📖 权益模拟测试（20 题）

Equity Investments

I. Lesson Focus

II. The Problem

Equity Investments typically accounts for 14–16% of the CFA Level I exam. The topic covers stock valuation models (absolute and relative), industry and company analysis, the efficient market hypothesis (EMH), security market index weighting methods, and behavioral biases. Candidates frequently lose marks on free-cash-flow valuation nuances, adjustments to multiples for differences in growth/risk/ROE, index return calculations under different weighting schemes, and correctly identifying which market anomaly supports or contradicts a particular form of market efficiency. This 20-question mock test reviews all core formulas and calculation logic while exposing common conceptual traps, enabling candidates to strengthen weak areas before the actual exam.

III. Equity Investment Knowledge Framework Review

The Equity Investments curriculum revolves around three central questions: why invest in equities, how to value equities, and how to construct equity portfolios. Equity securities represent residual claims; their value derives from the present value of expected future cash flows or from pricing relative to comparable companies. Candidates must master both absolute valuation techniques (dividend discount models, FCFE, and FCFF) and relative valuation multiples (P/E, P/B, EV/EBITDA), including their assumptions and limitations. In addition, the implications of different degrees of market efficiency for active versus passive management must be clearly understood.

IV. Dividend Discount Models (DDM) and Free-Cash-Flow Models

The Gordon (constant) growth model is a high-frequency exam topic: $$P_0 = \frac{D_1}{r - g}$$ where $r$ is the required rate of return and $g$ is the perpetual growth rate. The condition $r > g$ must always hold.

In multistage DDMs, the analyst calculates the present value of dividends during the high-growth period separately from the terminal value. Free-cash-flow models are equally important: FCFE is discounted at the cost of equity to obtain equity value directly, while FCFF is discounted at WACC and then net debt is subtracted to reach equity value.

Key relationship: sustainable growth rate $g = ROE \times b$, where retention ratio $b = 1 -$ dividend payout ratio. Exam questions frequently test inconsistencies between assumed growth rates and the company’s actual ROE and retention policy.

V. Relative Valuation and Multiple Adjustments

Price-to-earnings ratios can be expressed as leading (forward) P/E or trailing P/E. When using relative valuation, analysts must adjust for differences in expected growth, risk (beta), financial leverage, and accounting quality. Common tools include: - PEG ratio = (P/E) / growth rate (in percent) - Adjusted P/E that removes non-recurring items and reconciles differing accounting standards

EV/EBITDA is often preferred when capital structures differ because it is independent of leverage. A frequent trap is applying an industry-average multiple without adjusting for fundamental differences among companies.

VI. Security Market Indices and Weighting Methods

Index construction methods include price weighting, equal weighting, market-capitalization weighting, and fundamental weighting. Market-cap-weighted indices automatically “buy low, sell high” but can produce high concentration risk. Price-weighted indices (e.g., Dow Jones) are distorted by stock splits and require divisor adjustments.

Core formulas: - Price-weighted index = $\frac{\sum P_i}{\text{Divisor}}$ - Market-cap-weighted index return = $\sum w_i \times R_i$, where $w_i = \frac{P_i \times Q_i}{\sum (P_j \times Q_j)}$

VII. Efficient Market Hypothesis and Behavioral Finance

The efficient market hypothesis (EMH) exists in three forms: weak (technical analysis useless), semi-strong (fundamental analysis using public information useless), and strong (even insider information is reflected). Behavioral finance challenges EMH by documenting systematic biases such as: - Overconfidence - Anchoring - Herding - Loss aversion

Exam questions often ask which observed market anomaly supports or contradicts a specific form of market efficiency.

Worked Cases

Case 1: Two-Stage DDM Valuation

A company pays a current dividend $D_0 = 2.00$. Dividends are expected to grow at 15% for the next three years, then at a perpetual rate of 6%. The required return is 12%. Calculate the current intrinsic value.

Solution steps: 1. High-growth dividends: $D_1 = 2.30$, $D_2 = 2.645$, $D_3 = 3.04175$ 2. Terminal price at end of year 3: $P_3 = \frac{3.04175 \times 1.06}{0.12 - 0.06} = 53.74$ 3. Present value: $\frac{2.30}{1.12} + \frac{2.645}{1.12^2} + \frac{3.04175 + 53.74}{1.12^3} \approx 2.05 + 2.11 + 40.32 = 44.48$

Intrinsic value ≈ 44.48.

Case 2: Relative Valuation with Multiple Adjustments

Company A has a trailing P/E of 18.5, expected EPS growth of 12%, and beta = 1.1. Comparable Company B trades at P/E = 16.2 with 10% growth and beta = 1.0. Using the PEG approach and risk adjustment, determine whether A is overvalued.

Calculation: - A’s PEG = 18.5 / 12 = 1.542 - B’s PEG = 16.2 / 10 = 1.62 - Adjusted fair P/E for A ≈ 16.2 × (12/10) × (1.1/1.0)^0.5 ≈ 19.0 - Actual P/E of 18.5 is below the adjusted fair value → Company A is undervalued.

Case 3: Market-Cap-Weighted Index Return

An index contains three stocks with the following beginning-of-period data (in millions): - Stock X: price = 20, shares = 1, weight = 25% - Stock Y: price = 40, shares = 0.5, weight = 25% - Stock Z: price = 60, shares = 0.5, weight = 50%

End-of-period prices are 22, 36, and 75 respectively. Calculate the index return.

Solution: Beginning total market cap = (20×1) + (40×0.5) + (60×0.5) = 70
Ending total market cap = (22×1) + (36×0.5) + (75×0.5) = 83.5
Index return = (83.5 – 70) / 70 = 19.29%

Traps

Key Formulas

• $P_0 = \frac{D_1}{r - g}$ (Gordon constant-growth model)
• $g = ROE \times b = ROE \times (1 - \text{dividend payout ratio})$
• Justified leading P/E = $\frac{1 - b}{r - g}$
• Price-weighted index divisor adjustment: New divisor = Old divisor × (new price sum / old price sum)
• Market-cap-weighted return = $\sum w_i R_i$
• Sharpe ratio = $\frac{R_p - R_f}{\sigma_p}$
• Information ratio = $\frac{R_p - R_b}{\text{Tracking error}}$
• PEG = $\frac{P/E}{g (\%)}$

Practice Questions

Q1. According to the Gordon growth model, if the required return falls from 10% to 9% while growth remains 6%, the stock price will: A. Decrease by 25%
B. Increase by 33.3%
C. Increase by 25%
D. Decrease by 20%

Q2. Which situation is most appropriate for using a free-cash-flow-to-the-firm (FCFF) model? A. The company maintains a stable dividend payout policy
B. The company’s financial leverage is expected to change materially
C. The company is private and reliable dividend data are unavailable
D. The company’s beta is close to 1.0

Q3. A price-weighted index contains two stocks priced at 50 and 80. After the first stock undergoes a 1-for-2 split and the index level is kept unchanged by adjusting the divisor, the new divisor is closest to: A. 1.3
B. 2.6
C. 65
D. 130

Q4. In a semi-strong-form efficient market, which strategy is most likely to generate abnormal returns? A. Technical chart analysis
B. Post-earnings-announcement drift trading
C. Ranking stocks by publicly available P/E ratios
D. None of the above

Q5. A company has an ROE of 18% and a dividend payout ratio of 40%. Its sustainable growth rate is: A. 7.2%
B. 10.8%
C. 18.0%
D. 45.0%

Q6. Which statement about relative valuation is correct? A. EV/EBITDA is unaffected by capital structure and is therefore always superior to P/E
B. Industry-average P/E multiples require no adjustment for growth differences
C. A higher PEG ratio indicates the stock is more undervalued
D. In the comparable-company method, priority should be given to firms with similar growth, risk, and ROE

Q7. Behavioral finance’s “loss aversion” bias most likely causes investors to: A. Trade excessively
B. Hold losing stocks for too long
C. Over-concentrate in a single industry
D. Ignore macroeconomic information

Q8. A stock currently trades at 42. Next year’s expected dividend is 2.10, with perpetual growth of 5% and a required return of 11%. According to the DDM, the stock is: A. Overvalued (intrinsic value 35)
B. Undervalued (intrinsic value 42)
C. Fairly priced
D. Undervalued (intrinsic value 47.25)

Answers

Takeaways

• The Gordon model requires $r > g$ and a sustainable growth rate derived from ROE × retention.
• Always cross-verify absolute and relative valuations; never rely on a single model.
• Different index weighting methods produce distinct rebalancing behaviors and concentration risks.
• Market-efficiency form determines the value of active management: weak form rules out technical analysis; semi-strong rules out fundamental analysis of public information.
• Behavioral biases provide a framework for explaining market anomalies and are frequently contrasted with EMH on the exam.
• Valuation must incorporate accounting quality, expected changes in capital structure, and the sustainability of growth assumptions.