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Aktien (Equities): Übungsfragen zum CFA® Program Level I

Curriculum 2027 · Gewicht in der Prüfung: 11–14 %. Quelle: CFA Institute (geprüft am 28.10.2026)

Im Curriculum 2026 hieß dieses Themengebiet Equity Investments.

Aktien (im Curriculum 2026 Equity Investments genannt) behandeln die Organisation der Märkte, Indizes, Markteffizienz, Branchen- und Unternehmensanalyse sowie die Aktienbewertung.

Typische Missverständnisse

  • Alle Indizes gewichten ihre Bestandteile gleich. Preis-, gleich- und marktkapitalisierungsgewichtete Indizes liefern aus denselben Kursen unterschiedliche Renditen.
  • Markteffizienz bedeutet, dass Kurse immer richtig sind. Sie bedeutet, dass Kurse verfügbare Informationen so schnell widerspiegeln, dass dauerhafte Überrenditen schwer zu erzielen sind.
  • Ein niedriges Kurs-Gewinn-Verhältnis bedeutet, dass eine Aktie günstig ist. Es kann ebenso geringes erwartetes Wachstum oder hohes Risiko widerspiegeln.

Zwei gerechnete Lehrbeispiele

Eigene Lehrbeispiele von Preparaio, keine offiziellen Fragen des CFA Institute.

Beispiel 1: Im Wachstumsmodell zählt die Dividende des nächsten Jahres

Annahmen: Die Dividende eines Unternehmens wurde gerade gezahlt: D₀ = 1,80 je Aktie. Erwartet wird ein dauerhaftes Dividendenwachstum von 4 %, die geforderte Rendite beträgt 10 %.

  1. Schätze die nächste Dividende: D₁ = 1,80 × 1,04 = 1,872.
  2. Prüfe die Bedingung des Modells: Die geforderte Rendite liegt über der Wachstumsrate.
  3. Berechne die Differenz: 0,10 − 0,04 = 0,06.
  4. Schätze den Wert: 1,872 / 0,06 = 31,20 je Aktie.

Ergebnis und Stolperstein: Wer D₀ unmittelbar einsetzt, erhält 30,00 und unterschätzt den Wert nach diesem Modell. Das Ergebnis hängt stark von den Annahmen zu dauerhaftem Wachstum und geforderter Rendite ab; es ist eine Bewertungsübung und keine Kaufempfehlung.

Weiter: Die Gordon-Wachstumsformel ansehen

Beispiel 2: Die Indexgewichte bestimmen die Gesamtrendite

Annahmen: Ein marktkapitalisierungsgewichteter Kursindex enthält nur A und B. A hat eine Million Aktien zu 40, B zwei Millionen zu 30. Dividenden, Veränderungen der Aktienzahl und Kapitalmaßnahmen bleiben außer Betracht.

  1. Berechne die Marktwerte: A = 40 Millionen; B = 60 Millionen.
  2. Leite die Anfangsgewichte ab: 40 % und 60 %.
  3. Steigt A um 5 % und fällt B um 2 %, beträgt die Indexrendite 0,40 × 5 % + 0,60 × (−2 %) = 0,8 %.
  4. Ein Index mit Startwert 1.000 steht danach bei 1.008.

Ergebnis und Stolperstein: Der ungewichtete Durchschnitt von 1,5 % lässt die ungleichen Anfangsgewichte des Index außer Acht.

Weiter: Rechnungen zu Marktindizes üben

Was sich in diesem Themengebiet 2027 ändert

Beispielfragen

Kostenlos und ohne Konto. Zu jeder Frage gibt es den vollständigen Lösungsweg, einschließlich der Begründung, warum jede falsche Option falsch ist. Die Fragen sind eigene Aufgaben von Preparaio auf Englisch, keine offiziellen Fragen des CFA Institute.

1.

Maristella Skincare has always sold its products to wholesalers, which resell them to pharmacies. It now plans to sell directly to consumers through its own online store, at the same retail prices that pharmacies charge. Which effect on Maristella's margins should an analyst expect from this change in its business model?

Lösung und Erklärung

Richtige Antwort: A A higher gross margin, partly offset by higher selling and delivery costs

By selling at retail prices instead of wholesale prices, Maristella captures the markups that wholesalers and pharmacies used to earn, so revenue per unit and gross margin rise while product cost is unchanged. In exchange, it takes on marketing, shipping, returns and customer-service costs, which raise operating expenses and partly offset the gross margin gain.

Warum die anderen Optionen falsch sind

  • B: Selling direct does not give up a markup; it captures the markups that intermediaries used to earn, so revenue per unit rises.
  • C: The channel changes both the price Maristella receives per unit and the costs it bears, so its margins and cost structure change.

Kernregel: A company's choice of distribution channel determines how much of the final price it captures and which distribution costs it must bear.

Merksatz: Cutting out intermediaries raises revenue per unit and gross margin but shifts distribution costs onto the company.

2.

Mkhize Water Utilities has just paid an annual dividend of 2.60 per share. Dividends are expected to grow at a constant 3.25% a year indefinitely, and investors require a return of 8.50% on the shares. Using the Gordon growth model, the intrinsic value per share is closest to:

Lösung und Erklärung

Richtige Antwort: C 51.13

Next year's dividend is D1 = 2.60 × 1.0325 = 2.6845. Dividing by r − g = 0.085 − 0.0325 = 0.0525 gives V0 = 2.6845 / 0.0525 = 51.13.

Rechenweg

  1. D1 = 2.60 × 1.0325 = 2.6845
  2. r − g = 0.085 − 0.0325 = 0.0525
  3. V0 = 2.6845 / 0.0525 = 51.13

BA-II-Plus-Tastenfolge

2.6 × 1.0325 ÷ ( 0.085 − 0.0325 ) = [51.13]

Warum die anderen Optionen falsch sind

  • A: Discounts D1/(r − g) for one more year (51.13 / 1.085 = 47.13); the Gordon formula already gives the value today.
  • B: Divides the dividend just paid (2.60) by r − g instead of next year's dividend D1 = 2.6845.

Intermediate displayed workings may be rounded; retain full precision until the final answer.

Kernregel: The Gordon growth model values a share as next year's dividend divided by the required return minus the growth rate: V0 = D1/(r − g).

Merksatz: Gordon growth: put next year's dividend D1 in the numerator; the result is already today's value.

3.

Sepilok Data Systems has just paid an annual dividend of 1.35 per share. An analyst expects dividends to grow at 14.0% a year for the next three years and at 3.5% a year indefinitely thereafter. The required return on the shares is 9.75%. Using a two-stage dividend discount model, the intrinsic value of a Sepilok share today is closest to:

Lösung und Erklärung

Richtige Antwort: B 29.43

The high-growth dividends are D1 = 1.539, D2 = 1.75446 and D3 = 2.00008. The first stable-stage dividend is D4 = 2.00008 × 1.035 = 2.07009, so the terminal value at the end of Year 3 is 2.07009 / (0.0975 − 0.035) = 33.12140. Discounting at 9.75%: 1.539 / 1.0975 + 1.75446 / 1.0975^2 + (2.00008 + 33.12140) / 1.0975^3 = 1.40228 + 1.45658 + 26.56802 = 29.43.

Rechenweg

  1. D1 = 1.35 × 1.14 = 1.539; D2 = 1.539 × 1.14 = 1.75446; D3 = 1.75446 × 1.14 = 2.00008
  2. D4 = 2.00008 × 1.035 = 2.07009
  3. TV3 = 2.07009 / (0.0975 − 0.035) = 33.12140
  4. V0 = 1.539 / 1.0975 + 1.75446 / 1.0975^2 + (2.00008 + 33.12140) / 1.0975^3
  5. V0 = 1.40228 + 1.45658 + 26.56802 = 29.43

BA-II-Plus-Tastenfolge

CF; 2ND CLR WORK; CF0 = 0 ENTER ↓; C01 = 1.539 ENTER ↓ F01 = 1 ENTER ↓; C02 = 1.75446 ENTER ↓ F02 = 1 ENTER ↓; C03 = 35.12148 ENTER ↓ F03 = 1 ENTER ↓; NPV; I = 9.75 ENTER ↓; CPT [29.43]

Warum die anderen Optionen falsch sind

  • A: Discounts the terminal value over four periods instead of three; the terminal value computed from D4 is already a value at the end of Year 3.
  • C: Computes D4 by growing D3 at the 14.0% high-growth rate instead of the 3.5% long-run rate, which overstates the terminal value.

Intermediate displayed workings may be rounded; retain full precision until the final answer.

Kernregel: In a two-stage DDM, value = PV of the high-growth dividends + PV of the terminal value, where the terminal value at the end of Year n is D(n+1)/(r − g) discounted over n periods.

Merksatz: Build the terminal value from the first stable-growth dividend and discount it back from the end of the high-growth period.

4.

Naledi Sebego manages a fund that buys shares when their 50-day moving average price rises above their 200-day moving average. Extensive research shows that the Dravenian stock market, where she invests, is semi-strong-form efficient. Her strategy will most likely:

Lösung und Erklärung

Richtige Antwort: B fail to earn abnormal returns after costs, because prices already reflect all past market data

A moving-average crossover rule uses only past prices, which is the information set of the weak form. Because semi-strong-form efficiency means prices reflect all publicly available information, including past prices and trading volume, Sebego's rule should not earn risk-adjusted returns above the market after transaction costs.

Warum die anderen Optionen falsch sind

  • A: Public information includes past prices and trading volume as well as financial reports, so semi-strong-form efficiency also rules out profits from technical analysis.
  • C: The weak form already rules out profits from past price patterns; the strong form adds private information to what prices reflect.

Kernregel: Each form of market efficiency includes the weaker forms, so a semi-strong-form efficient market is also weak-form efficient and technical trading rules cannot earn abnormal returns.

Merksatz: Semi-strong-form efficiency implies weak-form efficiency, so technical rules should not earn abnormal returns.

5.

Oosthuizen Glass Holdings has bonds, cumulative preferred shares and common shares outstanding. If the company is liquidated, the holders of its preferred shares will most likely be paid:

Lösung und Erklärung

Richtige Antwort: B after the bondholders but before the common shareholders

Bondholders are creditors with contractual claims, so they are paid first. Preferred shareholders are owners, and their claim ranks after all creditors but ahead of the common shareholders, who hold the residual claim on whatever remains.

Warum die anderen Optionen falsch sind

  • A: The cumulative feature protects missed preferred dividends relative to common shareholders; it does not move preferred shares ahead of creditors.
  • C: Preferred shares have priority over common shares in liquidation; common shareholders receive only what is left after creditors and preferred shareholders are paid.

Kernregel: Preferred shares rank ahead of common shares, but behind all creditors, in claims on dividends and on assets in liquidation.

Merksatz: Liquidation order: creditors first, then preferred shareholders, then common shareholders.

6.

Lior Ben-David estimates the equity value of Nordasen Broadband by applying the median enterprise value-to-EBITDA ratio of five listed broadband operators to Nordasen's EBITDA and then subtracting its net debt. Which category of valuation model is he using?

Lösung und Erklärung

Richtige Antwort: C A multiplier model

Applying a peer EV/EBITDA multiple to Nordasen's EBITDA is the method of comparables, which is a multiplier (multiples-based) approach. Subtracting net debt converts the resulting enterprise value into equity value but does not change the category of model.

Warum die anderen Optionen falsch sind

  • A: A present value model discounts forecast dividends or free cash flows at a required return; Ben-David does not discount any cash flows.
  • B: An asset-based model restates individual assets and liabilities at fair value; deducting net debt from an enterprise value is not a valuation of the company's assets.

Kernregel: Present value models discount expected future cash flows, multiplier models apply price or enterprise value multiples, and asset-based models value a company's assets and liabilities directly.

Merksatz: Using a peer multiple, whether P/E or EV/EBITDA, is a multiplier model that gives relative, not absolute, value.

7.

The Aorere Resources Index is a market-capitalization-weighted price return index with the three constituents shown in the exhibit. No constituent issued or repurchased shares during the year. What is the index's price return for the year?

Aorere Resources Index constituents
ConstituentShares outstanding (millions)Price at start of yearPrice at end of year
Arapawa Gold90058.0059.00
Hokitika Nickel15024.5027.00
Waitaki Lithium60112.00123.00
Lösung und Erklärung

Richtige Antwort: A 3.09%

Beginning market capitalization is 900 × 58.00 + 150 × 24.50 + 60 × 112.00 = 52,200 + 3,675 + 6,720 = 62,595 million. Ending market capitalization is 900 × 59.00 + 150 × 27.00 + 60 × 123.00 = 53,100 + 4,050 + 7,380 = 64,530 million. The index return is 64,530 / 62,595 − 1 = 3.09%; Arapawa Gold, by far the largest constituent, rose only 1.72%, which holds the index return down.

Rechenweg

  1. Beginning market value = 900 × 58.00 + 150 × 24.50 + 60 × 112.00 = 62,595
  2. Ending market value = 900 × 59.00 + 150 × 27.00 + 60 × 123.00 = 64,530
  3. Return = 64,530 / 62,595 − 1 = 0.0309, or 3.09%

BA-II-Plus-Tastenfolge

900 × 59 = STO 1; 150 × 27 = STO + 1; 60 × 123 = STO + 1; 900 × 58 = STO 2; 150 × 24.5 = STO + 2; 60 × 112 = STO + 2; RCL 1 ÷ RCL 2 = ; − 1 = ; × 100 = [3.09]

Warum die anderen Optionen falsch sind

  • B: 7.25% is the simple average of the three constituent returns (1.72%, 10.20% and 9.82%), which is the equal-weighted return.
  • C: 7.46% is the price-weighted return (sum of ending prices / sum of beginning prices − 1), which ignores the number of shares outstanding.

Intermediate displayed workings may be rounded; retain full precision until the final answer.

Kernregel: A market-capitalization-weighted index return equals the change in the constituents' total market value divided by their total market value at the start of the period.

Merksatz: In a market-cap-weighted index, the largest companies dominate the return.

8.

An index provider is designing three versions of an index with the same three constituents, shown in the exhibit: one price weighted, one equal weighted and one market-capitalization weighted. In which version will Okavango Freight most likely have its smallest weight?

Index constituents
ConstituentShare priceShares outstanding (millions)Market capitalization (millions)
Okavango Freight12.0090010,800
Velasco Pharma85.00403,400
Kuroshima Robotics140.00152,100
Lösung und Erklärung

Richtige Antwort: A The price-weighted version

Okavango Freight is the largest company but has the lowest share price. Its weight is 12.00 / (12.00 + 85.00 + 140.00) = 5.1% in the price-weighted version, compared with 33.3% in the equal-weighted version and 10,800 / 16,300 = 66.3% in the market-cap-weighted version. Price weighting gives the largest company the least influence simply because of its low share price.

Warum die anderen Optionen falsch sind

  • B: Equal weighting gives each of the three constituents 33.3%, far more than Okavango's 5.1% weight under price weighting.
  • C: Market-cap weighting gives Okavango its largest weight, 66.3%, because it has by far the largest market capitalization.

Kernregel: Price weighting assigns weights in proportion to share prices regardless of company size, equal weighting gives each constituent the same weight, and market-cap weighting assigns weights by price times shares outstanding.

Merksatz: In a price-weighted index, a low share price means a low weight, however large the company.

9.

Analyst Abena Kyerewaa classifies three transactions by the type of market in which each takes place. Which of her classifications is least likely correct?

Lösung und Erklärung

Richtige Antwort: A An importer buying euros for delivery in two business days: derivative market

Settlement in two business days is the standard settlement for a spot currency trade, so the importer's purchase takes place in the spot (cash) market. A derivative, such as a currency forward, would fix the exchange rate today for delivery at a later date beyond normal settlement.

Warum die anderen Optionen falsch sind

  • B: This classification is correct: the issuer's sale of new securities is a primary market transaction, and a seven-year maturity places the notes in the capital market.
  • C: This classification is correct: buying existing securities from another investor is a secondary market trade, and 90-day bills are money market instruments.

Kernregel: Markets are classified by issuance (primary or secondary), by maturity (money markets for instruments of one year or less, capital markets for longer ones) and by delivery timing (spot markets for prompt delivery, derivative markets for contracts on future delivery).

Merksatz: Standard settlement within a few days is a spot trade; a derivative fixes terms today for later delivery.

10.

Chen Wei-Lun estimates that the current price of Matakana Telecom implies an expected return of 11.8%, while its CAPM required return is 12.6%. For Castellví Building Materials, the implied expected return is 8.9% and the CAPM required return is 7.7%. Based on expected alpha, Chen should most likely conclude that:

Lösung und Erklärung

Richtige Antwort: B Castellví is undervalued, and Matakana is overvalued

Castellví's expected alpha is 8.9% − 7.7% = +1.2%, so its price offers more than the return its risk requires, which signals undervaluation. Matakana's expected alpha is 11.8% − 12.6% = −0.8%: despite its higher implied return, its price does not compensate for its risk, so it appears overvalued.

Warum die anderen Optionen falsch sind

  • A: A high implied return in absolute terms is not enough; Matakana's implied return falls short of its 12.6% required return, giving a negative alpha.
  • C: Comparing implied returns across shares ignores their different risk; Castellví's implied return exceeds its own required return, giving a positive alpha.

Kernregel: Expected alpha = implied expected return − required return; a positive alpha signals undervaluation and a negative alpha overvaluation.

Merksatz: Judge value by comparing each share's implied return with its own required return.

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