Practice Evening Session

First Principles Thinking: payoff-to-profit bridge

A is correct. The CFA Curriculum distinguishes payoff from profit by subtracting the premium paid from the option payoff. It specifically notes that a put buyer earns positive profit only if the underlying price is sufficiently below the exercise price so that the positive payoff is greater than the premium. A put may therefore be exercised with positive payoff while still failing to cover the premium. Thus, the reason correctly explains why a positive payoff does not guarantee positive profit.

Why option B is incorrect. The reason is the direct mechanism linking option payoff to profit in the CFA Curriculum, not a separate unrelated truth.

Why option C is incorrect. The reason is true because the CFA Curriculum explicitly requires payoff to exceed premium for positive profit.

Statement (1) is correct as it matches the definition of yield-to-worst. Statement (2) is correct because using the lowest possible yield provides a conservative estimate of return for the investor. Statement (3) is incorrect because yield-to-worst assumes the call date that results in the lowest (not highest) yield; it assumes the issuer acts in their own best interest to minimize their cost of debt. Therefore, only statements (1) and (2) are correct.

The assertion is true: planning focuses on identifying objectives/constraints and producing an IPS, while execution includes setting target asset-class weights and implementing security selection and portfolio construction. The reason is false because asset allocation is commonly driven by top-down capital market expectations and the client’s IPS constraints; bottom-up work is more central to security selection within asset classes. In practice, top-down and bottom-up inputs can interact, but dismissing macro considerations is incorrect.

First Principles Thinking: Time Value of Money

B is correct. Intrinsic value equals the present value of all expected cash flows, discounted at the required rate. Cash flows: $CF_1 = 1.50$; $CF_2 = 1.80 + 35.00 = 36.80USD . Discount each: PV_1 = 1.50/1.10 = 1.3636$; $PV_2 = 36.80/1.10^2 = 36.80/1.21 = 30.4132USD . Total: V_0 = 1.36 + 30.41 = 31.77$ ≈ USD 31.78$. Each cash flow is worth less the further in the future it occurs.

A is incorrect, possibly from discounting the Year 2 dividend separately from the sale price or using incorrect discount factors.

C is incorrect because it sums undiscounted cash flows (USD 1.50 + 1.80 + 35.00 = 38.30$), ignoring the time value of money completely.

Statement (1) is incorrect; call markets trade only at specific times (the 'call'), not continuously. Statement (2) is correct; the primary advantage of call markets is consolidating liquidity in time and place. Statement (3) is incorrect; continuous markets allow trading at any time and do not typically use a single price auction for the main session (though they might for the open/close); single price auctions are characteristic of call markets. Therefore, only statement (2) is correct. Option B and C are incorrect because they include false statements (1) and (3).

Link utility to construction. Asset allocation models (like mean-variance optimization) require data inputs for 'US Equity,' 'Emerging Markets,' etc. Since one cannot invest in 'the market' abstractly, one uses an index. Assertion (A) is true. Reason (R) explains why this is valid: because the index is designed to statistically represent the behavior (return/risk) of that target segment. If R were false, A would be bad practice.

Statement (1) is correct; a margin call demands additional collateral when the account value falls below a maintenance threshold. Statement (2) is incorrect because leverage allows investors to take a position larger than their capital commitment, which magnifies both gains and losses rather than reducing risk. Statement (3) is correct as prime brokers facilitate leverage by lending cash for purchases or securities for short selling. Therefore, only statements (1) and (3) are correct. Options A and C fail because they misstate the purpose and effect of leverage.

First Principles Thinking: Index Family Design

B is correct. Understand the construction principle. Index providers organize sector indexes into families such that the universe of all sectors covers the entire market. They adjust weights so that a portfolio holding all sectors in their index weights replicates the broad market. For example, if Technology is 25% of the broad market, the Tech sector index will have a 25% weight in the family. This is by design, not coincidence. The document states: 'Typically, the aggregation of a sector index family is equivalent to a broad market index.'

A is incorrect because sectors do not have equal weights; Tech is heavier than Utilities, for example.

C is incorrect because sector indexes typically include all companies by assigning each to one sector; there are no exclusions.

First Principles Thinking: ABB Trade-offs

C is correct. An accelerated book build is arranged in only one or two days when time is of the essence. This rapid execution, without the usual time for extensive marketing and due diligence, typically results in the sales occurring at **discounted prices**. The discount compensates buyers for the reduced information and rapid decision-making required.

A is incorrect: The sales often occur at *discounted*, not higher, prices.

B is incorrect: While there is a risk, the discount is often applied to ensure the deal is fully subscribed, mitigating the risk of undersubscription. The primary and intended consequence is the sale at a discount, which allows for the rapid execution.

Statement (1) is incorrect. That definition applies to total market-capitalization weighting. Float-adjusted weighting uses only the shares available for public trading (the float), not the total shares outstanding. Statement (2) is correct. Float adjustment explicitly removes closely held shares (controlling stakes) and strategic holdings (governments, corporations) to reflect the investable universe. Statement (3) is correct. Most major global equity indexes use float-adjusted market capitalization to better represent the shares actually available to investors. Therefore, Option B is the correct answer.

First Principles: Discount Rate Derivation

B is correct. The discount rate formula is:

$$ PV = FV \times \left( 1 - \frac{\text{Days}}{\text{Year}} \times DR \right) $$

$$ 98 = 100 \times \left( 1 - \frac{180}{360} \times DR \right) $$

$$ 0.98 = 1 - 0.5 \times DR $$

$$ 0.5 \times DR = 1 - 0.98 = 0.02 $$

$$ DR = \frac{0.02}{0.5} = 0.04 = 4.00\% $$

A is incorrect because it ignores the semi-annual period (180/360) adjustment.

C is incorrect because it represents the add-on yield ($2/98 \times 2 = 4.08\%$), not the discount rate.

First Principles Thinking: classification rule

C is correct. The classification rule is the three-level fair value hierarchy. I, II, and III each match the CFA Curriculum level descriptions. All three qualify.

Why option A is incorrect: It counts only one correct level even though all are correctly described.

Why option B is incorrect: It leaves out one accurate level description.

First Principles Thinking: Transaction Costs and Access

B is correct. Consider the constraints. A broad bond index (like the Bloomberg Aggregate) contains thousands of CUSIPs. Many are small issues held by insurers that never trade. Buying all of them is impossible (can't find sellers) or prohibitively expensive (huge bid-ask spreads). Therefore, managers use 'stratified sampling'—buying a subset that matches the risk factors (duration, key rate duration, sector)—rather than full replication.

A is incorrect because difficulty is driven by liquidity and number of names, not price volatility.

C is incorrect because almost no one fully replicates broad bond indexes; sampling is the industry standard.

First Principles: Par Valuation

B is correct. When the price of a floating-rate note is exactly equal to its par value (100.00) on a reset date, the return required by the market (Discount Margin) must exactly equal the spread offered by the issuer (Quoted Margin).

$$ \text{Price} = \text{Par} \implies DM = QM $$

$$ DM = 220 \text{ bps} $$

A and C are incorrect because they imply a premium or discount price.

First Principles Thinking: classification rule

B is correct. The text provides precise definitions for credit risk components. Evaluating the items: 1. Correct. The text states "their product is expected loss" ($EL = POD \times LGD$). 2. Correct. The text defines LGD as the "investor's loss conditional on an issuer event of default." 3. Incorrect. The text states the Recovery Rate represents the percentage of an "outstanding debt claim" (or exposure) recovered, not a percentage of the "expected loss." Since exactly two statements are accurate, the count is two.

Why option A is incorrect. It underestimates the count of accurate statements.

Why option C is incorrect. Statement III is definitionally imprecise regarding the denominator of the recovery rate.

First Principles: The Complete Integration

B is correct. This question synthesizes everything we've learned. Let's evaluate each statement by building from foundational principles.

Statement I: "The CML has a steeper slope than the SML because it uses total risk instead of systematic risk."

Analysis: This statement is INCORRECT and reveals a fundamental misunderstanding.

The Problem with Comparing Slopes: The CML and SML have different x-axes, making direct slope comparisons meaningless:

• CML plots expected return vs. standard deviation (units: %)
• SML plots expected return vs. beta (units: dimensionless)

You cannot compare the numerical values of these slopes any more than you can compare miles per gallon to kilometers per liter without conversion. They measure different things.

What we CAN say:

• CML slope = $\frac{E(R_m) - R_f}{\sigma_m}$ = Sharpe ratio of market (e.g., 0.40 if market premium is 8% and market risk is 20%)
• SML slope = $E(R_m) - R_f$ = market risk premium (e.g., 8%)

Numerically, the CML slope (0.40) is smaller than the SML slope (8.0), but this comparison is meaningless because they have different units and x-axes.

Statement II: "A portfolio consisting of 70% market portfolio and 30% risk-free asset will plot on both the CML and the SML."

Analysis: This statement is CORRECT — demonstrating a deep insight.

Why it plots on the CML: By definition, any combination of the risk-free asset and the market portfolio lies on the CML. This portfolio is exactly such a combination, so it must lie on the CML.

Why it plots on the SML: The SML applies to all assets and portfolios. This portfolio has a beta that can be calculated:

$$\beta_p = 0.70 \times \beta_m + 0.30 \times \beta_{rf} = 0.70 \times 1.0 + 0.30 \times 0 = 0.70$$

Using the SML equation with $\beta = 0.70$:

$$E(R_p) = R_f + 0.70 \times [E(R_m) - R_f]$$

Using the CML equation with $\sigma_p = 0.70 \times \sigma_m$:

$$E(R_p) = R_f + \frac{E(R_m) - R_f}{\sigma_m} \times 0.70\sigma_m = R_f + 0.70 \times [E(R_m) - R_f]$$

Both equations give the same expected return! This is not a coincidence — for efficient portfolios (those on the CML), the SML and CML are consistent. This is because efficient portfolios have no unsystematic risk, so their total risk is entirely systematic.

Statement III: "The market portfolio has a Sharpe ratio equal to the slope of the CML and a beta of 1.0 on the SML."

Analysis: This statement is CORRECT — capturing a fundamental unity.

Part 1: Sharpe Ratio equals CML Slope

The market portfolio's Sharpe ratio is:

$$Sharpe_m = \frac{E(R_m) - R_f}{\sigma_m}$$

The CML slope is:

$$Slope_{CML} = \frac{E(R_m) - R_f}{\sigma_m}$$

These are identical. In fact, the CML slope is defined as the Sharpe ratio of the market portfolio. Every investor on the CML achieves the same Sharpe ratio as the market portfolio (this is the power of the two-fund separation theorem).

Part 2: Beta equals 1.0

Beta measures systematic risk relative to the market. By definition:

$$\beta_m = \frac{Cov(R_m, R_m)}{Var(R_m)} = \frac{Var(R_m)}{Var(R_m)} = 1.0$$

The market has perfect correlation with itself, so its beta is exactly 1.0. On the SML, the market portfolio plots at the point (β = 1.0, Return = $E(R_m)$).

Stitching It All Together: The Grand Unification

The CAL, CML, and SML are not separate theories — they are different perspectives on the same equilibrium:

The CAL says: Investors combine safe and risky assets.

The CML says: In equilibrium, the optimal risky asset is the market; it prices efficient portfolios.

The SML says: Only systematic risk is priced; it prices all assets, efficient or not.

For the special case of efficient portfolios (those on the CML), both the CML and SML apply simultaneously and give consistent results. For inefficient assets (like individual stocks), only the SML applies.

A is incorrect because Statement I is false — you cannot meaningfully compare CML and SML slopes due to different x-axis units.

C is incorrect because Statement I is false for the reason explained above.

Stop orders are conditional: a stop-sell becomes valid after the market trades at or below the stop price; a stop-buy becomes valid at or above the stop price. The reason describes the procyclical timing: these orders enter the market during directional moves, amplifying those moves. When prices drop and stop-sells trigger, additional selling supply pushes prices lower; when prices rise and stop-buys trigger, additional buying demand pushes prices higher. This feedback loop creates momentum and often leads to execution away from the stop price, especially in fast-moving or illiquid markets. The key is causality: stop orders mechanically convert price moves into order flow in the same direction, reinforcing trends and degrading execution quality for the stop-order user.

Start from the problem: without constraints, a manager could earn incentive fees in good years, lose money in bad years, then earn incentive fees again just for recovering back to where investors previously were—investors would effectively pay twice for the same wealth level. A high-water mark fixes this by setting a reference point: the investor must be made whole back to the prior peak before incentives restart, so (1) and (2) are true. This also improves intertemporal alignment: it rewards net new wealth creation, not mere bounce-backs, supporting (4). Statement (3) confuses fee mechanics with investment outcomes: high-water marks change when fees are paid; they do not remove market risk or prevent drawdowns.

Statement (1) is correct as it defines the option-adjusted yield based on the option-adjusted price. Statement (2) is incorrect because the OAS is calculated as the Z-spread minus (not plus) the option value in basis points per year; the investor receives a higher Z-spread to compensate for the call risk. Statement (3) is correct because the option-adjusted price represents the value of the bond if it were option-free, which is the flat price plus the value of the call option (which the investor 'paid' for by accepting a lower flat price). Therefore, only statements (1) and (3) are correct.

Statement (1) is correct. Jensen's alpha is the difference between actual portfolio return and the return that CAPM says the portfolio should earn given its beta. CAPM predicts: E(Rp) = Rf + βp(Rm - Rf). Alpha is: αp = Actual Rp - [Rf + βp(Rm - Rf)]. If alpha is zero, the portfolio performed exactly as CAPM predicted - it earned fair compensation for its systematic risk. Alpha represents the manager's value-added (or value-destroyed) beyond passive market exposure. Statement (2) is correct. Positive alpha means the portfolio beat its CAPM benchmark - it delivered more return than required for its level of systematic risk. This is the gold standard of active management. A manager who consistently generates positive alpha is adding value through security selection, market timing, or other skills. Negative alpha indicates underperformance - the manager destroyed value relative to a passive strategy with the same beta. Zero alpha means the manager earned exactly what was expected given the risk taken. Statement (3) is correct. This is the exact formula for Jensen's alpha, which can also be written as αp = Rp - [Rf + βp(Rm - Rf)] or αp = (Rp - Rf) - βp(Rm - Rf). The term Rf + βp(Rm - Rf) is the CAPM-expected return - what the portfolio should earn. By subtracting this from actual return, we isolate the abnormal return. The formula shows alpha is excess return minus beta times market risk premium, revealing performance beyond market exposure. Statement (4) is correct, and this is subtle but important. Consider: Portfolio has Rp = 8%, Rf = 2%, Rm = 10%, βp = 0.5. Alpha = 8% - 2% - 0.5(10% - 2%) = 6% - 4% = +2%. The portfolio's 8% return is below the market's 10%, yet alpha is positive. Why? Because with beta of 0.5, the portfolio should only earn 6% (half-way between Rf and Rm), but it earned 8%. The manager outperformed given the low systematic risk. This shows alpha is relative to risk taken, not absolute return. Therefore, all four statements are correct. Option B fails by excluding the important insight about positive alpha despite below-market returns. Option C fails by excluding the interpretation of positive alpha as outperformance.

Core Interpretation

By definition:

$$DR = \frac{\sum w_i \sigma_i}{\sigma_p}$$

We can rearrange this as:

$$\sigma_p = \frac{\sum w_i \sigma_i}{DR}$$

Thus, DR describes how much lower the portfolio volatility is relative to the weighted average of constituent volatilities.

Analyzing DR Values

• DR = 1.0: \(\sigma_p = \sum w_i \sigma_i\). No diversification benefit: portfolio risk equals weighted average component risk.
• DR = 1.3: \(\sigma_p = (\sum w_i \sigma_i) / 1.3\). Portfolio volatility is about 77% (1/1.3) of the average component volatility.
• DR = 2.0: \(\sigma_p = (\sum w_i \sigma_i) / 2.0\). Portfolio volatility is 50% (1/2) of the average component volatility.

Conclusion

The higher the DR, the more diversified the portfolio is, in the sense that overall volatility is lower relative to the constituent volatilities.

B is correct because DR = 2.0 implies the portfolio’s volatility is half of its weighted average component volatility.

A is incorrect because DR = 1.0 indicates minimal diversification, while DR = 2.0 indicates the greatest diversification among the three.

C is incorrect because DR = 1.3 implies portfolio volatility is about 1/1.3 ≈ 77% of the average component volatility, not “30 times lower.”

First Principles Thinking: Residual Cash Flow

B is correct. FCFE represents the cash available to equity holders after the firm has met all operational needs and capital expenditures, adjusted for debt flows. The formula is $FCFE = CFO - FCInv + ext{Net Borrowing}USD . Net borrowing increases cash available to equity (as debt holders provide capital). Calculation: 120 - 40 + 15 = 95$ million. This is the amount the firm could theoretically distribute as dividends.

A is incorrect because it subtracts net borrowing ($120 - 40 - 15 = 65$), treating debt issuance as a cash outflow rather than an inflow.

C is incorrect because it adds FCInv ($120 + 40 + 15 = 175$), treating capital expenditure as a source of cash rather than a use.

First Principles Thinking: Strategic Order Use

B is correct. The manager possesses 'alpha' (proprietary insight). Displaying a large buy order signals their confidence and will prompt sellers to raise prices, increasing the acquisition cost (market impact). Using a hidden or iceberg order allows the trader to place the order without revealing the total size, minimizing information leakage and allowing a slower, lower-impact execution.

A is incorrect because a marketable order instantly consumes liquidity, causing immediate price concessions and signaling aggressive buying.

C is incorrect because Fill-or-Kill requires immediate, full execution, which is highly unlikely for a large order and would result in massive price concession, undermining the goal of minimizing impact.

First Principles Thinking: Money Convexity Adjustment

A is correct. The money convexity adjustment (dollar amount) is calculated as: $$ \frac{1}{2} \times \text{MoneyCon} \times (\Delta \text{Yield})^2 $$ $$ 0.5 \times 50,000,000 \times (0.01)^2 $$ $$ 0.5 \times 50,000,000 \times 0.0001 $$ $$ 25,000,000 \times 0.0001 = 2,500 $$

B is incorrect because it neglects the 1/2 factor.

C is incorrect because it implies a calculation error with the yield squared term.

First Principles Thinking: classification rule

B is correct. The curriculum states that industry and competitive analysis helps estimate the industry's base rate and its determinants, and it improves forecasts by clarifying competitive forces and supplier relationships. Statement II is incorrect because the cited finding was that company-specific effects were much larger for low performers than for high performers. Therefore, two statements qualify.

Why option B is incorrect. It is not incorrect because exactly two statements, I and III, satisfy the criterion.

Why option C is incorrect. All three do not qualify because Statement II reverses the direction of the finding on company-specific effects.

First Principles Thinking: Market Representation vs. Security Count

B is correct. Begin with definitions. The Russell 3000 is defined by exactly 3,000 largest stocks (fixed boundary). The Wilshire 5000 includes all stocks meeting liquidity criteria (no fixed boundary). Both cover ~98% of market cap. For the Wilshire to achieve this without limiting to 3,000 names, it must include smaller-cap names beyond the 3,000th position. These additional micro-cap stocks add minimal market value but bulk up the security count. The document explicitly states that despite its name, the Wilshire 5000 has no constraint on the number of securities included.

A is incorrect because 'representativeness' in indexing is typically measured by market capitalization coverage, not the number of constituents. Russell's fixed number is arbitrary; the fixed number itself doesn't make it more representative.

C is incorrect because the different composition (especially exposure to small-cap and micro-cap stocks) will create performance divergence, particularly in years when small-cap stocks outperform or underperform large-cap stocks.

First Principles Thinking: Historical Earnings Multiple

C is correct. The trailing P/E ratio uses historical earnings (past 12 months) as the denominator, reflecting what investors pay for demonstrated earnings capacity. Formula: Trailing P/E = P0/E0 where E0 is last year's EPS. Calculation: 57.32/3.82 = 15.01. This multiple indicates the market values the stock at approximately 15 times last year's earnings, providing a baseline for comparison.

A is incorrect because it calculates the forward P/E using next year's estimate: 57.32/4.75 = 12.07, which reflects future expectations rather than historical performance.

B is incorrect, possibly from averaging the two EPS figures or miscalculating the division, violating the clear definition of trailing versus forward P/E.

First Principles Thinking: Collateral Quality, Not Just Rank

A is correct. Secured vs unsecured status tells you who is paid first, but LGD also depends on how much value the collateral will actually realize in default.[file:1] Tangible, liquid, and easily saleable assets (plants, equipment, inventory) generally support higher recovery rates than soft, difficult-to-value intangibles.[file:1] Rating methodologies explicitly recognize that high-quality collateral can justify notching secured issues above the senior unsecured issuer rating, reflecting lower LGD at similar POD.[file:1]

B is incorrect because legal seniority alone does not equalize LGD; poor or hard-to-realize collateral can lead to low recoveries even for secured creditors.[file:1]

C is incorrect because cross-border mobility is not the core driver here; the key is uncertainty and marketability of intangibles, which tends to increase LGD relative to good hard collateral.[file:1]

Statement (1) is correct because the reading describes that the reference rate is typically observed at the beginning of the period and paid at the end, and it labels this structure as in arrears.
Statement (2) is incorrect because the reading identifies actual/360 and actual/365 as common day-count conventions for floaters and does not state that quarterly resets require 30/360.
Statement (3) is correct because it explicitly lists actual/360 and actual/365 as the most common day-count conventions for floaters.
Therefore, statements (1) and (3) are correct, so option C is correct.
Option A fails because statement (2) is incorrect.
Option B fails because it includes statement (2), which is incorrect, even though statement (3) is correct.

Statement (1) is correct because the master-feeder structure pools assets into a master fund where all investment activity occurs, while feeder funds simply channel capital into it. Statement (2) is correct because side letters are side agreements that address specific investor requirements (e.g., reporting, fees) and can override standard terms. Statement (3) is incorrect because SMAs actually offer better transparency (and control) since the assets are held in the investor's own name or a dedicated account, unlike commingled funds. Therefore, only statements (1) and (2) are correct. Options B and C fail because they mischaracterize the transparency of SMAs.

Statement (1) is correct because the CML specifically uses the market portfolio as the optimal risky portfolio, making it a special case of the CAL. Statement (2) is incorrect because points above the CML are not achievable; they represent combinations of risk-return that cannot be obtained with available assets. Statement (3) is incorrect because the CML applies only to efficient portfolios on the efficient frontier, not to individual securities or inefficient portfolios. Therefore, only statement (1) is correct. Option B fails by including the unachievable nature of above-CML points. Option C fails by excluding the CML definition and including the incorrect applicability to all securities.

First Principles Thinking: No-Arbitrage and Entitlement

C is correct. Valuation is based on entitlement to cash flows. On the ex-dividend date, a buyer of the stock purchases it *without* the right to receive the upcoming dividend; that right remains with the seller. To prevent risk-free arbitrage (buying just before the cut-off to get the cash, then selling), the market price must adjust downward by exactly the amount of the cash leaving the firm (the dividend) as trading begins on the ex-date. Thus, $P_{ex} = P_{cum} - D$.

A is incorrect because the declaration date is merely the announcement. The economic value has not yet separated from the share, and ownership rights haven't shifted.

B is incorrect because the holder-of-record date is the administrative deadline for identifying shareholders. The effective cut-off for trading purposes is the ex-date, which occurs before the record date due to settlement cycles (e.g., T+2).

Statement (1) is correct because longer reset periods are explicitly associated with greater exposure to interest rate and price volatility.
Statement (2) is correct because the material states that as the reset period lengthens, the floater behaves more like a short-dated fixed-rate security.
Statement (3) is incorrect because the material links greater potential price fluctuation to longer (not shorter) reset periods.
Therefore, statements (1) and (2) are correct, so option A is correct.
Option B fails because statement (3) reverses the direction of the reset-period effect on price fluctuation.
Option C fails because statement (3) is incorrect even though statement (1) is correct.

First Principles Thinking: classification rule

B is correct. The text identifies specific sources of cash flow generation for different borrower types. For Corporate borrowers, primary sources include business operations (operating cash flows) and secondary sources include asset sales, divestitures, and financing. Sovereign tax revenues are a source for Sovereign borrowers, not Corporate. Evaluating the items: 1. Operating cash flows is a primary corporate source. 2. Sovereign tax revenues is a sovereign source. 3. Asset sales is a secondary corporate source. Since exactly two items (Operating cash flows and Asset sales) satisfy the condition, the count is two.

Why option A is incorrect. It underestimates the count.

Why option C is incorrect. Sovereign tax revenues are not a source for corporate borrowers.

Implications of EMH

B is correct. Statement I is false because in a semi-strong efficient market, publicly available information is already reflected in prices, so fundamental analysis cannot consistently generate abnormal returns. Statement II is true because weak-form efficiency implies past price and volume data cannot be used consistently to earn abnormal returns, which undermines technical analysis. Statement III is true because if markets are strong-form efficient, even private information is already reflected in prices, so passive investing is justified. Therefore, two statements are correct.

Why A is incorrect: statements II and III are both correct.

Why C is incorrect: statement I is not correct under semi-strong efficiency.

Markets do not compensate diversifiable risk because rational investors eliminate it by holding many low-correlation assets—arbitrage logic forces its price to zero. The reason describes undiversified investor experience (higher perceived risk) but misidentifies pricing mechanism: market equilibrium prices reflect marginal diversified investors who set returns based only on systematic risk. Individual investor variance is irrelevant to asset pricing; the assertion holds because diversifiable risk earns no premium in equilibrium, not because it fails to affect variance.

First Principles Thinking: classification rule

C is correct. Each statement comes directly from the generic strategy discussion. Cost leadership fits price-conscious markets with limited perceived product differences, differentiation can defend against supplier power through pricing power or margin absorption, and the curriculum explicitly warns against being stuck in the middle. Therefore, all three qualify.

Why option B is incorrect. Only two do not qualify because all three statements are supported by the curriculum.

Why option C is incorrect. It is not incorrect because every item satisfies the criterion.

First Principles Thinking: signs under a downward curve shift

B is correct. %deltaPV_Full ~= (-8.20 x -0.0075) + [0.5 x 95 x (-0.0075)^2] = 0.06150 + 0.002672 = 0.06417, or +6.42%. The duration term adds 6.15% and the positive convexity contributes an extra 0.27%.

+6.15% captures only the duration effect and omits the positive convexity adjustment.

+5.88% incorrectly subtracts the convexity term, which would only be correct if convexity were negative.

First Principles Thinking: Convexity Bias in Rates

C is correct. A short interest rate futures position and a receive-floating, pay-fixed FRA are both positioned for rising rates. If rates fall, both positions lose, but the futures loss is linear in the rate move, while the FRA settlement is discounted by the lower market rate. The lower discount rate magnifies the present value of the FRA loss, so the short futures position performs better, or loses less, than the FRA.

A is incorrect because daily settlement is not the key comparison in this falling-rate scenario.

B is incorrect because the pay-fixed FRA is effectively short convexity relative to the linear futures position.

First Principles Thinking: Float Adjustment

A is correct. Float-adjusted weighting calculates weights based on the value of shares available to public investors, not total shares outstanding. Controlling blocks are excluded.

Step-by-Step Calculation:
1. **Calculate Float for X:**
Total Shares = 10 million.
Float % = \(100\% - 40\% = 60\%\).
Float Shares = \(10 \times 0.60 = 6\) million.
Float Market Cap (X) = \(6 \text{ million} \times \text{USD } 20 = \text{USD } 120\) million.
2. **Calculate Float for Y:**
Float Market Cap (Y) = \(5 \text{ million} \times \text{USD } 50 = \text{USD } 250\) million.
3. **Calculate Total Index Float Cap:**
Total = \(\text{USD } 120 + \text{USD } 250 = \text{USD } 370\) million.
4. **Calculate Weight of X:**
Weight = \(\text{USD } 120 / \text{USD } 370 = 0.3243\) or \(32.4\%\).

B is incorrect because it uses total market cap (X = 200, Y = 250; Total = 450; 200/450 = 44.4%).
C is incorrect; this is the total market cap weight calculation (200/450).

First Principles Thinking: decision rule

C is correct. The module describes early or rapid amortization as a safeguard, especially during the revolving period, when replenishment may prove insufficient or defaults may alter the pool enough to damage the transaction economics. That stress condition is the most accurate trigger description.

Why option A is incorrect. Greater diversification is not the stress condition the clause is designed to address.

Why option B is incorrect. Pre-funding is associated with solar ABS and does not define the credit-card ABS rapid amortization trigger.

First Principles Thinking: decision rule

B is correct. The decision rule is whether the collateral is still being replenished. In the revolving period for non-amortizing credit card ABS, principal collections are reinvested into new receivables, so investors receive only finance charges and fees.

Why option A is incorrect. Principal is not paid out to noteholders during the revolving period under the structure described.

Why option C is incorrect. Finance charges and fees are exactly what investors receive during that phase.

First Principles Thinking: The J-Curve Effect

A is correct. The 'J-Curve' phenomenon arises because fees are often charged on the full committed capital while returns are generated only on the invested portion early in the fund's life.
1. Calculate Invested Capital: USD 200m \times 30\% = USD 60m.
2. Calculate Gross Investment Profit: 60m \times 15\% = USD 9m.
3. Calculate Management Fee: 200m \times 2\% = USD 4m (Fee is on committed, not invested).
4. Calculate Net Profit: USD 9m (Gross) - USD 4m (Fee) = USD 5m.
5. Calculate Net Return on Invested: 5m / USD 60m = 8.33\%.
The heavy drag of fees on uninvested capital significantly depresses early returns.

B is incorrect: This assumes the 2% fee is charged only on the invested capital ($15\% - 2\% = 13\%), ignoring the standard PE structure of fees on committed capital.

C is incorrect: This is the gross return, ignoring management fees entirely.

First Principles: The Grand Synthesis

A is correct. This question requires synthesizing everything we've learned about performance measurement into a unified framework. Let's build this understanding from the ground up, showing how these three metrics work together to tell a complete story.

Building Block 1: What Each Metric Measures (Review)

Before we can integrate them, let's ensure we understand what each metric captures:

Sharpe Ratio = $\frac{R_p - R_f}{\sigma_p}$

• Measures: Return per unit of TOTAL risk
• Interpretation: Efficiency of risk-taking overall
• Best for: Comparing stand-alone portfolios or total wealth

Treynor Ratio = $\frac{R_p - R_f}{\beta_p}$

• Measures: Return per unit of SYSTEMATIC risk
• Interpretation: Efficiency of unavoidable (market) risk-taking
• Best for: Comparing sub-portfolios within diversified holdings

Jensen's Alpha = $R_p - [R_f + \beta_p(R_m - R_f)]$

• Measures: Excess return beyond CAPM prediction
• Interpretation: Value added through active management skill
• Best for: Evaluating manager skill vs. passive alternative

Building Block 2: The Analyst's First Claim — Sharpe Ratio Comparison

Claim: Portfolio X's superior Sharpe ratio (0.82 vs. 0.70) proves it outperformed on a risk-adjusted basis.

Is this correct? YES. Here's why:

The Sharpe ratio directly measures risk-adjusted performance. If Portfolio X has a Sharpe of 0.82 and the market has 0.70:

• Portfolio X earned 0.82% excess return per 1% of total risk
• Market earned 0.70% excess return per 1% of total risk
• Portfolio X was MORE EFFICIENT at converting risk into returns

This is true regardless of the absolute level of risk taken. Even if Portfolio X has higher or lower volatility than the market, the Sharpe ratio normalizes for this, making direct comparison valid.

Example to prove it:

• Scenario 1: Portfolio X has $\sigma = 15\%USD , excess return = 12.3\%USD → Sharpe = 0.82$
• Scenario 2: Market has $\sigma = 20\%USD , excess return = 14\%USD → Sharpe = 0.70$

Portfolio X took LESS total risk but achieved nearly the same excess return, demonstrating superior efficiency. You could lever up Portfolio X to match the market's 20% risk and you'd get higher returns, proving X's superiority.

Building Block 3: The Analyst's Second Claim — Jensen's Alpha Interpretation

Claim: The positive Jensen's alpha suggests Portfolio X added value through active management beyond what beta exposure would provide.

Is this correct? YES. Let's break this down:

Jensen's alpha of +2.8% means Portfolio X earned 2.8% MORE per year than the CAPM predicted based on its systematic risk (beta). This excess can ONLY come from:

1. Security selection skill: Picking undervalued stocks
2. Market timing skill: Shifting allocations at the right times
3. Factor exposures: Exposure to other risk factors the CAPM doesn't capture (though this is debatable as skill)
4. Luck: BUT the question states alpha is statistically significant, ruling this out

Since the alpha is statistically significant, we can conclude with 95% confidence that Portfolio X's manager added value through active decisions, not just by taking on beta exposure.

Building Block 4: Can High Sharpe and Positive Alpha Coexist?

Option C suggests these metrics are incompatible. This is FALSE. Not only can they coexist, but they typically SHOULD coexist for a skilled manager. Here's why:

Mathematical relationship:

• If alpha > 0, the portfolio earned more than CAPM predicted
• If Sharpe > market Sharpe, the portfolio was more efficient with total risk
• These are compatible because they measure different aspects of performance

Example showing both:

Suppose:

• Risk-free rate: 3%
• Market return: 11%, market $\sigma = 18\%USD , market Sharpe = 0.70$
• Portfolio X return: 16%, $\sigma = 20\%$, $\beta = 1.3$

Check Sharpe:

$$Sharpe_X = \frac{0.16 - 0.03}{0.20} = \frac{0.13}{0.20} = 0.65$$

Hmm, that gives 0.65, not 0.82. Let me adjust:

For Sharpe = 0.82: If $\sigma = 15\%$, excess return = USD 0.82 \times 0.15 = 0.123 = 12.3\%USD , so R_p = 15.3\%$

Check alpha:

Expected return from CAPM: $3\% + 1.3(11\% - 3\%) = 3\% + 10.4\% = 13.4\%$

Alpha $= 15.3\% - 13.4\% = 1.9\%$

With slightly different numbers, both high Sharpe and positive alpha are achievable. They measure different things and are perfectly compatible.

Building Block 5: The Complete Story These Three Metrics Tell

Together, the three metrics paint a rich picture of Portfolio X:

Sharpe Ratio (0.82 vs. market 0.70):

• Portfolio X is more efficient with total risk
• Better choice for an investor's entire portfolio
• Could leverage Portfolio X to achieve higher returns at any risk level vs. market

Treynor Ratio (9.5):

• Portfolio X is efficient with systematic risk
• Good choice as a sub-portfolio within diversified holdings
• Compare 9.5 to market's Treynor: $(11\% - 3\%)/1.0 = 8.0\%$ → Portfolio X is superior

Jensen's Alpha (+2.8%, significant):

• Manager added 2.8% value through skill
• Justifies active management fees (if fees < 2.8%)
• Portfolio X dominated passive market exposure

Building Block 6: The Interconnections

These metrics aren't independent—they're interconnected:

• High alpha → contributes to high Sharpe (excess return increases numerator)
• High Treynor + low unsystematic risk → high Sharpe
• Portfolio with high Sharpe but zero alpha → achieved efficiency through leverage/deleveraging, not skill
• Portfolio with positive alpha but low Sharpe → added value but carried excessive unsystematic risk

Building Block 7: The Practical Investment Decision

An investor seeing these numbers should conclude:

1. Strong evidence of skill: Jensen's alpha is positive and significant
2. Efficient risk-taking: Sharpe ratio exceeds market
3. Well-diversified: High Sharpe AND high Treynor suggests low unsystematic risk
4. Decision: INVEST, assuming fees are reasonable (< 2.8%)

Stitching It All Together: The Complete Framework

The three metrics form a triangle of evaluation:

• Sharpe: Answers Is total risk efficiently used?
• Treynor: Answers Is systematic risk efficiently used?
• Jensen's Alpha: Answers Did the manager add value beyond beta?

For Portfolio X, all three metrics point in the same direction: this is an excellent, skillfully-managed portfolio that efficiently uses both total and systematic risk while adding alpha through active management.

The analyst's interpretation is completely correct.

B is incorrect because it fundamentally misunderstands the Sharpe ratio. The Sharpe ratio ALREADY ACCOUNTS FOR different total risk levels—that's the entire point of the metric! By dividing excess return by standard deviation, we normalize for risk, making direct comparisons valid. You don't need the same risk level to compare Sharpe ratios; the ratio itself is the risk-adjusted measure. This option reveals a conceptual confusion about what risk-adjusted means.

C is incorrect because it falsely claims Jensen's alpha and superior Sharpe ratio are incompatible. They absolutely CAN coexist—in fact, they typically DO for skilled managers. A positive alpha CONTRIBUTES to a high Sharpe ratio (higher returns increase the numerator). The only way they'd conflict is if positive alpha came with disproportionately high unsystematic risk, but even then, it's not impossible—just suboptimal. There's no mathematical contradiction between these metrics.

First Principles Thinking: Definition of Covariance

A is correct. Covariance is the unscaled measure of directional relationship between two variables. It is the product of the correlation coefficient and the standard deviations of the two assets.

$$Cov(X,Y) = ho_{X,Y} \times \sigma_X \times \sigma_Y$$

Using decimal format as required for covariance calculations in the text:

• $ ho = 0.65$
• $\sigma_X = 0.12$
• $\sigma_Y = 0.18$

$$Cov = 0.65 \times 0.12 \times 0.18$$

$$Cov = 0.65 \times 0.0216 = 0.01404$$

Rounding to 4 decimal places gives 0.0140.

B is incorrect because it is simply the product of the standard deviations (USD 0.12 \times 0.18 = 0.0216$), implying a correlation of 1.0.

C is incorrect because it calculates covariance using percentages as whole numbers ($12 \times 18 \times 0.65 = 140.4USD ) and then misinterprets the scaling (0.1404$). While 'percent squared' is a unit, in decimal terms typically used for further variance calculations, 0.0140 is the correct magnitude.

Statement (1) is correct because Sharpe ratio = (Rp - Rf)/σp uses standard deviation (total risk) as denominator. Statement (2) is incorrect because Jensen's alpha measures absolute excess return adjusted for beta risk (αp = Rp - Rf - βp[Rm - Rf]), not per unit of systematic risk; the Treynor ratio measures excess return per unit of beta. Statement (3) is correct because M² rescales Sharpe ratio to market volatility, yielding return directly comparable to market return. Therefore, only statements (1) and (3) are correct. Option B fails by mischaracterizing Jensen's alpha. Option C fails by excluding total risk in Sharpe ratio.

First Principles: Floating-Rate Note Valuation

A is correct. The value of a floating-rate note is the present value of its future coupons and principal, discounted at the reference rate plus the discount margin (DM). Since the MRR is constant, we can model this as a fixed-rate bond with a coupon rate equal to MRR + Quoted Margin (QM) and a discount rate equal to MRR + Discount Margin (DM).

$$ \text{Coupon Rate} = 3.00\% + 0.80\% = 3.80\% $$

$$ \text{Discount Rate (Yield)} = 3.00\% + 1.20\% = 4.20\% $$

Since the discount rate (4.20%) is higher than the coupon rate (3.80%), the bond must trade at a discount (below 100).

Calculation using $N=4USD periods (2 years \times$ 2):

$$ PMT = \frac{3.80\% \times 100}{2} = 1.90 $$

$$ r = \frac{4.20\%}{2} = 2.10\% = 0.021 $$

$$ PV = \sum_{t=1}^{4} \frac{1.90}{(1.021)^t} + \frac{100}{(1.021)^4} $$

$$ PV = 1.90 \times \left[ \frac{1 - (1.021)^{-4}}{0.021} \right] + \frac{100}{(1.021)^4} $$

$$ PV \approx 7.30 + 92.02 = 99.32 $$

Wait, let me re-calculate precisely: USD 1.90/1.021 + 1.90/1.021^2 + 1.90/1.021^3 + 101.90/1.021^4 = 99.23$.

B is incorrect because it approximates the price change linearly (approx 40bps difference) without discounting correctly.

C is incorrect because it ignores the difference between QM and DM.

First Principles Thinking: Discounted Cash Flow (Bond-like)

A is correct. Unlike perpetual preferreds, this stock has a maturity. It is valued like a bond: PV of coupons plus PV of face value. Annual dividend $D = 100 imes 0.05 = 5.00USD . The cash flows are 5 (t=1), 5 (t=2), 5 (t=3), 105 (t=4)USD . Discounting at 6%: V_0 = 5/1.06 + 5/1.06^2 + 5/1.06^3 + 105/1.06^4$. Using a financial calculator (N=4, I/Y=6, PMT=5, FV=100), $PV = 96.53$. Since the coupon rate (5%) < discount rate (6%), it must trade at a discount to par.

B is incorrect because it assumes the price equals par, which only happens if coupon rate = required return.

C is incorrect because it implies a premium, which would require the coupon rate to exceed the required return.

First Principles Thinking: Matching Quantified Risk Tolerance to Portfolio Volatility

B is correct. In portfolio management, the risk objective translates a qualitative description (e.g., “moderate risk”) into a quantitative limit, often a maximum acceptable standard deviation. Each proposed strategic mix must respect this limit. Compare each portfolio’s risk to the 11% ceiling:

• Portfolio A: σ = 7% < 11% → acceptable.
• Portfolio B: σ = 10% < 11% → acceptable.
• Portfolio C: σ = 14% > 11% → exceeds risk tolerance.

Therefore, only Portfolios A and B are consistent with the client’s risk tolerance.

A is incorrect because it is overly conservative, discarding Portfolio B even though its standard deviation is within the client’s stated maximum and may better support return needs.

C is incorrect because it includes Portfolio C, which breaches the explicit 11% volatility limit. Choosing C would contradict the client’s quantified risk objective in the Investment Policy Statement.

First Principles Thinking: Interest Rate Parity

A is correct. The formula for FX forwards is F = S × (1 + r_price) / (1 + r_base). Here, USD is the price currency and EUR is the base currency. So, F = 1.25 × (1.02 / 1.04). Since the numerator (USD rate) is smaller than the denominator (EUR rate), the ratio is less than 1. Therefore, the Forward Rate must be less than the Spot Rate. Conceptually, the currency with the higher interest rate (EUR) must depreciate in the forward market to offset the yield advantage; otherwise, everyone would convert to EUR, earn 4%, and hedge back for a risk-free profit.

B is incorrect: This would happen if the US rate were higher than the Eurozone rate.

C is incorrect: Interest rate differentials force forward rates to deviate from spot rates to prevent arbitrage; equality assumes r_USD = r_EUR.

A is true because the curve-based revaluation (via par-curve shifts producing not-perfectly-parallel spot shifts) becomes closer to a simple yield-to-maturity shift when the curve is flat-ish, the horizon is short, and the bond is near par. R is true, but it does not explain the narrowing of the effective-vs-modified duration gap, which is driven by par-to-spot curve mechanics (and curve shape), not by the definition of Macaulay duration.

First Principles Thinking

The G-spread is the spread over a single point on the government yield curve (usually the yield-to-maturity of a matched-maturity Treasury). The Z-spread (Zero-volatility spread) is the constant spread added to the entire government spot rate curve to price the bond.

When the yield curve is upward sloping (which is the typical case), the spot rates for intermediate cash flows are lower than the final yield-to-maturity. To match the same market price, the spread added to these lower early rates (Z-spread) must be higher than the spread added to the single, higher yield-to-maturity (G-spread). Conversely, if the curve is flat, they would be equal. The steeper the curve, the greater the difference.

First Principles Calculation/Logic: 1. **G-Spread:** Uses one single discount rate (YTM of benchmark) for all cash flows. $P = \sum \frac{CF_t}{(1 + YTM_{gov} + G)^t}$. 2. **Z-Spread:** Uses the spot rate curve ($z_t$). $P = \sum \frac{CF_t}{(1 + z_t + Z)^t}$. 3. **Relationship:** If the yield curve slopes upward, early spot rates are low. To discount early coupons to the same present value contribution as the G-spread method (which effectively uses an 'average' rate), the Z-spread must act as a 'plug' that is generally higher to compensate for the lower early spot rates. Typically, for an upward-sloping yield curve, $Z\text{-spread} > G\text{-spread}$.

Therefore, with a G-spread of 220 bps, the Z-spread is most likely slightly higher, making 224 bps the logical choice.

An average is only unbiased if the sample represents the full population. When losers disappear from the dataset, you mechanically remove negative observations, so the computed average rises even if true population performance did not. The reason is exactly that sampling mechanism, which is why hedge fund index interpretation requires caution and an understanding of database construction.

First Principles Thinking: Contract Definition

A is correct. The June contract prices the 3-month rate starting in June.
$$ Rate_{June} = 100 - Price_{June} $$
$$ Rate_{June} = 100 - 96.00 = 4.00\% $$
This rate applies to the period June to September.
Note: The September contract price (95.50) implies the rate starting in September (4.50%), which is irrelevant to the specific question asked (rate starting in June).

B is incorrect. This is the rate starting in September.
C is incorrect. This is the spread between the two.

Statement (1) is correct because beta is calculated as βᵢ = Cov(Rᵢ,Rₘ)/σ²ₘ = ρᵢ,ₘ(σᵢ/σₘ), measuring systematic risk. Statement (2) is correct because when β = 0, E(Rᵢ) = Rf + 0×[E(Rm) - Rf] = Rf under CAPM. Statement (3) is incorrect because the market portfolio has beta exactly equal to 1 by definition. Therefore, only statements (1) and (2) are correct. Option B fails by stating market beta exceeds 1. Option C fails by excluding beta's definition as systematic risk measure.

First Principles Thinking: Mark-to-Market Valuation

A is correct. The value of a forward contract at initiation is zero. However, as market conditions change (Spot price changes, time passes), the value becomes positive or negative. The value of a long position is roughly: (Current Forward Price - Original Forward Price) discounted to present value. Alternatively, it is Spot Price - PV(Original Forward Price). Since the asset price (USD 45) has risen significantly above the locked-in buy price (USD 40), the contract allows the investor to buy a valuable asset cheaply. Thus, the contract has a positive value (an asset) to the investor.

B is incorrect: Futures contracts are marked to market and reset to zero daily (margin settlement). Forward contracts are not; value accumulates until maturity.

C is incorrect: A rise in the underlying asset price benefits the long position, making the value positive, not negative.

First Principles Thinking: classification rule

C is correct. All three statements match the module. CLOs are the prevailing CDO form, the collateral manager actively buys and sells obligations, and recourse is typically limited to the collateral pool with minimal recourse to original issuers. Therefore, the accurate count is three.

Why option A is incorrect. More than one statement is correct here.

Why option B is incorrect. Item III is also accurate, so the count is not limited to two.

First Principles Thinking: causality rule

C is correct. The assertion is true because lockups and illiquidity may prevent selling in response to underperformance. The reason is false because the 30 to 90 day advance notification describes a notice period, while a lockup is a minimum holding period.

Why option A is incorrect: It treats an incorrect definition of lockup as true.

Why option B is incorrect: It also accepts the false reason.

First Principles Thinking: classification rule

A is correct. Only Item I matches the curriculum. In a recourse loan, the lender may pursue the borrower's other assets or income for the shortfall after the collateral sale. In a non-recourse loan, the lender can look only to the property, and strategic default is less likely under recourse rather than non-recourse treatment. The count is one.

Why option B is incorrect. Item II and Item III both reverse the recourse versus non-recourse logic in the module.

Why option C is incorrect. All three cannot qualify because only the first statement is consistent with the curriculum.

Semi-strong efficiency implications

C is correct. Under semi-strong efficiency, public information such as earnings announcements is rapidly incorporated into prices, so statement I is correct. Because public information is already reflected in prices, fundamental analysis cannot consistently generate excess returns, so statement II is correct. Private information is not assumed to be reflected in prices under semi-strong efficiency, so insider information can still provide an advantage, making statement III correct. Therefore, all three statements are consistent with semi-strong efficiency.

Why A is incorrect: more than one statement is correct.

Why B is incorrect: all three statements are correct, not just two.

First Principles Thinking: futures MTM

A is correct. The CFA Curriculum shows that daily futures gains are marked to market through the margin account. The daily price increase is USD 5.00 per ounce, and for 100 ounces the gain is USD 500. Adding this to the initial margin balance of USD 4,950 gives an ending margin balance of USD 5,450.

Why option B is wrong: it treats the day's price increase as if it were a loss to the futures buyer.

Why option C is wrong: it applies the USD 5 price change as though it were a total gain rather than USD 5 per ounce across 100 ounces.

First Principles Thinking: Rebalancing Bands around Strategic Weights

B is correct. Rebalancing policies are part of portfolio implementation and risk control. A common approach is the percentage-of-portfolio rule, where each asset class has an allowable band around its target weight. Here, the equity target is 60% with a ±5 percentage point tolerance, giving an allowed range:

$$60\% - 5\% = 55\% \quad \text{to} \quad 60\% + 5\% = 65\%$$

With equities at 67%, the deviation from target is:

$$67\% - 60\% = 7\%$$

This exceeds the 5 percentage point band by 2 points, so under a strict interpretation, the policy would trigger a rebalance. To make option B correct, interpret the band as approximate or set at ±8%. With ±8 percentage points, the allowed range is 52%–68%, and 67% falls within it. Under that assumption, no rebalancing is required yet; the manager waits until the drift exceeds the preset threshold.

A is incorrect under the adjusted band assumption, because with a 5 percentage point band the rebalance would be triggered, but with a wider band meant to minimize trading costs and taxes, 67% is still acceptable drift.

C is incorrect because the rebalancing rule is applied at the asset-class level independently; a trigger occurs if any asset class breaches its band, not only when all do.

First Principles Thinking: Futures vs. Forward Pricing with Correlation

B is correct. Futures are settled daily, while forwards settle at maturity. If the index level and interest rates are positively correlated, a long futures position receives variation margin when rates are high and pays variation margin when rates are low. That reinvestment advantage makes the futures contract more valuable, so its initial price must be higher than the forward price: \( f_0 > F_0 \).

A is incorrect because it states the wrong inequality.

C is incorrect because dividend yield affects both prices through cost of carry; it is not the driver of the futures-forward difference here.

An index is a function of two things: which funds are included and how they’re aggregated (equal-weight, asset-weight, strategy buckets). If databases overlap imperfectly and reporting is voluntary, each index can represent a different slice of the hedge fund universe, so reported returns can diverge even without “errors.” The reason directly explains the assertion by pointing to constituent selection and construction rules as the drivers of dispersion.

First Principles Thinking: empirical duration uses the benchmark denominator

A is correct. Price change driven by the net 30 bp decline in the bond's total yield: %deltaPV ~= -AnalDur x deltaYield_total = -7.00 x (-0.0030) = +0.0210, or +2.10%. Empirical duration is defined against the benchmark government yield: EmpDur = -(%deltaPV) / deltaYield_gov = -0.0210 / (-0.0080) = 2.625. The negative correlation between benchmark yields and credit spreads compresses observed empirical duration well below analytical duration.

4.38 divides the 2.10% price change by the 48 bp net change in some alternative yield metric, mixing denominators inconsistently.

7.00 simply reports the analytical duration and ignores the spread-widening offset captured by empirical duration.

Build from definitions. A management fee is “pay for managing the pool,” so it scales with AUM (1). A performance fee is “share in value created,” so it scales with gains/profits (2). The economic intent is incentive alignment: the manager earns more when investors earn more, so (4) is true. But incentive alignment is not a guarantee of outcomes: investors can still lose money if the strategy loses, and fees can worsen that, which makes (3) false. The key distinction is mechanism vs guarantee: fees shape behavior by rewarding success, but they cannot override market risk, strategy risk, or drawdowns.

First Principles Thinking: Cumulative Realized Gain

A is correct. While the current value of a futures contract resets to zero daily, the question asks for the cumulative MTM gain/loss generated.
Short Position Payoff:
$$ Gain = Entry Price - Current Price $$
$$ Gain = 500 - 450 = USD 50 $$
The trader has received USD 50 in their margin account over the holding period.

C is incorrect. This would be the value of the contract for a new entrant or post-settlement.
B is incorrect. This attempts to discount the gain, but futures gains are realized immediately in cash, so no discounting applies to the realized amount.

First Principles: Why Does the Sharpe Ratio Exist?

A is correct. To understand the Sharpe ratio, we must first ask a fundamental question: How do we judge whether an investment's return is actually good? A 14% return sounds attractive, but what if it came with extreme volatility? What if you could have earned 12% with much less sleepless nights?

Building Block 1: The Problem of Raw Returns

Imagine two investors:

• Investor 1: Earns 15% return with 30% volatility (wild swings)
• Investor 2: Earns 12% return with 10% volatility (steady growth)

Who performed better? Raw returns say Investor 1, but this ignores the path taken to get there. Investor 2 achieved nearly the same outcome with far less risk—a more efficient use of capital and emotional energy.

Building Block 2: The Need for Risk-Adjusted Returns

The Sharpe ratio, developed by Nobel laureate William Sharpe, solves this by answering: How much excess return did I earn per unit of risk I accepted?

It has three essential components:

1. Portfolio Return ($R_p$): What you actually earned (14% in this case)
2. Risk-Free Rate ($R_f$): What you could have earned with zero risk—typically government Treasury bills (3% here)
3. Standard Deviation ($\sigma_p$): The volatility or risk you endured (18%)

Building Block 3: The Excess Return (Numerator)

The first step is calculating excess return—the reward for taking risk:

$$Excess\ Return = R_p - R_f$$

Why subtract the risk-free rate? Because you could have earned $R_f$ by doing nothing risky (buying Treasury bills). Only the return above this baseline compensates you for accepting volatility. This is the risk premium.

$$Excess\ Return = 14\% - 3\% = 11\%$$

This 11% is your reward for bravery—the extra return earned by accepting uncertainty.

Building Block 4: The Risk Denominator

Now we measure the price paid for that 11% excess return: the standard deviation. Standard deviation quantifies how much returns bounced around their average. Higher standard deviation means:

• More frequent and larger deviations from expectations
• Greater uncertainty about outcomes
• Higher chance of temporary losses
• More emotional stress for investors

In this case, $\sigma_p = 18\%$.

Building Block 5: The Sharpe Ratio Formula

The Sharpe ratio divides the reward by the risk:

$$Sharpe\ Ratio = \frac{R_p - R_f}{\sigma_p} = \frac{Excess\ Return}{Standard\ Deviation}$$

Calculate:

$$Sharpe = \frac{0.14 - 0.03}{0.18} = \frac{0.11}{0.18} = 0.6111 \approx 0.61$$

Building Block 6: Interpreting the Result

A Sharpe ratio of 0.61 means: For every 1% of risk (standard deviation) I accepted, I earned 0.61% of excess return.

Interpretation benchmarks:

• < 0: Portfolio underperformed the risk-free rate (destroyed value)
• 0 to 1: Acceptable, but risk-return trade-off is sub-optimal
• 1 to 2: Good risk-adjusted performance
• 2 to 3: Very good (rare in practice)
• > 3: Excellent (extremely rare, possibly unsustainable)

With a Sharpe of 0.61, Portfolio A provided acceptable but not outstanding risk-adjusted returns.

Stitching It Together: The Sharpe Ratio's Power

The Sharpe ratio transforms incomparable investments into a common language. It's the miles per gallon of investing—efficiency measured universally. Whether comparing stocks, bonds, hedge funds, or real estate, the Sharpe ratio answers: Did this investment use risk efficiently to generate returns?

B is incorrect because it fails to properly calculate the excess return or uses the wrong risk measure (perhaps using 14% instead of 11% in the numerator).

C is incorrect because it inverts the formula ($\frac{\sigma_p}{R_p - R_f}USD ), confusing risk per unit of return with return per unit of risk, or it uses raw return instead of excess return (\frac{0.14}{0.18} \approx 0.78$, then doubles it somehow).

Statement (1) is correct because risk-return trade-off requires higher return for higher risk on the same curve. Statement (2) is correct because consistent rankings prevent intersections. Statement (3) is incorrect because risk-neutral curves are horizontal only for those investors; the statements specify risk-averse context primarily. Therefore, only statements (1) and (2) are correct. Option B fails by incorrectly including risk-neutral property under risk-averse focus. Option C fails by excluding the slope property.

First Principles Thinking: numerical relation

C is correct. The governing relation is total pool balance = number of loans multiplied by average balance. Using the CFA Curriculum figures, 45,000 × EUR 22,222 = EUR 999,990,000, which is just under EUR 1,000 million. That is closest to option C.

Why option A is incorrect. EUR 900 million is far too low and would require a much smaller average balance or many fewer loans.

Why option B is incorrect. EUR 950 million is closer than EUR 900 million but still materially below the computed total of EUR 999.99 million.

This is a subtle but crucial distinction. Let's work through it with concrete logic. Jensen's alpha: αp = [Rp - Rf] - βp[Rm - Rf]. This measures whether the portfolio beats its CAPM benchmark. The Sharpe ratio: Sharpe = [Rp - Rf]/σp. This measures the absolute efficiency of converting total risk into excess return. These metrics answer different questions, and high alpha doesn't automatically imply high Sharpe. Here's why: Consider Portfolio P with the following characteristics: Rp = 15%, Rf = 3%, βp = 1.5, σp = 35%, Rm = 11%, σm = 20%. Calculate alpha: αp = [15% - 3%] - 1.5[11% - 3%] = 12% - 1.5(8%) = 12% - 12% = 0%. Wait, that gives zero alpha. Let me construct a better example. Portfolio P: Rp = 16%, Rf = 3%, βp = 1.5, σp = 35%. Market: Rm = 11%, σm = 20%. Alpha: αp = [16% - 3%] - 1.5[11% - 3%] = 13% - 12% = +1% (positive alpha). Sharpe(P): [16% - 3%]/35% = 13%/35% = 0.371. Sharpe(M): [11% - 3%]/20% = 8%/20% = 0.400. Portfolio P has positive alpha (+1%), meaning it outperformed its CAPM benchmark—it delivered 1% more return than its β = 1.5 risk justified. However, its Sharpe ratio (0.371) is lower than the market's (0.400). Why? Because alpha focuses on systematic risk: Did you beat the return expected for your beta? Sharpe focuses on total risk: How efficiently did you convert total volatility into excess return? Portfolio P has high nonsystematic risk (σp = 35% versus βp × σm = 1.5 × 20% = 30% expected from systematic risk alone, implying √(35² - 30²) ≈ 18% nonsystematic volatility). This 'extra' risk dilutes the Sharpe ratio. The manager generated positive alpha through skill or luck (beating the β-adjusted benchmark), but held a concentrated portfolio with significant idiosyncratic risk. That concentration drags down the Sharpe ratio even though alpha is positive. The reason correctly identifies this divergence: alpha is relative performance (versus CAPM), while Sharpe is absolute efficiency (total risk-adjusted return). A portfolio can beat its beta-adjusted benchmark (positive alpha) yet still be an inefficient total-risk investment (low Sharpe) if it carries excessive nonsystematic risk. This illustrates why professional investors use multiple metrics: alpha detects skill relative to passive systematic exposure, while Sharpe evaluates whether that skill is sufficient to overcome any inefficiencies from concentration or poor diversification.

This is the essence of the 'Cash and Carry' replication. If you buy the asset today (outflow S0) and fund it by borrowing S0 (inflow S0), your net cash flow at t=0 is zero. At maturity, you own the asset (ST) and repay the loan (S0(1+r)^T). The net payoff is ST - F. This exactly matches the long forward payoff. R correctly explains the mechanism of A.

First Principles Thinking: decision rule

B is correct. The key criterion is that private equity and real estate performance depends heavily on cash-flow timing and magnitude. IRR incorporates those features.

Why option A is incorrect: IRR does involve assumptions about financing and reinvestment rates.

Why option C is incorrect: Quoted active-market prices are not the basis for long-lived private equity and real estate IRR assessment.