ = weights of Asset 1 and Asset 2
σ₁², σ₂² = variances of Asset 1 and Asset 2
Cov(R₁, R₂) = covariance between returns

Step-by-Step Derivation:

Start with definition: Var(aX + bY) = a²Var(X) + b²Var(Y) + 2abCov(X,Y).
Substitute: a = w₁, b = w₂; X = R₁, Y = R₂.
Expand: yields the formula above.

The covariance term captures how assets move together: a negative covariance reduces overall risk. The standard deviation is the square root of variance:

σₚ = √(σₚ²)

Calculating Expected Return CFA Level I 2025 Portfolio Management

Expected return is the probability-weighted average of possible outcomes or a weight-based sum for portfolios:

Single Asset:
E(R) = ∑ Pᵢ × Rᵢ
Where Pᵢ is the probability of outcome i.
Two-Asset Portfolio:
E(Rₚ) = w₁E(R₁) + w₂E(R₂)

Example: If Asset 1 has E(R₁)=8% and Asset 2 has E(R₂)=5%, with w₁=0.6 and w₂=0.4, then

E(Rₚ) = 0.6×8% + 0.4×5% = 4.8% + 2.0% = 6.8%

Accurate computation of E(R) is crucial for all subsequent risk-return measures.

Covariance and Correlation

Covariance measures joint variability:

Cov(R₁, R₂) = E[(R₁ - E(R₁))(R₂ - E(R₂))]

Correlation coefficient (ρ) normalizes covariance:

ρ₁₂ = Cov(R₁, R₂) / (σ₁σ₂)

ρ ∈ [–1, +1]
- –1: perfect negative correlation
- 0: no linear relationship
- +1: perfect positive correlation

Correlation informs diversification: pairing assets with low or negative ρ reduces portfolio risk.

CAPM in 2025: Using Beta Today

The Capital Asset Pricing Model (CAPM) links expected return to systematic risk (β):

E(Rᵢ) = R_f + βᵢ [E(R_m) – R_f]

R_f (Risk-Free Rate): proxied by U.S. 3-month T-bill yield ≈ 4.23% (June 2025)
Equity Risk Premium (ERP): current ERP ≈ 4.33% (reflecting expected excess return over T-bills)
E(R_m): implied market return ≈ R_f + ERP = 4.23% + 4.33% = 8.56%

Example: For an asset with β=1.2:

E(Rᵢ) = 4.23% + 1.2 × (8.56% - 4.23%) = 4.23% + 1.2 × 4.33% = 4.23% + 5.20% = 9.43%

Understanding CAPM’s inputs—especially current R_f and ERP—is pivotal for realistic return estimates in 2025 markets.

Mean-Variance Optimization & Efficient Frontier

Harry Markowitz’s Mean-Variance Optimization (MVO) constructs the efficient frontier: portfolios offering the highest return for a given level of risk. Key steps:

Compute expected returns, variances, and covariances for n assets.
Solve the quadratic optimization:
max_w { wᵀE[R] - λ wᵀΣw } subject to ∑ wᵢ = 1, wᵢ ≥ 0
where Σ is the covariance matrix and λ controls risk aversion.
Plot the resulting frontier; the global minimum variance portfolio lies at its leftmost point.

Adding a risk-free asset yields the Capital Market Line (CML), tangent to the frontier at the market portfolio. The slope of the CML is the market Sharpe ratio. CFA Level I 2025 Portfolio Management

Risk-Adjusted Performance Metrics

Evaluating portfolios requires adjusting returns for risk. Core measures include:

Sharpe Ratio (uses total risk σₚ):
Sharpe = (E(Rₚ) - R_f) / σₚ
indicating excess return per unit of volatility.
Treynor Ratio (uses systematic risk βₚ):
Treynor = (E(Rₚ) - R_f) / βₚ
suitable for well-diversified portfolios.
Jensen’s Alpha:
α = E(Rₚ) - [R_f + βₚ(E(R_m) - R_f)]
measures manager value added above CAPM prediction.
Modigliani–Modigliani (M²):
M² = Sharpe × σ_m + R_f
expresses Sharpe in percentage return units.

These metrics help compare strategies on a like-for-like basis.

Advanced Techniques: Hierarchical Risk Parity (HRP)

HRP, introduced by López de Prado (2016), addresses estimation errors in MVO by:

Clustering assets via hierarchical clustering on distance derived from correlations.
Quasi-diagonalizing the covariance matrix following the tree structure.
Allocating risk across clusters to achieve risk parity without solving quadratic programs.

HRP often yields more robust out-of-sample performance than traditional MVO in regimes with highly correlated assets.

Real-World Example with 2025 Data

Assumptions:

Asset A: E(Rₐ)=8.0%, σₐ=15.0%
Asset B: E(R_b)=5.0%, σ_b=10.0%
Correlation ρₐᵦ=0.25 (reflecting modest positive linkage)
Risk-free rate R_f=4.23% (3-month T-bill)
ERP=4.33%

Portfolio with wₐ=0.6, w_b=0.4:

Expected Return:
E(Rₚ) = 0.6×8.0% + 0.4×5.0% = 6.8%
Variance:
σₚ² = 0.6²×0.15² + 0.4²×0.10² + 2×0.6×0.4×0.15×0.10×0.25 = 0.0081 + 0.0016 + 0.0045 = 0.0142 σₚ = √0.0142 = 11.92%
Sharpe Ratio:
Sharpe = (6.8% - 4.23%) / 11.92% = 0.214
CAPM Expected Return (βₚ computed via covariance formula):
βₚ = [wₐCov(Rₐ,R_m) + w_bCov(R_b,R_m)] / Var(R_m)
(Omitted detailed calc for brevity.)

Such concrete examples bridge theory and exam application.

Common Pitfalls of CFA Candidates

Misusing Beta: Treating β as total risk rather than systematic risk
Overlooking Correlations: Assuming diversification from any number of assets without checking ρ
Ignoring Estimation Error in MVO inputs, leading to unstable allocations (“error maximization”)
Misapplying CAPM: Using outdated R_f or ERP values, yielding unrealistic E(Rᵢ)
Behavioral Biases: Letting loss aversion or familiarity bias drive “flavor-of-the-month” positioning
Assuming Bond Diversification: Underestimating rising stock-bond correlation in 2025, which may be as high as 0.67 on a rolling basis

For CFA Level I 2025 candidates, mastery of Risk-Return Basics involves:

Deriving and applying variance and covariance formulas.
Calculating expected returns for assets and portfolios.
Understanding CAPM in the context of current R_f (≈ 4.23%) and ERP (≈ 4.33%).
Constructing the efficient frontier and CML.
Applying risk-adjusted metrics (Sharpe, Treynor, Jensen’s α, M²).
Exploring advanced methods like HRP.
Avoiding common pitfalls by using up-to-date market data and robust techniques.

This comprehensive grasp not only drives exam success but also forms the analytical core for navigating modern, complex markets.

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