Unit 8 Assessment — Risk & Return

📊 Return & Risk Measures

📐 CAPM & SML

🔗 Portfolio Theory

⚖️ Risk Classification

Return & Risk Measures

Expected ReturnE(R) = Σ [P_i × R_i]

Variance (σ²)σ² = Σ [P_i × (R_i − E(R))²]

Standard Deviation (σ)σ = √Variance — measures total risk

Coefficient of VariationCV = σ ÷ E(R) — risk per unit of return

Historical Avg ReturnAvg = Σ Returns ÷ N periods

CAPM & Security Market Line

CAPM Required Returnr_i = r_RF + (RP_M) × β_i

Market Risk PremiumRP_M = r_M − r_RF

Beta Interpretationβ=1.0 → market risk · β>1 → aggressive · β<1 → defensive

SML EquationRequired return = f(beta) → straight line

Overvalued / UndervaluedExpected < Required → overvalued; Expected > Required → undervalued

Portfolio Theory

Portfolio Expected ReturnE(R_p) = Σ w_i × E(R_i)

Diversification BenefitCombining assets reduces unsystematic risk

Correlation Coefficientρ = +1: no diversification benefit; ρ = −1: perfect hedge

Efficient FrontierSet of portfolios with max return per unit of risk

Portfolio Betaβ_p = Σ w_i × β_i

Risk Classification

Systematic (Market) RiskAffects all firms · cannot be diversified away · measured by beta

Unsystematic (Firm-Specific)Unique to one firm · diversification eliminates this

Total Riskσ² = Systematic Risk + Unsystematic Risk

Stand-Alone RiskRisk of holding a single asset (uses σ or CV)

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out of 100 points

—

Section 1

—/40

Multiple Choice

Section 2

—/20

True / False

Section 3

—/20

Short Answer

Section 4

—/20

Extended Response

⚠ Sections 3 & 4 are teacher-graded. Use the rubric selectors below to finalize the score.

Multiple Choice

Select the best answer · Includes CAPM, beta, expected return & portfolio calculations

2 pts each · 40 pts

Click the best answer. Use the formula reference and asset class strip above for calculation questions. Each question is worth 2 points.

True or False

Click TRUE or FALSE for each statement

2 pts each · 20 pts

Select TRUE or FALSE for each statement. Each is worth 2 points.

Short Answer

Show all calculations + explain in 2–4 sentences · Teacher-graded

5 pts each · 20 pts

Answer in 2–4 complete sentences. Show every calculation step clearly. Rubric selectors appear after grading.

Extended Response — Swanson Initiative Portfolio Risk Analysis

3-stock portfolio · CAPM · Diversification · Investment recommendation · Teacher-graded

20 pts

Read the scenario carefully. Write a well-organized analytical memo of at least 8 sentences. Show all calculations with labeled steps. Use and underline at least four unit vocabulary terms.

📋 Scenario — The Swanson Initiative: Building a Youth Investment Portfolio

The Swanson Initiative has approved $30,000 for a diversified equity portfolio to demonstrate long-term wealth-building to BBYM youth participants. The investment committee is evaluating three stocks. As student portfolio analyst, you must analyze the risk and return of each position, build the portfolio, and write a recommendation memo.

Stock A — Utility (Defensive)

Weight: 40% · Beta: 0.6 · Expected Return: 8%

Stock B — Consumer (Moderate)

Weight: 35% · Beta: 1.1 · Expected Return: 11%

Stock C — Tech (Aggressive)

Weight: 25% · Beta: 1.8 · Expected Return: 15%

Market Conditions

Risk-free rate (r_RF): 4.5% · Market return (r_M): 10.5% · Market Risk Premium: 6.0%

35 Write your full portfolio analysis memo covering all four parts: (a) Calculate the portfolio's weighted average expected return and weighted average beta — show all work; (b) Using CAPM, calculate the required return for each of the three stocks individually (r_RF = 4.5%, RP_M = 6.0%) — show each calculation and state whether each stock appears overvalued, undervalued, or fairly valued by comparing its expected return to its CAPM required return; (c) Explain the difference between systematic risk and unsystematic risk — identify which type each stock's beta measures, and explain what diversification does to the portfolio's total risk; (d) Write a 2–3 sentence portfolio recommendation to the Swanson Initiative committee explaining whether this 3-stock mix is appropriate for a youth community trust fund, referencing the portfolio beta and the risk-return tradeoff. Use at least four underlined vocabulary terms.

📋 Teacher Scoring Rubric

Criterion	Excellent (Full)	Proficient (Partial)	Developing (Minimal)	Score
Part (a) — Portfolio E(R) & Beta E(R_p) = .40×8% + .35×11% + .25×15% = 3.2+3.85+3.75 = 10.8% · β_p = .40×0.6+.35×1.1+.25×1.8 = 0.24+0.385+0.45 = 1.075	Both E(R_p) = 10.8% and β_p = 1.075 correct with weighted steps shown	One calculation correct; minor arithmetic error on other	Both wrong or no work shown	/5
Part (b) — CAPM for Each Stock A: 4.5+6×0.6=8.1% (expected 8% ≈ fairly valued / slightly overvalued) · B: 4.5+6×1.1=11.1% (expected 11% ≈ fairly valued) · C: 4.5+6×1.8=15.3% (expected 15% → slightly overvalued)	All 3 CAPM calculations correct; overvalued/undervalued/fair judgment made for each with comparison shown	2 of 3 CAPM values correct; valuations partially stated	Fewer than 2 correct; no valuation comparison	/6
Part (c) — Systematic vs. Unsystematic Risk	Clearly defines both risk types; correctly states beta measures systematic risk; explains diversification eliminates unsystematic risk but not systematic	Both types defined but diversification explanation incomplete	Only one type defined; no diversification connection	/5
Part (d) — Portfolio Recommendation	References portfolio β ≈ 1.075 (slightly aggressive); thoughtful recommendation with risk-return tradeoff reasoning; appropriate for youth wealth-building with proper risk acknowledgment	Recommendation made; beta cited but tradeoff analysis thin	Recommendation with no beta or risk-return discussion	/4

Extended Response Total: — / 20

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Sections 1 & 2 auto-grade instantly. Use the rubric selectors for Sections 3 & 4.

Risk &Return

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