CFA Level 1 Practice Questions: 50 Exam-Difficulty MCQs [Free Quiz]

CFA Level 1 Practice Questions: Test Yourself With 50 Exam-Difficulty MCQs

The CFA Level 1 exam consists of 180 multiple-choice questions spread across two 135-minute sessions. Each question is crafted to test not just memorisation, but your ability to apply financial concepts under time pressure. The best way to prepare is to practise with questions that mirror the real exam in tone, difficulty, and structure.

This free quiz contains 50 CFA Level 1 practice questions organised by topic area, each followed by the correct answer and a concise explanation. Whether you are three months out or three weeks out, working through these questions will sharpen your recall, expose weak topics, and build exam-day confidence.

How to Use These Practice Questions Effectively

Random drilling rarely produces lasting improvement. Here is a structured approach used by high-scoring candidates:

• Timed blocks: Aim for 90 seconds per question. The real exam allows roughly 90 seconds per question across 180 questions in two sessions.
• Topic isolation first: Work through each topic section without mixing. Once you have identified weak areas, focus revision there before attempting mixed sets.
• Answer, then read: Commit to an answer before reading the explanation. This forces active recall rather than passive recognition.
• Log your errors: Keep an error log noting which topics and question types trip you up repeatedly. This reveals patterns that targeted revision can fix.
• Score yourself: Use the scoring guide at the end of this article to benchmark your readiness.

Ethics & Professional Standards (Questions 1–8)

Ethics carries the highest single weight in the CFA Level 1 curriculum (15–20%) and CFA Institute applies an ethics adjustment for candidates near the minimum passing score, so a strong ethics performance can help borderline candidates. Expect questions on the Code of Ethics, the seven Standards of Professional Conduct, and the Global Investment Performance Standards (GIPS).

Question 1

A CFA charterholder manages a discretionary equity portfolio and also provides investment advice to a family member using the same strategy at no charge. The charterholder does not disclose this arrangement to the employer. According to the CFA Institute Standards of Professional Conduct, the charterholder has most likely violated:

1. Standard IV(A) – Loyalty to Employer only
2. Standard VI(B) – Priority of Transactions only
3. Standard IV(A) – Loyalty to Employer and Standard VI(A) – Disclosure of Conflicts
4. No standard, because no compensation was received

Answer: C
Explanation: Providing investment services outside of employment — even without compensation — constitutes an outside business activity that must be disclosed to the employer (Standard IV(A)). Additionally, managing a family member's account using the same strategy creates a potential conflict of interest that must be disclosed (Standard VI(A)). The absence of compensation does not eliminate the obligation to disclose.

Question 2

During a research conference, an analyst overhears a senior executive of a listed company say, "Our new product launches have been far better than the market expects; we should see some very different numbers next quarter." The analyst immediately updates her model and issues a revised buy recommendation. This action most likely violates:

1. Standard II(A) – Material Nonpublic Information
2. Standard V(A) – Diligence and Reasonable Basis
3. Standard I(C) – Misrepresentation
4. No standard; conference remarks are considered public information

Answer: A
Explanation: The executive's comment is material (it would affect an investor's decision) and nonpublic (made in a small-group setting, not broadly disseminated). Trading or making recommendations based on such information violates Standard II(A). The fact that the analyst was present at a conference does not automatically make the information public.

Question 3

An investment management firm claims GIPS compliance for its equity composite. During a verification review, it is discovered that the firm excluded two small underperforming portfolios from the composite because they were managed by a departing portfolio manager. Under GIPS, this exclusion is:

1. Permitted if the portfolios were transferred to the departing manager's personal account
2. Permitted if the portfolios represented less than 5% of total firm assets
3. Not permitted; all fee-paying discretionary portfolios must be included in at least one composite
4. Permitted during the quarter in which the manager departed

Answer: C
Explanation: GIPS requires that all actual, fee-paying, discretionary portfolios be included in at least one composite. Excluding underperforming accounts to improve composite performance is a direct violation. There is no minimum asset threshold that exempts accounts from inclusion, and a manager's departure does not suspend composite requirements.

Question 4

A research analyst is pressured by his investment banking colleagues to raise his rating on a company from "Hold" to "Buy" ahead of a secondary equity offering the bank is underwriting. The analyst believes a "Hold" rating is appropriate. According to the Standards, the analyst should:

1. Raise the rating temporarily because institutional loyalty is a key duty
2. Refuse to change the rating and, if necessary, report the pressure to compliance
3. Change the rating only if the analyst can document a reasonable basis for the upgrade
4. Withdraw coverage entirely to avoid the conflict

Answer: B
Explanation: Standard I(B) – Independence and Objectivity requires that analysts not allow business relationships to influence their investment recommendations. The analyst must maintain the hold rating if it reflects honest analysis. Escalating to compliance is appropriate when internal pressure threatens independence. Option C is incorrect because changing the rating purely to please investment banking — while then manufacturing a justification — would also violate the standard.

Question 5

A portfolio manager receives a gift of two business-class airline tickets from a broker-dealer whose trading commissions the manager regularly directs. The manager accepts the tickets without disclosing them to the employer. This action most likely violates:

1. Standard I(B) – Independence and Objectivity and Standard IV(B) – Additional Compensation Arrangements
2. Standard VI(A) – Disclosure of Conflicts only
3. Standard III(A) – Loyalty, Prudence, and Care only
4. No standard, because gifts from brokers are customary in the industry

Answer: A
Explanation: Accepting gifts from a broker whose business the manager controls creates an incentive that could bias trade direction decisions, violating Standard I(B). Additionally, accepting compensation beyond the employment relationship without written consent from the employer violates Standard IV(B). Industry custom does not override the Standards.

Question 6

An analyst's research report states that a company's earnings per share grew at "an average rate of 18% per year over the past five years." The actual growth rate was 12% compounded annually. The analyst used a simple arithmetic average of annual growth rates. This practice most likely violates:

1. Standard V(B) – Communication with Clients and Prospective Clients
2. Standard I(C) – Misrepresentation
3. Standard V(A) – Diligence and Reasonable Basis
4. Standard II(B) – Market Manipulation

Answer: B
Explanation: Presenting an arithmetic average of growth rates as the "average growth rate" when a geometric (compounded) rate is the correct representation for multi-period performance is misleading. It overstates growth by 6 percentage points and constitutes a misrepresentation under Standard I(C). Standard V(B) also has merit (communication must be fair and complete), but I(C) is the primary violation given the inaccuracy of the figure itself.

Question 7

An investment advisor has a client with a stated risk tolerance of "moderate" and a five-year investment horizon. The advisor places the client in a concentrated position in a single small-cap biotechnology company because the advisor personally believes it has exceptional return potential. Which Standard is most directly violated?

1. Standard III(C) – Suitability
2. Standard III(A) – Loyalty, Prudence, and Care
3. Standard I(D) – Misconduct
4. Standard V(A) – Diligence and Reasonable Basis

Answer: A
Explanation: Standard III(C) requires that investments be suitable for the client's specific situation — risk tolerance, return objectives, time horizon, and constraints. A concentrated single-stock position in a small-cap biotech is inconsistent with a moderate risk profile. The advisor's personal conviction about the stock's potential does not override the suitability obligation.

Question 8

A member who is also a CFA candidate learns of an irregularity in the CFA exam administration — specifically, that another candidate was using unauthorised materials. The member takes no action. Under the CFA Institute Standards and Code of Ethics, the member has most likely:

1. Not violated any standard, because enforcement is the responsibility of exam administrators
2. Violated Standard VII(A) – Conduct as Participants in CFA Institute Programs
3. Violated Standard I(A) – Knowledge of the Law
4. Violated Standard I(D) – Misconduct

Answer: B
Explanation: Standard VII(A) covers conduct as participants in CFA Institute programs and requires members and candidates to not engage in, assist, or condone cheating. Witnessing a violation and taking no action is a form of passive complicity that may be considered a violation. The duty extends beyond the individual candidate to the integrity of the program.

Quantitative Methods (Questions 9–13)

Question 9

An analyst observes the following annual returns for a fund over four years: +20%, –10%, +15%, –5%. What is the fund's geometric mean annual return (rounded to two decimal places)?

1. 5.00%
2. 4.22%
3. 3.85%
4. 5.26%

Answer: B
Explanation: Geometric mean = [(1.20)(0.90)(1.15)(0.95)]^(1/4) – 1. The product is 1.20 × 0.90 = 1.08; × 1.15 = 1.242; × 0.95 = 1.1799. The fourth root of 1.1799 ≈ 1.04222, so the geometric mean return ≈ 4.22%. The arithmetic mean (20 – 10 + 15 – 5)/4 = 5%, which is always greater than or equal to the geometric mean when returns vary.

Question 10

A stock price follows a lognormal distribution. The continuously compounded annual return has a mean of 10% and a standard deviation of 20%. What is the probability that the stock price one year from now is below its current level? (Assume standard normal table: z = –0.5 → 0.3085)

1. 30.85%
2. 69.15%
3. 38.21%
4. 50.00%

Answer: A
Explanation: The stock price falls below its current level when the continuously compounded return is negative. z = (0 – 0.10) / 0.20 = –0.50. P(Z < –0.50) = 0.3085 = 30.85%. The lognormal stock price assumption means prices cannot go negative, but they can fall — and here the probability of a decline is approximately 30.85%.

Question 11

A portfolio manager runs a regression of portfolio excess returns on market excess returns and finds: alpha = 1.2%, beta = 0.85, R² = 0.72. Which statement is most accurate?

1. 72% of total portfolio return is explained by the market
2. 72% of portfolio return variability is explained by variability in market returns
3. The portfolio has 85% of the market's systematic risk and 28% idiosyncratic risk
4. The alpha of 1.2% is statistically significant

Answer: B
Explanation: R² represents the proportion of the dependent variable's variance explained by the independent variable(s). It is not the proportion of return, but of return variability. Option A mischaracterises R² as relating to level of return. Option C confuses beta (sensitivity measure) with a proportion of risk. Option D cannot be determined without the standard error of alpha.

Question 12

An analyst computes a 95% confidence interval for mean annual return as [6.2%, 13.8%]. Which interpretation is correct?

1. There is a 95% chance the true mean lies in this interval
2. 95% of annual returns will fall within this range
3. If the same sampling procedure were repeated many times, 95% of intervals constructed would contain the true mean
4. The probability that the mean exceeds 13.8% is 2.5%

Answer: C
Explanation: A confidence interval is a frequentist concept. The correct interpretation is that 95% of such intervals, constructed via the same methodology across repeated samples, would capture the true (fixed) population mean. Option A is the common misinterpretation — the true mean is either in this specific interval or not; probability does not apply to it once the interval is calculated. Option D overstates precision.

Question 13

A hypothesis test yields a p-value of 0.03 at a significance level of 5%. Which conclusion is correct?

1. There is a 3% probability that the null hypothesis is true
2. Reject the null hypothesis; the result is statistically significant at the 5% level
3. Fail to reject the null hypothesis; the p-value must be below 1% to reject at 5%
4. The alternative hypothesis has a 97% probability of being correct

Answer: B
Explanation: A p-value of 0.03 is less than the significance level of 0.05, so we reject the null hypothesis. Options A and D are common misconceptions — the p-value is not the probability that H₀ is true, nor is (1 – p) the probability that H₁ is true. The p-value is the probability of observing results as extreme as, or more extreme than, those observed, assuming H₀ is true.

Economics (Questions 14–18)

Question 14

A central bank increases the policy rate by 75 basis points unexpectedly. Holding all else constant, the most likely immediate effect on the domestic currency's exchange rate and bond prices is:

1. Currency appreciates; bond prices fall
2. Currency depreciates; bond prices rise
3. Currency appreciates; bond prices rise
4. Currency depreciates; bond prices fall

Answer: A
Explanation: Higher interest rates attract foreign capital seeking better yields, increasing demand for the domestic currency and causing it to appreciate. Meanwhile, rising rates lower the present value of future bond cash flows, causing bond prices to fall. This is one of the most frequently tested relationships in CFA Economics.

Question 15

Country A has a current account deficit. According to the absorption approach, which condition is necessary to reduce this deficit without a change in the exchange rate?

1. Domestic absorption must rise relative to domestic output
2. Domestic output must rise relative to domestic absorption
3. Domestic investment must rise while savings remain constant
4. Government spending must fall while exports remain constant

Answer: B
Explanation: The absorption approach defines the current account balance as Output (Y) minus Absorption (A = C + I + G). A current account deficit means A > Y. To reduce the deficit, output must grow faster than absorption, i.e., the economy must produce more than it absorbs domestically. Option C would worsen the deficit (higher investment = higher absorption).

Question 16

In a perfectly competitive market, a firm is producing at a quantity where: Price = $50, AVC = $40, ATC = $60, MC = $50. In the short run, the firm should:

1. Shut down immediately
2. Continue producing and earn an economic profit
3. Continue producing but accept an economic loss
4. Reduce quantity until MC falls below AVC

Answer: C
Explanation: The firm is operating at the profit-maximising point (P = MC). However, since P ($50) < ATC ($60), the firm earns an economic loss. Since P ($50) > AVC ($40), the firm covers its variable costs and contributes to fixed costs — so it should continue producing in the short run rather than shut down. The shutdown rule only applies when P < AVC.

Question 17

According to the Fisher Effect, if the nominal interest rate is 8% and expected inflation is 3%, the real interest rate is approximately:

1. 5.00%
2. 4.85%
3. 5.15%
4. 11.24%

Answer: B
Explanation: The exact Fisher Equation: (1 + real) = (1 + nominal)/(1 + inflation) = (1.08)/(1.03) = 1.04854. So real rate ≈ 4.85%. The approximation (8% – 3% = 5%) is close but not the precise answer. Exam questions often test whether you apply the exact formula versus the approximation.

Question 18

An economy is in a recession with a negative output gap. The central bank keeps rates near zero, and fiscal authorities have already deployed significant stimulus. The IS curve has shifted left. According to the IS-LM framework, which policy tool can still be effective?

1. Further cuts to the policy rate below zero (negative rates)
2. Quantitative easing to shift the LM curve right
3. Reducing government expenditure to restore fiscal balance
4. No effective tools exist once zero lower bound is reached

Answer: B
Explanation: At the zero lower bound, conventional rate cuts lose effectiveness. Quantitative easing (central bank purchases of assets) expands the money supply and shifts the LM curve to the right, lowering long-term rates and stimulating aggregate demand even without cutting short-term rates further. Option C would be contractionary and worsen the recession.

Financial Statement Analysis (Questions 19–26)

Question 19

A company uses the LIFO inventory method. Compared to a company using FIFO during a period of rising prices, the LIFO company will report:

1. Higher net income and higher ending inventory
2. Lower net income and lower ending inventory
3. Higher COGS and higher ending inventory
4. Lower COGS and lower net income

Answer: B
Explanation: Under LIFO during rising prices, the most recently purchased (higher-cost) inventory is expensed first, leading to higher COGS, lower gross profit, and lower net income. Ending inventory consists of older, lower-cost units, so it is lower than under FIFO. Lower COGS under FIFO means higher inventory on the balance sheet and higher profit.

Question 20

Company X reports the following (in millions): Net income = $120, Depreciation = $40, Increase in accounts receivable = $25, Decrease in accounts payable = $10, Capital expenditure = $60, Repayment of long-term debt = $30. What is free cash flow to the firm (FCFF)?

1. $65 million
2. $95 million
3. $125 million
4. $105 million

Answer: A
Explanation: CFO = Net income + Depreciation – Increase in AR – Decrease in AP = 120 + 40 – 25 – 10 = $125 million. FCFF = CFO – Capex = 125 – 60 = $65 million. Debt repayment is a financing cash flow, not included in FCFF. FCFF represents cash available to all capital providers before financing decisions.

Question 21

A company enters into a 5-year finance lease. At inception, the right-of-use asset equals the present value of lease payments: $200,000. The annual lease payment is $48,000, the implicit rate is 8%, and annual depreciation is $40,000. In Year 1, the effect on the income statement compared to an operating lease is:

1. Higher total expense because interest and depreciation exceed the operating lease expense
2. Lower total expense in Year 1 under the finance lease
3. The same total expense; only the classification differs
4. Cannot be determined without knowing the lease term

Answer: A
Explanation: Under a finance lease, Year 1 expense = depreciation ($40,000) + interest (8% × $200,000 = $16,000) = $56,000. Under an operating lease, the straight-line expense would be $48,000 per year. So the finance lease front-loads more total expense in early years ($56,000 > $48,000). This relationship reverses in later years as the outstanding liability declines.

Question 22

A firm's return on equity (ROE) increased from 12% to 18% over two years. A DuPont analysis reveals that net profit margin declined from 8% to 6% and asset turnover improved marginally. The most likely driver of the ROE increase is:

1. Improved operating efficiency
2. Increased financial leverage
3. Expansion in revenue
4. Tax rate reductions

Answer: B
Explanation: In the DuPont decomposition, ROE = Net Profit Margin × Asset Turnover × Financial Leverage. Since profit margin declined and asset turnover improved only marginally, the significant ROE increase from 12% to 18% (50% jump) must be driven by a large increase in the equity multiplier (financial leverage). Higher debt means fewer equity dollars supporting the same asset base.

Question 23

Under IFRS, a company recognises revenue from a long-term construction contract using the percentage-of-completion method. During Year 2, cost incurred to date = $6 million, total estimated cost = $10 million, total contract price = $15 million. Revenue recognised in Year 2, if Year 1 revenue recognised was $4.5 million, is:

1. $4.5 million
2. $9.0 million
3. $4.5 million already recognized; Year 2 adds $4.5 million more
4. $9.0 million cumulative; Year 2 revenue = $4.5 million

Answer: D
Explanation: Percentage of completion = 6/10 = 60%. Total revenue to date = 60% × $15 million = $9.0 million. Year 1 recognised $4.5 million, so Year 2 revenue = $9.0 million – $4.5 million = $4.5 million. The key step is computing cumulative revenue, then subtracting prior periods.

Question 24

Which of the following items is most likely classified as an investing activity on the cash flow statement under both US GAAP and IFRS?

1. Dividends paid to shareholders
2. Purchase of a subsidiary's equity stake
3. Interest paid on a bank loan
4. Proceeds from issuing bonds

Answer: B
Explanation: Purchasing a subsidiary's equity stake is an acquisition of a long-term investment — an investing activity under both frameworks. Under US GAAP, dividends paid and interest paid are financing and operating activities respectively. Under IFRS, these can be classified differently (interest paid may be operating or financing; dividends paid may be operating or financing), but buying an equity stake is investing under both.

Question 25

A company reports a deferred tax liability of $50 million that is expected to reverse in 3 years. An analyst adjusting for quality of earnings should treat this deferred tax liability as:

1. Equity, because it will never be paid in cash
2. A true liability, discounted at the risk-free rate to its present value
3. A liability, but the analyst may question whether timing differences will actually reverse
4. Operating income, because it results from accelerated depreciation

Answer: C
Explanation: Deferred tax liabilities are real obligations IF the underlying timing differences reverse. Analysts should assess whether reversal is likely — e.g., if a company is growing and continually investing in new assets with accelerated depreciation, the DTL may grow indefinitely and never become a cash outflow. The analyst treats it as a liability but exercises judgement about whether it truly represents a future cash obligation.

Question 26

An analyst is comparing two companies in the same industry. Company A uses straight-line depreciation; Company B uses accelerated depreciation. Both companies have identical assets and began operations simultaneously. In the early years of asset life, Company B will most likely report:

1. Higher net income and higher book value of assets
2. Lower net income and lower book value of assets
3. Lower net income and higher book value of assets
4. Higher net income and lower book value of assets

Answer: B
Explanation: Accelerated depreciation charges more depreciation expense in early years, reducing reported net income below that of a straight-line user. Because cumulative depreciation is higher, the net book value (cost minus accumulated depreciation) of assets is also lower. This makes B appear less profitable and less asset-rich than A in early years, even if underlying operations are identical.

Corporate Issuers (Questions 27–31)

Question 27

A firm is evaluating a project with an initial outlay of $500,000. The project produces after-tax cash flows of $150,000 per year for five years, with a discount rate of 10%. The NPV is closest to:

1. $69,000
2. $250,000
3. $56,861
4. $75,000

Answer: A
Explanation: PV of annuity = 150,000 × [1 – (1.10)^–5] / 0.10 = 150,000 × 3.79079 ≈ $568,619. NPV = $568,619 – $500,000 ≈ $68,619, closest to $69,000 (option A). The positive NPV indicates value creation, so the project should be accepted. Option C ($56,861) is a common distractor formed by using the wrong annuity factor.

Question 28

A company has 40% debt and 60% equity in its target capital structure. The pre-tax cost of debt is 6%, the cost of equity is 12%, and the marginal tax rate is 30%. The WACC is:

1. 9.6%
2. 8.88%
3. 8.40%
4. 9.12%

Answer: B
Explanation: WACC = (0.40 × 6% × (1 – 0.30)) + (0.60 × 12%) = (0.40 × 4.20%) + (0.60 × 12%) = 1.68% + 7.20% = 8.88%. The tax shield on interest is critical — the after-tax cost of debt is 4.20%, not 6%. This is one of the most commonly tested WACC calculations.

Question 29

Under the Modigliani-Miller framework with taxes and no other market imperfections, the optimal capital structure for a value-maximising firm is:

1. 100% equity to minimise distress costs
2. 50% debt and 50% equity as a practical balance
3. 100% debt to maximise the tax shield on interest
4. Irrelevant — capital structure does not affect firm value

Answer: C
Explanation: MM with corporate taxes shows that firm value increases with the tax shield (PV of tax shield = T × D). If the only imperfection is taxes, the model implies that maximum leverage maximises firm value. In practice, bankruptcy costs, agency costs, and financial distress costs prevent this — leading to the trade-off theory. But strictly within the MM-with-taxes framework, maximum debt is theoretically optimal.

Question 30

A company's board votes to repurchase 10% of outstanding shares in the open market. Assuming the market is efficient and the repurchase price equals intrinsic value, the effect on remaining shareholders' wealth is:

1. Positive, because EPS increases
2. Zero, because value is simply transferred from departing to remaining shareholders
3. Negative, because the company is reducing its cash reserves
4. Positive only if funded by debt (leverage increases)

Answer: B
Explanation: In an efficient market, if the repurchase price equals intrinsic value, shareholders who sell receive fair value and those who remain continue to hold shares worth the same per-share intrinsic value. No wealth is created or destroyed — it is redistributed. If the company repurchases at a price below intrinsic value, remaining shareholders benefit at the expense of those who sell.

Question 31

A company's dividend payout ratio is 40%, ROE is 15%, and the required rate of return is 12%. The expected dividend next year (D₁) is $2.00 per share. Using the Gordon Growth Model, the stock's intrinsic value is closest to:

1. $50.00
2. $60.00
3. $66.67
4. $72.22

Answer: C
Explanation: Sustainable growth rate g = Retention ratio × ROE = (1 – 0.40) × 15% = 0.60 × 15% = 9%. V = D₁ / (r – g) = $2.00 / (0.12 – 0.09) = $2.00 / 0.03 = $66.67. The key Level 1 trap is confusing D₀ (the last dividend paid) with D₁ (the next expected dividend). When D₁ is given directly, no growth adjustment is needed in the numerator. Also confirm that r > g; otherwise the model is not applicable.

Equity Investments (Questions 32–36)

Question 32

An analyst uses the price-to-book (P/B) ratio to compare two banks. Bank A: ROE = 18%, required return = 12%, sustainable growth rate = 8%. Bank B: ROE = 10%, required return = 12%, sustainable growth rate = 4%. Which bank should trade at a higher P/B multiple?

1. Bank B, because its growth rate implies a higher earnings multiple
2. Bank A, because ROE exceeds the required return
3. Both should trade at P/B = 1.0 in an efficient market
4. Cannot be determined without the dividend payout ratio

Answer: B
Explanation: Justified P/B = (ROE – g) / (r – g). Bank A: (0.18 – 0.08) / (0.12 – 0.08) = 0.10 / 0.04 = 2.5x. Bank B: (0.10 – 0.04) / (0.12 – 0.04) = 0.06 / 0.08 = 0.75x. When a company's ROE exceeds its cost of equity, it creates value per dollar of book value — justifying a P/B above 1.0. Bank B destroys value (ROE < required return), warranting a discount to book value.

Question 33

Which of the following best describes the weak form of the Efficient Market Hypothesis (EMH)?

1. All publicly available information is reflected in current prices
2. All information, including insider information, is reflected in prices
3. Past price and volume data cannot be used to generate consistent excess returns
4. Fundamental analysis cannot generate excess returns in the long run

Answer: C
Explanation: Weak form EMH states that current prices reflect all historical price and volume data. This means technical analysis — which relies on past price patterns — cannot generate consistent alpha. Option A describes semi-strong form EMH. Option B describes strong form EMH. Option D is a consequence of semi-strong form efficiency.

Question 34

A company is expected to pay dividends of $1.00, $1.50, and $2.00 at the end of Years 1, 2, and 3. After Year 3, dividends are expected to grow at a constant 5% rate forever. The required return is 10%. The stock's intrinsic value today is closest to:

1. $33.12
2. $35.80
3. $38.44
4. $31.18

Answer: B
Explanation: Terminal value at end of Year 3 = D₄ / (r – g) = ($2.00 × 1.05) / (0.10 – 0.05) = $2.10 / 0.05 = $42.00. PV of D₁ = $1.00/1.10 = $0.909. PV of D₂ = $1.50/1.21 = $1.240. PV of (D₃ + TV) = ($2.00 + $42.00)/1.331 = $44.00/1.331 = $33.058. Total intrinsic value ≈ $0.909 + $1.240 + $33.058 = $35.21, closest to $35.80 (option B). The key skill is combining the multi-stage dividend stream with a Gordon model terminal value, then discounting every cash flow back to today.

Question 35

A firm has EPS of $5.00, pays no dividends, and has an ROE of 20%. Its peers trade at a forward P/E of 15x. Using the justified forward P/E approach, the firm's intrinsic P/E relative to peers is:

1. Lower, because the firm pays no dividends
2. Higher, because the firm's earnings growth rate exceeds peers
3. Equal, because P/E multiples are sector-driven
4. Cannot be determined without the required return on equity

Answer: D
Explanation: The justified P/E = (1 – b) / (r – g), where b is the plowback (retention) ratio and g = b × ROE. With 0% payout, b = 1, g = 1 × 20% = 20%. The justified P/E = 0 / (r – 0.20). Without knowing r, the multiple is undefined (if r = 20%, the denominator = 0; if r < 20%, the firm has an infinite justified P/E). The required return is essential.

Question 36

A depository receipt traded in India represents shares of a US company listed on the NYSE. An arbitrageur notices the DR is trading at a 3% premium to the implied price based on the underlying US shares, adjusted for the USD/INR exchange rate. In an efficient market, this discrepancy will most likely:

1. Persist indefinitely due to regulatory barriers on cross-border arbitrage
2. Be eliminated as arbitrageurs short the DR and buy the US shares
3. Widen because Indian retail investors will continue buying the premium-priced DR
4. Result in the US share price rising to close the gap

Answer: B
Explanation: Arbitrage pressure will eliminate the premium. Traders short the overpriced DR in India while simultaneously buying the underpriced underlying US shares, locking in the spread. Supply of DRs increases (shorting) while demand for US shares increases, bringing prices into alignment. This is the law of one price in action. In practice, cross-border transaction costs and regulatory limits may slow but rarely prevent convergence entirely.

Fixed Income (Questions 37–41)

Question 37

A 5-year bond with a 6% annual coupon is priced at $92 per $100 face value. Which of the following is true?

1. The bond's yield to maturity is less than 6%
2. The bond's yield to maturity is greater than 6%
3. The bond's current yield equals its yield to maturity
4. The bond is trading at a premium

Answer: B
Explanation: A bond trading below par (price < face value) always has a YTM above its coupon rate. Investors receive the coupon payments plus a capital gain (buying at $92, receiving $100 at maturity), so total return exceeds the coupon yield. Conversely, bonds above par have YTM below coupon rate. This relationship is foundational to fixed income.

Question 38

A bond's modified duration is 6.5 years, and its convexity is 55. If interest rates fall by 80 basis points, the approximate percentage change in bond price is:

1. +5.18%
2. +5.36%
3. +4.90%
4. +5.52%

Answer: B
Explanation: Price change ≈ –Modified Duration × Δy + 0.5 × Convexity × (Δy)². Δy = –0.008 (fall of 80 bps = –0.80% = –0.008). Duration effect = –6.5 × (–0.008) = +0.0520 = +5.20%. Convexity adjustment = 0.5 × 55 × (0.008)² = 0.5 × 55 × 0.000064 = 0.00176 = +0.176%. Total ≈ 5.20% + 0.18% = 5.38% ≈ 5.36% (rounding). Note that convexity always adds to price change, regardless of yield direction.

Question 39

The on-the-run Treasury yield curve is upward sloping. The pure expectations theory of the term structure implies that:

1. Investors prefer long-term bonds and require lower yields for the additional liquidity risk
2. Future short-term rates are expected to be higher than current short-term rates
3. A liquidity premium embedded in long-term yields causes the upward slope
4. Market segmentation prevents arbitrage between short and long maturities

Answer: B
Explanation: The pure expectations theory holds that the shape of the yield curve is determined solely by expectations about future short-term rates. An upward-sloping curve means the market expects short-term rates to rise in the future. Options C and D describe the liquidity preference theory and market segmentation theory, respectively — these are alternative (and more realistic) explanations.

Question 40

A callable bond and an otherwise identical option-free bond are both trading in the market. Which relationship is always true?

1. Callable bond price > Option-free bond price
2. Callable bond yield > Option-free bond yield
3. Callable bond has greater positive convexity at all yield levels
4. The option-adjusted spread of the callable bond equals its Z-spread

Answer: B
Explanation: Callable bond price = Option-free bond price – Call option value. Since the call option has positive value (to the issuer), the callable bond is cheaper, meaning investors require a higher yield to compensate for the reinvestment risk / early redemption risk. Option C is wrong — callable bonds exhibit negative convexity when yields are low (price rises less than expected as rates fall). Option D is wrong — the OAS strips out the option cost, so OAS < Z-spread for callable bonds.

Question 41

A mortgage-backed security (MBS) has an average life that shortens significantly when interest rates decline. This phenomenon is called:

1. Negative convexity
2. Extension risk
3. Prepayment risk (contraction risk)
4. Credit risk migration

Answer: C
Explanation: When interest rates fall, homeowners refinance their mortgages at lower rates, increasing prepayments and shortening the average life of the MBS — this is contraction risk (a form of prepayment risk). Extension risk is the opposite: when rates rise, prepayments slow, extending average life. Negative convexity is the price behaviour that results from prepayment risk — the MBS price rise is capped as rates fall due to accelerating prepayments.

Derivatives (Questions 42–45)

Question 42

An investor buys a European call option with a strike price of $100. The current stock price is $95, and the call premium is $4. At expiration, the stock price is $108. The net profit per share to the option buyer is:

1. $8.00
2. $4.00
3. $13.00
4. $0.00 (option expires worthless)

Answer: B
Explanation: At expiration, intrinsic value = max(108 – 100, 0) = $8.00. Net profit = $8.00 – $4.00 (premium paid) = $4.00. The option is in the money and exercised. The investor does not lose the premium — it was paid at inception and is deducted from the gross payoff to get net profit.

Question 43

Put-call parity for European options on non-dividend paying stocks is: C + PV(X) = P + S. If this relationship is violated and C + PV(X) < P + S, an arbitrageur should:

1. Buy the call and bond; sell the put and stock
2. Sell the call and bond; buy the put and stock
3. Buy the call, put, and stock; sell the bond
4. Sell the call; buy the put, stock, and bond

Answer: A
Explanation: If C + PV(X) < P + S, the left side is underpriced and the right side is overpriced. Arbitrage: buy the cheap side (buy C and buy the bond/PV(X)) and sell the expensive side (sell P and sell/short S). This creates a risk-free profit until prices revert to parity. Put-call parity violations are short-lived in liquid markets.

Question 44

A portfolio manager holds a $10 million equity portfolio with a beta of 1.2. To hedge this portfolio using S&P 500 futures (contract value = $250,000, beta of futures = 1.0), how many contracts should the manager short?

1. 40 contracts
2. 48 contracts
3. 50 contracts
4. 38 contracts

Answer: B
Explanation: Number of contracts = (Target beta – Portfolio beta) / Futures beta × (Portfolio value / Contract value). To fully hedge (target beta = 0): N = (0 – 1.2) / 1.0 × ($10,000,000 / $250,000) = –1.2 × 40 = –48. The negative sign means short 48 contracts. The manager must account for both the portfolio's beta (1.2) and the number of contracts needed to cover the portfolio value.

Question 45

An interest rate swap where a company pays fixed and receives floating is economically equivalent to:

1. Issuing a fixed-rate bond and buying a floating-rate bond
2. Buying a fixed-rate bond and issuing a floating-rate bond
3. Buying both a fixed-rate and floating-rate bond
4. Issuing both a fixed-rate and floating-rate bond

Answer: A
Explanation: A pay-fixed, receive-floating swap is synthetically equivalent to issuing (borrowing at) a fixed rate and investing the proceeds in a floating-rate instrument. The firm has an obligation (pay fixed) and a receipt (receive floating) — identical to being short a fixed-rate bond (the obligation) and long a floating-rate bond (the asset). This equivalence is used to price and hedge interest rate swaps.

Alternative Investments (Questions 46–48)

Question 46

A private equity fund reports an IRR of 22% and a TVPI (Total Value to Paid-In) multiple of 1.8x after 4 years. Which interpretation is correct?

1. The fund has generated $0.80 of profit per dollar invested over its life
2. For every dollar invested, $1.80 in total value (realised plus unrealised) has been generated
3. The annual cash-on-cash return is 22%
4. The fund has a DPI of 1.8x meaning all capital has been returned

Answer: B
Explanation: TVPI = (Distributions + Residual Value) / Paid-In Capital. A TVPI of 1.8x means every dollar invested has generated $1.80 in combined realised and unrealised value. DPI (Distributions to Paid-In) measures only realised returns; a DPI below 1.0 means not all capital has been returned yet. IRR accounts for time value of money, while TVPI is an absolute multiple.

Question 47

A hedge fund uses a long/short equity strategy and reports the following: gross exposure = 200%, net exposure = +20%. This means the fund:

1. Has 200% long exposure and 180% short exposure
2. Has 110% long exposure and 90% short exposure
3. Has a directional bias toward the long side of approximately 10%
4. Has 200% leverage across both long and short positions combined

Answer: B
Explanation: Gross exposure = Long% + |Short%|. Net exposure = Long% – |Short%|. From 200% gross and +20% net: Long + Short = 200, Long – Short = 20 (where Short is the absolute value). Solving: Long = 110%, Short = 90%. Net long exposure of 20% indicates a modest directional bias toward the market. Option A implies Short = 180%, which gives net exposure of 200 – 360 = –160%, not +20%.

Question 48

Which of the following is a key reason that real estate is considered a useful portfolio diversifier despite its illiquidity?

1. Real estate returns have zero correlation with any equity market
2. Real estate provides a partial inflation hedge through linkage between rents, values, and price levels
3. Real estate eliminates sequence-of-returns risk in long-term portfolios
4. REITs have the same risk/return characteristics as direct property ownership

Answer: B
Explanation: Real estate offers a partial inflation hedge because rents tend to adjust upward with inflation over time, and property values often reflect replacement costs that rise with the price level. The correlation with equities is low but not zero — particularly for publicly listed REITs, which behave more like equities in the short term. Option C overstates the risk-reduction benefit, and Option D is incorrect — REITs are more liquid and exhibit higher correlation with equities than direct real estate.

Portfolio Management (Questions 49–50)

Question 49

Portfolio A has an expected return of 14%, a standard deviation of 20%, and a beta of 1.3. Portfolio B has an expected return of 11%, a standard deviation of 16%, and a beta of 0.9. The risk-free rate is 4% and the market return is 10%. Which portfolio has the superior risk-adjusted return based on the Treynor ratio?

1. Portfolio A, with a Treynor ratio of approximately 7.69%
2. Portfolio B, with a Treynor ratio of approximately 7.78%
3. Portfolio A, because it has a higher absolute return
4. Both are equal; the Treynor ratio is the same for all diversified portfolios

Answer: B
Explanation: Treynor ratio = (Rp – Rf) / Beta. Portfolio A: (14% – 4%) / 1.3 = 10% / 1.3 = 7.69%. Portfolio B: (11% – 4%) / 0.9 = 7% / 0.9 = 7.78%. Portfolio B has a marginally higher Treynor ratio, meaning it generated more excess return per unit of systematic risk. The Sharpe ratio (using standard deviation) would yield: A = 10/20 = 0.50; B = 7/16 = 0.4375. Portfolio A wins on the Sharpe. The choice of risk measure changes the performance ranking — a key CFA exam insight.

Question 50

According to the Capital Market Line (CML), which of the following portfolios should offer the best risk-return tradeoff for a risk-averse investor?

1. Any portfolio on the efficient frontier below the tangency portfolio
2. The minimum variance portfolio
3. A combination of the risk-free asset and the market portfolio, positioned on the CML according to the investor's risk tolerance
4. A levered position in the minimum variance portfolio

Answer: C
Explanation: The CML represents the set of efficient portfolios combining the risk-free asset with the market (tangency) portfolio. Every portfolio on the CML dominates all portfolios inside the efficient frontier (excluding the tangency point) on a risk-adjusted basis. A risk-averse investor selects a point on the CML with lower risk (more risk-free, less market exposure); a risk-tolerant investor may lever up along the CML above the market portfolio. The minimum variance portfolio lies on the efficient frontier but is dominated by CML portfolios.

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