Decompose a portfolio into factor exposures

Learning goals

• Calculate the scenario’s predicted excess return.
• Explain why 7.2% applies to this case.
• Identify the case-specific assumption or failure mode before taking action.

Draft · approximately 30 minutes, excluding further revision.

Shared case and decision context

A portfolio has excess-return model alpha=0.5%, market beta 1.2 and value-factor beta 0.4. Scenario market excess return is 6% and value factor return 2%. A manager calls the entire predicted return security-selection skill.

Economic or professional mechanism

A multifactor model separates systematic exposures from the residual under a particular model. Statistical, macroeconomic and fundamental models define factors differently. Factor betas are estimated conditional relationships; an omitted factor can contaminate estimated alpha. Risk attribution also needs the factor covariance matrix and specific-risk assumptions.

Apply, challenge and communicate

Predicted excess return is 8.5%, of which 8% comes from the two stated factor contributions. Only the 0.5% intercept is model alpha, and even it is not proven skill without uncertainty and omitted-factor checks. Monitor exposures through time because portfolio composition and market relationships can change.

APT assumptions, arbitrage checks and active-risk sources

In a multifactor arbitrage-pricing framework, well-diversified exposures with the same factorloadings should command consistent expected returns when arbitrage is restricted and residual risk can be diversified. This is not a claim that any individual mispriced stock offers a riskless trade. Check funding, shorting, transaction costs, model adequacy and whether residual risk truly cancels.

Supplementalexample: A has exposures(1,0), B(0,1), and C(0.5,0.5), expected excessreturns 6%,4%,7%. A 50/50 portfolio of A and B matches C’s loadings with expected 5%. The 2-point gap suggests relative mispricing under the model; short C/long A, B is not riskfree if specific risks remain. Active trackingvariance separates factor mismatch from security-specific risk under the covariance model. A high IR from an omitted factor should not be labeled selection skill.

Formula and assumptions

Expected excess return=alpha+sum(beta_j*factor return_j)

Case analysis with explicit assumptions

1. A portfolio has excess-return model alpha=0.5%, market beta 1.2 and value-factor beta 0.4. Scenario market excess return is 6% and value factor return 2%. A manager calls the entire predicted return security-selection skill.
2. Method: Expected excess return=alpha+sum(beta_j*factor return_j)
3. Case result: 8.50%. Predicted excess return is 8.5%, of which 8% comes from the two stated factor contributions. Only the 0.5% intercept is model alpha, and even it is not proven skill without uncertainty and omitted-factor checks. Monitor exposures through time because portfolio composition and market relationships can change.

Errors to catch

• Do not replace the stated assumptions with an unstated shortcut. Reconcile units, timing and the claim being valued or duty being assessed.
• No statistical scrutiny is not a defensible conclusion for these case facts.

Original knowledge check

Answer every question before checking. Review explanations after submitting; retry starts a new attempt.

Sources and coverage status

These original lessons are drafts. Public outlines are used to check scope; the official learning-outcome text and proprietary question banks are not reproduced here. Follow the source for exam-year requirements and updates.

• Reference · www.cfainstitute.org
• Reference · www.investor.gov