Practice Evening Session

First Principles Thinking: Volatility Dampening

A is correct. Mark-to-model valuation (Level 3) relies on periodic appraisals or theoretical inputs rather than continuous market auction prices. This process inherently smooths data.
Mechanism: True market prices jump instantly to reflect news. Models often anchor to past values or adjust slowly (autocorrelation).
Result: This smoothing reduces the standard deviation (denominator of Sharpe) without necessarily reducing the mean return (numerator).
Conclusion: A smaller denominator artificially inflates the Sharpe ratio. This is a key risk in analyzing reported alternative investment metrics.

B is incorrect: While fees might lower returns, the valuation method itself tends to smooth the path of returns rather than systematically lowering the aggregate mean return.

C is incorrect: Level 3 compliance is an accounting standard for disclosure, not a guarantee of statistical equivalence to market pricing. The smoothing bias persists regardless of compliance.

First Principles Thinking: classification rule

A is correct. The CFA curriculum defines commercial paper as short-term unsecured notes used for working capital, seasonal cash needs, or bridge financing, so Item I is correct. Item II is incorrect because commercial paper is unsecured. Item III is incorrect because the CFA curriculum says corporate commercial paper typically matures in less than three months. Therefore, only one item satisfies the criterion.

Why option B is incorrect. Only Item I is supported; the other two contradict the unsecured and very short-term nature of commercial paper.

Why option C is incorrect. All three are not correct because the CFA curriculum does not describe commercial paper as secured or longer than one year.

Let's build the bridge between the two frameworks. The CML plots E(R) vs. σ and includes only efficient portfolios—combinations of Rf and the market portfolio M. Point M (the market itself) lies on the CML with coordinates [σm, E(Rm)]. The SML plots E(R) vs. β and applies to all assets. Since beta measures an asset's covariance with the market scaled by market variance—βi = Cov(Ri, Rm)/σ²(m)—the market's beta with itself is Cov(Rm, Rm)/σ²(m) = σ²(m)/σ²(m) = 1. Plugging βm = 1 into the SML equation E(R) = Rf + β[E(Rm) - Rf] gives E(Rm) = Rf + 1 × [E(Rm) - Rf] = E(Rm), confirming the market portfolio sits on the SML at coordinates [1, E(Rm)]. Now, why is M the only risky asset on both lines? The CML restricts its domain to efficient portfolios (the market portfolio and its leveraged/deleveraged versions). Individual securities and inefficient portfolios lie below the CML because they contain uncompensated nonsystematic risk. However, all assets—efficient or not—lie on the SML in equilibrium, as the SML prices assets based solely on their beta (systematic risk). The market portfolio is special: it's the tangency portfolio (CML) and it has β = 1 (SML). Other efficient portfolios (like 50% Rf + 50% M) lie on the CML but have β ≠ 1 (β = 0.5 in this case), placing them elsewhere on the SML. Individual stocks lie on the SML (at their respective betas) but below the CML (due to nonsystematic risk). Only M satisfies both CML membership (efficiency) and the SML coordinate [β = 1, E(Rm)]. The reason correctly explains this: βm = 1 by construction, and M is the unique tangency portfolio that defines the CML. These two properties together ensure M is the intersection point of the two frameworks.

The SML plots CAPM equilibrium: required return = Rf + β[Rm - Rf]. A point above the SML means the asset's estimated return exceeds the return commensurate with its beta risk, signaling undervaluation (price too low relative to expected cash flows). The reason correctly identifies the mechanism: positive alpha ≡ E(Ri) > [Rf + βi(Rm - Rf)] ≡ above SML. This excess expected return relative to systematic risk directly explains why the security merits purchase—it offers superior risk-adjusted return, exploiting mispricing.

C is correct. The CFA curriculum states that investors usually require a committed backup line of credit, or liquidity enhancement, to address rollover risk. A credit rating does not itself ensure repayment if rollover is not possible.

First Principles Thinking: Linear Weighted Average

B is correct. The expected return of a portfolio is the weighted average of the expected returns of the individual component assets. Unlike risk, returns are additive.

$$E(R_p) = \sum w_i R_i$$

Calculation:

• Asset 1 contribution: USD 0.20 \times 5\% = 1.0\%$
• Asset 2 contribution: USD 0.30 \times 10\% = 3.0\%$
• Asset 3 contribution: USD 0.50 \times 15\% = 7.5\%$

Total = USD 1.0\% + 3.0\% + 7.5\% = 11.5\%$

A is incorrect because it represents a simple average of the returns ($(5+10+15)/3 = 10$), ignoring the fact that half the portfolio is in the highest-return asset.

C is incorrect because it overweights the high-return asset beyond 50% or makes an arithmetic error.

First Principles Thinking: Multiple Dimensions of Default Risk

B is correct. Ability to avoid default depends on having enough cash (or convertible assets) when obligations fall due. Three quantitative dimensions matter: leverage (stock of debt), coverage (income vs. interest), and liquidity (near-term cash and committed facilities). Lower leverage reduces required deleveraging in stress, but if coverage is weak and liquidity thin, the firm can still be unable to make upcoming payments. Conversely, moderately higher leverage combined with robust interest coverage and ample liquidity can provide stronger short- and medium-term protection against default. Credit analysis is holistic; the question asks which is safer overall, not on a single metric. On that basis, Firm B’s stronger capacity to meet debt service and near-term obligations often outweighs a modest leverage disadvantage.

A is incorrect: leverage is important but not absolute. A lightly levered company with poor liquidity and thin coverage may be forced into default during a cash-flow shock even though its balance sheet appears strong.

C is incorrect: default is a flow and timing problem, not just a stock problem. Focusing solely on leverage ignores income generation and cash-access constraints that can precipitate failure even at moderate debt levels.

Statement (1) is incorrect because the text states 'An increase in the range of future price changes increases the value of the call option' and generally 'an increase in volatility... increases option value.' Volatility generally increases the value of both calls and puts (due to asymmetric upside). Statement (2) is correct as 'A higher expected price change indicates higher volatility' and this increases value. Statement (3) is correct as the text explicitly states 'the size of the up and down price movements should match the underlying asset volatility'.

The cost advantage arises from the production function of passive management: the strategy is replication rather than continuous price discovery and selection. With fewer research-intensive activities and generally more predictable turnover rules, resources devoted to analyst coverage and active trading are typically lower. That directly explains why passive fees and operating costs tend to be lower.

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.

First Principles Thinking: Horizon of Cash Flows

C is correct. Start from the idea that credit risk is about whether promised cash flows can be met when due. For a given issuer, different maturities rely on cash flows from different future periods. Short-dated instruments depend mainly on current business conditions and existing product lines, while long-dated bonds depend on more distant, uncertain cash flows. When a firm undertakes a strategic shift whose payoffs and risks materialize over a decade or more, the cash flows relevant for servicing very long-maturity debt are most exposed to execution, competitive, and technology risk. Even if probability of default is measured at the issuer level, the mechanism driving that default is most likely tied to failure of long-horizon strategies. Hence the 15-year notes, whose principal and late coupons are funded by the post-transition business model, bear the greatest sensitivity to execution risk.

A is incorrect: while cross-default provisions can equalize default events across issues, they do not equalize exposure to the underlying business risk over different horizons. Commercial paper mainly depends on near-term liquidity from existing operations.

B is incorrect: 5-year notes sit between short and long horizon. They are exposed to some transition risk but still rely significantly on current business lines, so they are less sensitive than 15-year notes to a strategy playing out over 10–15 years.

First Principles Thinking: Fees Apply to Specific Bases

C is correct. A hedge fund’s net return equals the change in NAV after subtracting (1) the management fee and (2) any incentive fee that is earned only after meeting the high-water mark and hurdle requirement.

Governing relationships. Let $P_1$ be beginning NAV and $P_2$ be end-of-year NAV before fees. Management fee: $$\text{MF}=m\,P_2$$. Incentive fee base (given it is net of management fee and above the hurdle applied to the HWM): $\text{Base}=\left(P_2-\text{MF}\right)-\left(P_{\text{HWM}}(1+h)\right)$. Incentive fee: $\text{IF}=p\,\max(0,\text{Base})$. Net NAV: $P_{2,\text{net}}=P_2-\text{MF}-\text{IF}$. Net return: $r_{\text{net}}=\frac{P_{2,\text{net}}}{P_1}-1$.

Numeric application. $$\text{MF}=0.02\times 560=11.2$$. NAV net of management fee $=560-11.2=548.8$. Hurdle-adjusted HWM $$=520\times 1.05=546.0$$. Excess $=548.8-546.0=2.8$. $$\text{IF}=0.20\times 2.8=0.56$$. Net NAV $=560-11.2-0.56=548.24$. Net return $=548.24/500-1=0.09648\approx 9.65\%$.

A is incorrect because it ignores the hurdle rate and charges the incentive fee simply on gains above the HWM (net of management fee), overstating the incentive fee and understating the investor’s net return.

B is incorrect because it calculates the incentive fee on gains above the hurdle-adjusted HWM using the gross end-of-year NAV (before subtracting the management fee from the incentive base), violating the stated “net of management fee” convention.

First Principles Thinking: Underwriting Commitment

C is correct. In an **underwritten offering** (or firm commitment offering), the investment bank acts as a **principal**, guarantees the sale of the issue at a negotiated price, and buys any undersubscribed securities. In a **best effort offering**, the investment bank acts only as a **broker** (an agent) and promises to use its best efforts to sell the issue but does *not* guarantee a specific amount will be sold.

A is incorrect: This statement is the opposite of the fact. The guarantee exists in an underwritten offering, not a best effort offering .

B is incorrect: In an underwritten offering, the bank acts as a principal, not an agent who guarantees the sale. The best effort offering correctly describes the bank as a broker (agent).

Statement (1) is correct because the G-spread is defined as the spread over an actual or interpolated government bond yield. Statement (2) is correct because the I-spread compares the bond to the swap rate, while the G-spread compares it to the government yield; if I-spread > G-spread, the benchmark swap rate must be lower than the benchmark government yield (since Total Yield is constant). Statement (3) is incorrect because while the Z-spread (zero-volatility spread) assumes zero volatility, it does not assume a flat yield curve; it measures the spread over the entire spot rate curve. Therefore, only statements (1) and (2) are correct.

First Principles Thinking: Sources of Yield

D is correct. All statements are true. Statement 1 is the standard decomposition formula. Statement 2 is true because timber volume grows over time (capital appreciation), whereas farmland volume is constant (crops are income, not capital growth). Statement 3 and 4 are true because the 'Roll' is the convergence of the future price to the spot price; if the curve slopes down (Backwardation), the future price rises to meet spot, creating a profit.

No distractors are correct here as all statements are valid based on fundamental definitions.

First Principles Thinking: Unpacking the Forward Formula

B is correct. The relationship between Spot and Forward for a non-income paying asset is determined solely by the risk-free rate.
Formula: $$ F_0(T) = S_0 (1+r)^T $USD
105 = 100 (1+r)^1USD .
1.05 = 1+rUSD .
r = 0.05 = 5\%$.

A is incorrect. It assumes continuous compounding ($ln(1.05) = 4.88\%USD ).
C is incorrect. It calculates discount yield (5/105$).

First Principles Thinking: Multi-Period Discounting

A is correct. The value is the sum of the present values of all expected cash flows. Cash flows are $CF_1 = 1.50USD and CF_2 = 1.80 + 35.00 = 36.80$ (dividend + sale price). Discount at 10%. $PV_1 = 1.50 / 1.10 = 1.3636$. $PV_2 = 36.80 / 1.10^2 = 36.80 / 1.21 = 30.4132USD . Total Value V_0 = 1.36 + 30.41 = 31.776...USD , rounded to 31.78$.

B is incorrect because it might fail to discount the terminal value correctly or use a single period discount factor for the second year.

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

First Principles Thinking: Internal Rate of Return

A is correct. The YTM is mathematically an Internal Rate of Return (IRR). A fundamental property of the IRR calculation is the implicit assumption that intermediate cash flows (coupons) are reinvested at the IRR (the YTM) itself until maturity. If reinvested at a different rate, the actual realized return will differ from the YTM.

B is incorrect: Reinvesting at spot rates is a more realistic assumption for total return analysis, but strictly speaking, YTM assumes a single constant reinvestment rate.

C is incorrect: The risk-free rate is usually lower than the YTM of a corporate bond.

First Principles Thinking: capital allocation line and two-fund separation

B is correct. Statement I is correct: the CFA Curriculum derives the CAL equation and states its slope is $\frac{E(R_i) - R_f}{\sigma_i}$, which represents the additional required return for every increment in risk, sometimes called the market price of risk. Statement II is correct: the CFA Curriculum states the two-fund separation theorem holds that all investors regardless of taste, risk preferences, and initial wealth will hold a combination of the risk-free asset and the optimal portfolio of risky assets. Statement III is incorrect: the CFA Curriculum shows (via the example of Kelly with A=2 and Jane with A=4) that a more risk-averse investor's optimal portfolio lies to the left (lower risk, lower return) on the CAL, not to the right. Therefore, two statements (I and II) are correct.

Option A is incorrect because both the CAL slope definition and the two-fund separation theorem are explicitly stated in the CFA Curriculum.

Option C is incorrect because Statement III reverses the relationship — higher risk aversion leads to an optimal portfolio with less risk (further left on the CAL), not more risk.

Start from purpose. Traditional long-only funds are usually constrained (eligible assets, leverage limits, benchmark-relative framing). Hedge funds are structured to pursue a return objective using a wider toolkit, so flexibility (1) and tools like shorting, derivatives, and leverage (2) are common. Now tie objective to behavior: “absolute return” means the manager is trying to make money in many environments, not just beat an index in up markets, so (4) fits. Statement (3) contradicts first principles: if your goal is to track an index, you reduce active bets and complexity; hedge funds exist largely to do the opposite—take targeted risks (often hedged) and monetize them, not replicate an index.

First Principles Thinking: Information Leakage and Market Impact

C is correct. Large orders, when displayed, signal aggressive trading intent, prompting other traders to trade ahead or change quotes unfavorably (strategic behavior). Hidden and Iceberg orders conceal the full size, minimizing information leakage and, consequently, reducing the negative price impact that is common with large orders.

A is incorrect because a large market order would execute immediately, likely causing maximum negative price impact (slippage).

B is incorrect because Good-till-cancelled (GTC) relates only to the order's validity period, not its visibility or size management.

Let's check the math. FV = 100, Rate = 10%, 1 year. Discount Price = 100 * (1 - 0.10) = 90. Add-on Price: 100 / (1 + 0.10) = 90.90. The Add-on price is HIGHER. Assertion A says Discount Price is Higher. So A is False. Reason R is True: Discount subtracts from FV (linear reduction). Add-on divides FV (hyperbolic reduction). Dividing by 1.10 removes 'less' than subtracting 10% of the total. Wait, subtracting 10% of 100 is 10. Dividing 100/1.1 is 90.90 (discount of 9.1). So the discount price (90) is LOWER than the add-on price (90.90). Thus A is False.

First Principles Thinking: Biological Assets

B is correct. Timberland is a unique asset class defined by biological optionality. First, the 'factory' concept means the asset manufactures its own inventory via photosynthesis—trees grow volume regardless of the economy. Second, the 'warehouse' concept means you are not forced to sell; if lumber prices crash, you store the value 'on the stump' where it continues to grow. Finally, the geographic concentration of investable private timberland is historically centered in the US (approx. 50%).

Statement 3 is incorrect (making A, C, and D wrong): Timberland returns are driven by biological growth and local land values, not corporate earnings. Therefore, they historically show very low or zero correlation with public equities, which is their primary value for diversification.

First Principles Thinking: classification rule

A is correct. The CFA curriculum states that investment-grade bonds derive a larger share of YTM from the government benchmark and typically carry few or no restrictive covenants, so Item I is correct. Item II is incorrect because high-yield issuers face shorter maturities and more investor constraints. Item III is incorrect because the CFA curriculum describes high-yield debt as more equity-like, not more bond-like. Hence, only one item matches the rule.

Why option B is incorrect. Two items do not qualify because the CFA curriculum assigns tighter restrictions and more equity-like cash flows to high-yield debt.

Why option C is incorrect. All three are not consistent with the contrast; only Item I reflects the stated investment-grade characteristics.

It is crucial to distinguish between the 'price' of the contract (the quote, for example, 100) and the 'value' (PV of gain/loss). At initiation, no money changes hands (except margin, which is collateral, not payment). The market 'price' is the specific number that sets the current net present value (NPV) of entering the contract to zero for both parties.

First Principles Thinking: Information Asymmetry and Pricing

B is correct. The tendency for initial prices to be lower (and subsequently rise) is due to the **underwriter's conflict of interest** and the first-time issuer's fear of an undersubscribed IPO conveying unfavorable information. This dynamic is **less important in a seasoned offering** because **trading in the secondary market helps identify the proper price** for the offering, reducing the information asymmetry and pricing uncertainty .

A is incorrect: While seasoned offerings may have lower costs, the primary reason for the price difference is the level of information asymmetry and the existing secondary market price discovery .

C is incorrect: Undersubscribed IPOs convey unfavorable information, which issuers try to avoid by setting a low price, but IPOs are *not* always undersubscribed. Oversubscription or undersubscription can happen in both IPOs and seasoned offerings.

First Principles Thinking: Sample Selection Bias

A is correct. Identify the data constraint. Repeat sales methodology requires observing the same property sold at two points in time to measure price appreciation. However, most properties transact infrequently—many only once in decades. The properties that do sell repeatedly are a non-random sample: they might be in more volatile neighborhoods, smaller/more liquid properties, or distressed sales. High-quality commercial properties held by institutions may never appear in repeat sales data. Furthermore, transaction volume is low, so index updates are infrequent and based on sparse data. This creates selection bias: the index may not represent the broader market's performance. The document categorizes real estate indexes as 'appraisal indexes, repeat sales indexes, and real estate investment trust (REIT) indexes,' noting that repeat sales is one approach to handling the 'highly illiquid market and asset class with infrequent transactions.'

B is incorrect because repeat sales indexes cannot provide real-time pricing; they require actual transactions, which are infrequent, resulting in lagged and sparse price observations.

C is incorrect because repeat sales indexes specifically avoid appraisals; they use actual transaction prices. The confusion is with appraisal indexes, which do rely on periodic professional valuations.

First Principles Thinking: Cost of Carry (Continuous)

A is correct. Equity indices usually use continuous compounding conventions in CFA Level I (Module 6).
$$ f_0(T) = S_0 e^{(r - q)T} $$
$$ S_0 = 4,000 $$
$$ Net Rate = 0.03 - 0.01 = 0.02 $$
$$ T = 0.5 $$
$$ f_0(T) = 4,000 \times e^{0.02 \times 0.5} $$
$$ f_0(T) = 4,000 \times e^{0.01} $$
$$ f_0(T) \approx 4,000 \times 1.01005 $$
$$ f_0(T) = 4,040.20 $$

B is incorrect. It ignores the dividend yield (\( 4000 e^{0.03 \times 0.5} \)).
C is incorrect. It uses discrete compounding: 4000(1.02)^{0.5} = \( 4039.8 \), which is close but different, or perhaps \( 4000(1+0.02/2) = 4040 \). The exponential term is specific.

First Principles Thinking: Lifecycle of a Security

A is correct. Consider the fundamental nature of the instrument. Equities are perpetual instruments; they remain in an index unless the company merges, goes bankrupt, or fails criteria. Bonds have a defined maturity date. As time passes, bonds mature and leave the index. Furthermore, issuers frequently issue new debt to refinance or fund operations. This constant stream of maturing bonds exiting and new issues entering creates structurally high turnover, independent of market volatility.

B is incorrect because bond prices are generally less volatile than equity prices, and volatility itself does not dictate the structural entry/exit of the instrument as maturity does.

C is incorrect because criteria for broad market indexes are generally stable; the turnover comes from the securities changing (maturing), not the rules changing.

Statement (1) is incorrect because contracts (like derivatives) are generally classified as financial assets regardless of whether the underlying is a financial security or a physical commodity; the contract itself is a financial instrument. Statement (2) is correct as commodities and real assets are tangible and classified as physical assets, distinct from securities, currencies, and contracts which are financial assets. Statement (3) is incorrect because pooled investment vehicles (including ETFs) are classified as equities (ownership interests), not debt, even if they hold debt securities. Therefore, only statement (2) is correct. Option A is incorrect because statement (1) is false. Option C is incorrect because both statements (1) and (3) are false.

First Principles Thinking: Duration and Convexity Combined

A is correct. The total estimated price change is the sum of the duration effect and the convexity adjustment: $$ \%\Delta P \approx \left[ -\text{AnnModDur} \times \Delta \text{Yield} \right] + \left[ \frac{1}{2} \times \text{AnnConvexity} \times (\Delta \text{Yield})^2 \right] $USD Duration effect: $ -4.0 \times 0.02 = -0.08 = -8.0\% $USD Convexity adjustment: $ 0.5 \times 20.0 \times (0.02)^2 = 10 \times 0.0004 = 0.004 = +0.4\% $USD Total change: $ -8.0\% + 0.4\% = -7.6\% $$

B is incorrect as it only accounts for duration.

C is incorrect as it subtracts the convexity adjustment instead of adding it.

First Principles Thinking: Bid-Ask Spread

A is correct. Trace the cash flows. The investor buys at the Ask (USD 20.10) and sells at the Bid (USD 20.00). The loss is USD 0.10. This amount stays with the dealer. Why? The dealer stands ready to trade at any time (offering immediacy). The spread compensates the dealer for 1) Inventory risk (holding the asset), 2) Order processing costs, and 3) Adverse selection risk (trading against informed traders). The 'round-trip' cost to the liquidity taker is exactly the bid-ask spread.

B is incorrect: Market impact refers to the price moving against you (e.g., Ask moves to 20.15) due to trade size. This example assumes fixed quotes.

C is incorrect: Opportunity cost usually refers to unfilled orders or missed trades, not the explicit cost of crossing the spread.

First Principles Thinking: utility function computation

B is correct. $U = E(r) - \frac{1}{2}A\sigma^2 = 0.12 - 0.5 \times 4 \times 0.25^2 = 0.12 - 0.5 \times 4 \times 0.0625 = 0.12 - 0.125 = -0.005 = -0.50\%$. The high risk aversion and high variance result in a negative utility, indicating this investor would prefer the risk-free asset if it offered more than -0.50%.

A is incorrect. This results from omitting the $\frac{1}{2}$ factor: USD 0.12 - 4 \times 0.0625 = 0.12 - 0.25 = -0.13$. The $\frac{1}{2}$ is an integral part of the utility formula and must not be dropped.

C is incorrect. This equals the expected return alone and ignores the risk penalty entirely, which would only be correct for a risk-neutral investor where $A = 0$.

When a bond trades at a premium, the investor loses that premium over the life of the bond. If the bond is called early (at the call price, which is usually lower than the market price), this loss happens faster, dragging down the return. Thus, the yield-to-call is the lowest potential yield (YTW). The reason correctly identifies this accelerated amortization mechanism.

The formula correctly derives from variance of linear combination, with Cov capturing co-movement. The reason fails because low/negative Cov(ρ < 1) allows portfolio variance below weighted average, enabling diversification benefit—the assertion's covariance term enables this subadditivity.

First Principles Thinking: Worst-Case Return Scenario

A is correct. Yield to worst identifies the minimum yield an investor could realize across all possible redemption scenarios—maturity or any call date at its respective call price. For each possibility, calculate the yield: YTM (if held to maturity), yield to first call, yield to second call, etc. The lowest of these is the yield to worst. This conservative measure protects investors by revealing the worst plausible outcome if the issuer exercises the call option in its own interest. It assumes the issuer acts optimally from its perspective, which typically means calling when yields are low (disadvantaging the bondholder).

B is incorrect: Yield to worst does not consider default scenarios; it examines different redemption paths assuming the issuer honors its obligations. Default analysis involves recovery rates and credit spreads, not yield to worst calculations.

C is incorrect: YTM minus call option value conceptually describes the option-adjusted yield, not yield to worst. Yield to worst is a scenario-based minimum yield calculation, not an option-value adjustment.

First Principles Thinking: Mark-to-Market and Margin Balance

B is correct. The question asks for the margin balance per contract and does not specify a contract multiplier, so the price changes are treated as per-contract gains and losses.

Day 1:
Loss = \( 1{,}800 - 1{,}750 = 50 \).
Balance = \( 6{,}000 - 50 = 5{,}950 \).
Since \( 5{,}950 > 4{,}500 \), no margin call occurs.

Day 2:
Gain = \( 1{,}790 - 1{,}750 = 40 \).
Ending balance = \( 5{,}950 + 40 = 5{,}990 \).

A is incorrect because the balance does not fall to maintenance margin.

C is incorrect because the Day 1 loss and Day 2 gain do not exactly offset.

Zero correlation with the market yields β = ρ(σi/σm) = 0, so the asset contributes no systematic risk. CAPM pricing equation E(Ri) = Rf + βi[E(Rm) - Rf] collapses to Rf when β = 0. The reason mechanically shows why: Cov = 0 ⇒ β = 0 ⇒ no market risk premium earned. Only systematic risk earns compensation; uncorrelated assets carry only diversifiable (unpriced) risk, thus earning only the time-value baseline (Rf).

First Principles Thinking: Cost of Carry with Continuous Yields

A is correct. For indices with continuous yields, the cost of carry is the net of the risk-free rate and the dividend yield.
Formula: $$ F_0(T) = S_0 e^{(r - q)T} $USD
S_0 = 4000USD .
r = 0.03USD .
q = 0.015USD .
T = 0.25USD (3 months).
Calculation:
$ F = 4000 \times e^{(0.03 - 0.015) \times 0.25} $USD
$ F = 4000 \times e^{0.015 \times 0.25} $USD
$ F = 4000 \times e^{0.00375} $USD
$ F = 4000 \times 1.003757 $USD
$ F = 4,015.028 $$
Rounded to 4,015.03.

B is incorrect. It likely assumes $T=1$ ($4000 \times e^{0.015} = 4060USD ).
C is incorrect. It likely subtracts the net rate or reverses signs (4000 \times e^{-0.00375}$).

First Principles Thinking: Duration from Price Change

B is correct. Rearranging the duration formula \( \Delta P/P \approx -ModDur \times \Delta y \) to solve for duration: \( ModDur \approx -(\Delta P/P) / \Delta y \). Here \( \Delta P = 96 - 100 = -4 \), so \( \Delta P/P = -4/100 = -0.04 = -4\% \), and \( \Delta y = 0.01 \). Thus \( ModDur \approx -(-0.04) / 0.01 = 0.04 / 0.01 = 4 \). Mental check: 4% price drop for 1% yield rise implies duration of 4. This reverse-engineering of duration from observed price changes is commonly used by traders and risk managers to calibrate models and estimate real-world sensitivities, validating theoretical duration calculations against market behavior.

A is incorrect because duration of 2 would imply only a 2% price change for a 1% yield change: \( 2 \times 1\% = 2\% \), but the observed change is 4%. This answer halves the actual sensitivity, possibly confusing the magnitude of the price change (4 points) with the percentage change (4%) or miscalculating the ratio. Using duration of 2 would underestimate risk by 50%.

C is incorrect because duration of 8 would imply an 8% price change for a 1% yield change, double the observed 4% change. This might result from using the absolute price change (4 points) without converting to a percentage, or doubling the calculation somewhere: \( 8 = 2 \times 4 \). This overstates interest rate sensitivity by a factor of 2, leading to excessive hedging or risk aversion.

First Principles Thinking: classification rule

B is correct. Preferred priority applies to dividends and assets → I qualifies → II fails (voting rights not always equivalent) → III qualifies → count = 2.

A is incorrect because two statements are correct — cumulative dividend catch-up (I) and higher liquidation claim over common shareholders (III).

C is incorrect because statement II is false: preferred shareholders typically have limited or no voting rights, not equivalent to common shareholders.

First Principles Thinking: Certain Payoff

A is correct. In the binomial model, a properly hedged portfolio has the same value in both the up and down states. We can calculate the value in either state.

1. Identify payoffs:
Up state (\( S_1 = 100 \)): call value is \( 100 - 80 = 20 \).
Down state (\( S_1 = 60 \)): call value is \( 0 \).

2. Calculate portfolio value (\( V_1 \)):
The portfolio consists of long 50 shares and short 100 calls.
Up state: \( (50 \times 100) - (100 \times 20) = 3000 \).
Down state: \( (50 \times 60) - (100 \times 0) = 3000 \).

Since the value is USD 3,000 in both states, this is the certain value of the portfolio.

B is incorrect because it miscalculates the hedge math.

C is incorrect because it ignores the short option liability.

First Principles Thinking: Classification Stability

B is correct. Consider the boundary conditions. A broad market index (e.g., Russell 3000) includes almost everything; a stock only leaves if it dies or becomes tiny. A style index has strict boundaries (e.g., P/E < 15). Stock prices and earnings are dynamic. A stock can easily drift from 'Value' to 'Growth' or 'Mid-Cap' to 'Large-Cap' as its price changes. This 'style drift' forces the index provider to sell the stock from one index and buy it for another, resulting in structurally higher turnover than a buy-and-hold broad market index.

A is incorrect because value metrics (price ratios) are highly sensitive to price changes, making them unstable, not stable.

C is incorrect because the broad market does not require rebalancing when a stock changes style, whereas the style index does.

Limits to market efficiency

B is correct. Statement I is correct because short-selling restrictions can prevent investors from trading against overvalued securities. Statement II is correct because transaction costs can make apparent arbitrage opportunities unprofitable. Statement III is false because even if capital were abundant, other frictions and risks would still prevent perfect efficiency in practice. Therefore, two statements are correct.

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

Why C is incorrect: statement III is incorrect.

Statement (1) is correct because individual variances become negligible, leaving average covariance. Statement (2) is correct because portfolio risk depends primarily on average correlation in large portfolios. Statement (3) is incorrect because expected return remains weighted average, unaffected by diversification. Therefore, only statements (1) and (2) are correct. Option B fails by claiming diversification boosts return. Option C fails by excluding the variance-covariance relation.

Price efficiency requires that all information—positive and negative—be incorporated. Investors with positive information can buy, pushing prices up. But investors with negative information face a constraint if they don't already own the asset: they can only refrain from buying, which is passive and doesn't directly move the price downward. Short selling removes this asymmetry by allowing traders to sell shares they don't own, creating active selling pressure that lowers prices. The reason is the mechanism: without short selling, negative information remains latent—it can't be monetized through trade, so prices don't adjust downward until the information becomes public or a holder sells. This creates a systematic upward bias and delays price discovery, especially for overvalued or fraudulent firms. Restrictions on short selling thus reduce market quality, not improve it.

First Principles Thinking: Effective Convexity

B is correct. Using the finite difference formula: $$ \text{EffConv} = \frac{PV_- + PV_+ - 2PV_0}{(\Delta \text{Curve})^2 \times PV_0} $$ $PV_- = 100.85$
$PV_+ = 99.20$
$PV_0 = 100$
$\Delta \text{Curve} = 0.001USD (10 bps) $ \text{Numerator} = 100.85 + 99.20 - 200 = 0.05 $$ $$ \text{Denominator} = (0.001)^2 \times 100 = 0.0001 $$ $$ \text{Result} = 0.05 / 0.0001 = 500 $$

A is incorrect; half the result.

C is incorrect; 1.5 times the result.

First Principles Thinking: classification rule

B is correct. Equity is residual and discretionary → I qualifies (last claim) → II fails (fixed/finite is debt) → III qualifies (dividends discretionary) → count = 2.

A is incorrect because both the last claim on assets (I) and discretionary distributions (III) describe equity investors — count is two.

C is incorrect because statement II (fixed and finite claim on cash flows) describes debt; equity claims are residual and open-ended.

Statement (1) is correct because a high-water mark prevents managers from earning performance fees on the recovery of past losses; fees are paid only on net new profits. Statement (2) is incorrect because fee layering in funds of funds (paying fees to the fund-of-funds manager on top of fees to underlying managers) raises the cost for investors. Statement (3) is correct as the '1 or 30' structure is designed to reward alpha generation, paying the greater of the base fee or the alpha-based incentive. Therefore, only statements (1) and (3) are correct. Options A and C fail because they incorrectly claim fee layering lowers costs.

Begin with a simple balance-sheet view: a fund holds assets; investors hold claims on the fund; redemptions are cash outflows. If many investors redeem quickly, the fund may be forced to sell assets at bad prices (fire sales), harming remaining investors and potentially destabilizing the strategy. Lockups (1) and gates (2) are contractual tools that slow outflows, giving the manager time to unwind positions more orderly and protect the strategy’s economics—this is exactly the forced-sale logic in (3). Statement (4) reverses the meaning: these terms reduce liquidity (investor flexibility) in exchange for better asset-liability matching and protection against runs.

First Principles Thinking: Fee Layering Reduces the End Investor’s Return

A is correct. The investor earns the underlying net performance of the two hedge funds and then pays an additional management and incentive fee at the fund-of-funds level.

Governing relationships. Start capital $P_1$ equals total invested (here, 200). End capital before FoF fees $P_2$ equals the sum of end values (here, 240). FoF management fee: $\text{MF}=mP_2$. Because the incentive fee is calculated independently of the management fee, FoF incentive fee: $\text{IF}=p(P_2-P_1)$. Net return: $r_{\text{net}}=\frac{P_2-\text{MF}-\text{IF}}{P_1}-1$.

Numeric application. $$P_1=120+80=200$$ and $P_2=150+90=240$. $$\text{MF}=0.01\times 240=2.4$$. $$\text{IF}=0.10\times (240-200)=4.0$$. Net return $=\frac{240-2.4-4.0}{200}-1=\frac{233.6}{200}-1=0.168=16.80\%$.

B is incorrect because it calculates the incentive fee after deducting the FoF management fee (i.e., on $$P_2-P_1-\text{MF}$$), but the problem states the incentive fee is calculated independently.

C is incorrect because it ignores FoF-level fees entirely, reporting only the gross FoF performance $$240/200-1=20\%$$.

First Principles Thinking: Option Payoffs

D is correct. Reason (R) is true: The manager has limited liability (floor at zero fees) but unlimited upside participation. This payoff profile—flat on the downside, linear on the upside—is characteristic of a Call option, not a Put option. Therefore, Assertion (A) is false; the structure resembles a Long Call option held by the manager, not a Short Put.

First Principles Thinking: Order of Operations

C is correct. Assertion (A) is true: The standard industry practice (and the method used in CFA curriculum) is to calculate management fees first, deduct them, and then calculate incentive fees on the remaining profit. However, Reason (R) is false regarding the justification. Management fees are operating expenses. While deducting them first does lower the incentive fee base, the primary reason they are deducted is that they are a guaranteed liability regardless of performance, not specifically to safeguard the investor's net attribution. Furthermore, incentive fees are often charged on gross profits in some jurisdictions or specific LPAs; the 'net' argument is a consequence, not the universal governing rule.

Statement (1) is correct because σp² = w1²σ1² + w2²σ2² + 2 w1 w2 Cov(R1,R2). Statement (2) is correct because when ρ=1, σp = w1 σ1 + w2 σ2. Statement (3) is incorrect because only true when perfectly correlated; otherwise, risk is less. Therefore, only statements (1) and (2) are correct. Option B fails by including the always-weighted-average misconception. Option C fails by excluding the covariance necessity.

TLDR: Bond prices like lower yields more than they hate higher yields. The curve is shaped like a smile (convex).

Detailed Breakdown:
Assertion (A) is true. This is the definition of positive convexity. Prices rise more when yields fall than they drop when yields rise by the same amount.
Reason (R) is true and explains A. As yields fall (moving left on the x-axis), the slope (duration) increases (steepens). As yields rise (moving right), the slope decreases (flattens). This curvature protects the downside and boosts the upside.

Calculator Illustration (Convexity):
Consider 30-year, 6% coupon, trading at 6% YTM. Price = 100.
[2nd] [CLR TVM]
30 [N], 6 [I/Y], 6 [PMT], 100 [FV] -> PV = -100.
Scenario 1: Yield rises 2% to 8%.
8 [I/Y] -> [CPT] [PV] = -77.48 (Drop of 22.52)
Scenario 2: Yield falls 2% to 4%.
4 [I/Y] -> [CPT] [PV] = -134.58 (Rise of 34.58)
Rise (34.58) > Drop (22.52). Convexity at work.

Start from the most basic building block: a CAL represents all possible portfolios formed by mixing a risk-free asset (zero risk, return Rf) with any risky portfolio. The equation E(Rp) = Rf + [(E(Rrisky) - Rf)/σrisky] × σp shows that as you vary the weight in the risky asset, you trace out a straight line in risk-return space. Now, the key insight: not all risky portfolios are created equal. Some offer better risk-adjusted returns than others. The efficient frontier identifies portfolios with maximum return for each level of risk. When you draw a line from Rf to touch the efficient frontier, the tangency point identifies the single risky portfolio with the steepest slope—the highest Sharpe ratio [(E(R) - Rf)/σ]. This tangency portfolio is the market portfolio under CAPM assumptions (homogeneous expectations, all investors hold it). The CML is the unique CAL that uses this optimal risky portfolio. The reason correctly explains this by noting that while many CALs exist (one for each possible risky portfolio choice), only the CAL connecting Rf to the market portfolio earns the designation 'CML.' The assertion is therefore a definitional consequence: CML ⊂ CAL, and the reason provides the economic logic—optimality via tangency—that distinguishes the CML from the broader family of CALs.

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: Matrix Pricing and Linear Interpolation

C is correct. Matrix pricing estimates the yield of an illiquid bond by adding a credit spread to an interpolated benchmark yield matching the bond's maturity.

1. **Interpolate the Benchmark Yield:**
The bond has a 3-year maturity. The benchmarks are 2-year and 5-year.
Total interval = $5 - 2 = 3$ years.
Distance from lower bound = $3 - 2 = 1$ year.
Interpolation weight = $1 / 3$.
$$ \text{Benchmark}_{3y} = 2.15\% + \frac{1}{3} \times (3.45\% - 2.15\%) $$
$$ \text{Benchmark}_{3y} = 2.15\% + \frac{1}{3} \times (1.30\%) $$
$$ \text{Benchmark}_{3y} = 2.15\% + 0.433\% = 2.583\% $$

2. **Add the Credit Spread:**
Estimated Yield = Interpolated Benchmark + Spread
Estimated Yield = USD 2.583\% + 1.20\% = 3.783\%$.

A is incorrect because it is the benchmark yield without the spread.

B is incorrect because it incorrectly interpolates or calculates the spread application.

First Principles Thinking: Benefits of Ownership

A is correct. The Cost of Carry model states: Forward Price = (Spot Price - PV of Benefits + PV of Costs) × (1 + r)^T. Dividends are benefits of owning the underlying asset. When you buy a forward, you do not receive these dividends; the spot holder does. Therefore, the forward price must be discounted to reflect this 'missing' value. If you ignore the dividend (set Benefits = 0), the starting base for the forward calculation is just the Spot Price (USD 50) rather than the Spot Price minus PV of Dividends. Consequently, the calculated forward price will be erroneously high.

B is incorrect: Ignoring the dividend overstates the cost of carry (since dividends reduce the net cost of holding), leading to a higher, not lower, price.

C is incorrect: Dividends absolutely affect forward pricing because they represent a discrepancy in cash flows between holding the spot asset and holding a forward derivative.

First Principles Thinking: Correlation-Adjusted Duration

A is correct. Start with yield decomposition: bond yield = benchmark + spread. Analytical duration assumes independent movements (ρ = 0); empirical duration incorporates historical correlation. Here, β(spread vs. benchmark) = −0.75 (75 bps widening per 100 bps benchmark drop). For a 160 bps benchmark decline, predicted spread widening = 160 × (75/100) = 120 bps. Net yield change = −160 + 120 = −40 bps (a modest fall). Empirical duration ≈ AnalyticalDur × (net yield change / benchmark change) = 7.2 × (40/160) = 7.2 × 0.25 = 1.8. The governing mechanism: negative correlation (flight-to-quality) causes spreads to offset benchmark moves, reducing realized price sensitivity. Boundary: if β = 0 (no correlation), empirical = analytical; if β = −1 (perfect offset), empirical ≈ 0. Edge case: in a risk-on scenario, β might be positive (spreads tighten as benchmarks fall), amplifying price gains and raising empirical duration above analytical.

B is incorrect: 5.4 would result from a 75% ratio applied incorrectly (7.2 × 0.75 = 5.4), perhaps assuming the spread widening proportionally scales duration without accounting for the net yield change. This violates the first principle that duration measures price sensitivity to yield (the sum of benchmark and spread changes), not to each component in isolation—the 75% correlation reduces the effective yield move to 25% of the benchmark shift, not 75%.

C is incorrect: 7.2 (unchanged analytical duration) ignores the empirical correlation entirely, assuming benchmark and spread move independently. This is the classic analytical-duration pitfall for credit-risky bonds: it overstates price appreciation in a flight-to-quality event because it fails to subtract the offsetting spread-widening effect. The first-principles error is treating the bond as if it were a government bond (spread ≈ 0), contradicting the observed BBB rating and historical β.

This is selection bias in time. If only funds with good early results choose to start reporting, and the database includes their earlier “good” months retroactively, the dataset becomes skewed toward successes. The reason is the causal mechanism: it explains why the sample of “observed histories” is not random, which mechanically pushes average returns upward compared with what investors could have earned in real time.

First Principles Thinking: Pricing Outcomes

B is correct. The issuer and the investment bank jointly set the offering price. If they set a price that buyers consider **too high**, the offering will be **undersubscribed**, meaning they will fail to sell the entire issue at that price. Conversely, if the price is set too low, the offering will be oversubscribed .

A is incorrect: Setting the price **too low** will result in the offering being **oversubscribed**, not undersubscribed .

C is incorrect: The underwriter's market-making commitment (providing liquidity/price support after the IPO) is a related service, but the initial undersubscription is a consequence of the price being too high relative to market demand.

Statement (1) is correct; shelf registrations allow issuers to sell seasoned securities piecemeal, providing flexibility. Statement (2) is incorrect; rights offerings are priced below the current market price to incentivize exercise and compensate for dilution. Statement (3) is correct; investors in private placements demand a liquidity premium (higher return/lower price) because the securities cannot be easily traded in secondary markets. Therefore, statements (1) and (3) are correct. Option A fails because statement (2) is false. Option C fails because statement (2) is false.

First Principles Thinking: Break-Even Rates

A is correct. To be indifferent between investing for 1 year at 3% or locking in 5% for two years, the rate in the second year must compensate for the low starting rate. Since the average return over 2 years (5%) is higher than the first year (3%), the second year must be significantly higher than the average to pull it up. Specifically, roughly $2 \times 5 - 3 = 7\%$. Thus, it must be higher than 5%.

B is incorrect: If the future rate were 5%, the average of 3% and 5% would be 4%, not the 5% required.

C is incorrect: Lower rates would pull the 2-year average down below 3%, not up to 5%.

Statement (1) is correct; open-end funds issue and redeem shares directly with investors at NAV. Statement (2) is correct; closed-end funds issue a fixed number of shares that trade on secondary markets, often at discounts or premiums to NAV. Statement (3) is incorrect because ETFs are technically open-ended funds (or unit investment trusts) that have a creation/redemption mechanism with authorized participants, which keeps their price close to NAV, unlike traditional closed-end funds. Therefore, statements (1) and (2) are correct. Option B and C fail because statement (3) is false.

First Principles Thinking: classification rule

A is correct. The CFA Curriculum classifies forwards, futures, and swaps as firm commitments because counterparties are required to exchange in the future, whereas options are contingent claims because one party has a right that determines whether settlement occurs. Item I is a firm commitment because a swap requires a series of exchanges. Item II is a contingent claim because the call buyer has a right after paying a premium. Item III is a firm commitment because a forward seller agrees to a future exchange at a pre-agreed price. Therefore, only one item is a contingent claim.

Why option B is incorrect. Counting two would wrongly place either the swap or the forward into the contingent-claim category, contrary to the CFA Curriculum classification.

Why option C is incorrect. All three cannot qualify because the CFA Curriculum explicitly labels swaps and forwards as firm commitments.

Statement (1) is correct; placing a buy order higher than the current best bid (but not high enough to trade immediately) establishes a new best bid, thus 'making a new market.' Statement (2) is correct; a sell order priced below the best bid is aggressively priced and will execute immediately against the bid, making it a marketable limit order. Statement (3) is incorrect; an order at the best bid 'makes the market' (joins the best price), whereas an order 'behind the market' would be at a lower price than the best bid. Therefore, statements (1) and (2) are correct. Option B and C fail because statement (3) is incorrect.

First Principles Thinking: Net Asset Value per Share

A is correct. From the fundamental accounting equation: Assets = Liabilities + Equity. Rearranged: Equity = Assets - Liabilities. This represents the residual claim of equity holders after satisfying all debt obligations. Net Asset Value = 1,200 - 750 = USD 450 million. Per share: 450/20 = USD 22.50. This assumes fair market values accurately reflect economic worth of assets and liabilities.

B is incorrect because it divides liabilities by shares (750/20 = 37.50), which has no economic meaning as liabilities represent obligations, not equity value.

C is incorrect because it divides total assets by shares (1,200/20 = 60), ignoring that debt holders have prior claims on those assets that must be subtracted.

First Principles Thinking: covariance from correlation and standard deviations

B is correct. $Cov(R_A, R_B) = \rho_{AB} \times \sigma_A \times \sigma_B = 0.60 \times 0.15 \times 0.20 = 0.0180$. The covariance is the product of the correlation coefficient and both standard deviations.

A is incorrect. This results from mistakenly using variances instead of standard deviations: USD 0.60 \times 0.15^2 \times 0.20^2 = 0.60 \times 0.0225 \times 0.04 = 0.00054$, or from a decimal placement error. The formula requires standard deviations, not variances.

C is incorrect. This results from omitting the correlation coefficient entirely: USD 0.15 \times 0.20 = 0.03$. The correlation is a required component of the covariance formula and cannot be ignored.

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: 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.

Statement (1) is correct because money markets are defined by the trading of short-term debt instruments (one year or less), such as repos and CDs. Statement (2) is correct because capital markets are for raising long-term capital, involving longer-duration debt and equities. Statement (3) is incorrect because commercial paper is a short-term instrument (less than one year), so it trades in the money market, not the capital market, even if issued by a corporation. Therefore, statements (1) and (2) are correct. Option B fails because statement (3) is false. Option C fails because statement (3) is false.

Mean-variance assumes elliptical distributions (normal-like); leptokurtosis (fat tails) implies higher crash probabilities not scaled by σ, violating framework assumptions. The reason identifies the distributional deviation—excess kurtosis elevates tail risk undetected by variance—directly explaining analysis limitations.

Start from mechanics. Leverage is “more exposure per dollar of equity,” so any return shock is scaled up—good or bad—making (1) true. Derivatives often require only margin/premium, so they can deliver meaningful exposure with less initial cash than buying the underlying (2). Because leverage and derivatives can create nonlinear payoffs and large losses in stressed markets, hedge funds emphasize risk controls (limits, VAR/stress tests, liquidity management, hedges) to avoid blowups, supporting (4). Statement (3) is the classic trap: derivatives are tools; risk depends on the position’s sensitivity and structure, not the instrument label. A derivative can reduce risk (hedge) or increase it (levered bet).

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).

Verify facts. Assertion (A) is true; the DJIA is the most famous price-weighted index. Reason (R) is also true; the Nikkei 225 is also price-weighted. However, the fact that the Nikkei is price-weighted (R) is not the explanation for why the DJIA is price-weighted (A). They are independent facts about two different major indices that share a methodology.

First Principles Thinking: Premium/Discount Determination

B is correct. Price equals \( PV = 6/1.04 + 106/(1.05)^2 = 5.77 + 96.15 = 101.92 \), which exceeds 100 (par). The bond trades at a premium because the 6% coupon exceeds both relevant spot rates (4% and 5%). From first principles, when cash flows exceed what the market requires (spot rates), investors pay a premium to obtain those superior flows. The premium of 1.92 represents the excess present value of receiving 6% coupons when the market only requires 4-5% returns. This no-arbitrage pricing ensures investors cannot construct a cheaper synthetic equivalent using zero-coupon bonds, maintaining market efficiency.

A is incorrect because par pricing (PV = 100) occurs when the coupon rate equals the yield-to-maturity, which would require the weighted average discount rate to equal 6%. Since both spot rates (4%, 5%) are substantially below 6%, the bond must trade above par. The par rate for this spot curve would be approximately 4.98%, well below the 6% coupon, confirming premium pricing.

C is incorrect because discount pricing (PV < 100) requires the coupon to fall below the discount rates. Here, the 6% coupon exceeds both the 4% and 5% spot rates, creating excess cash flows that command a premium. Discount pricing would require spot rates above 6%, making the bond's coupons deficient relative to market requirements, which contradicts the given rates.

Government equivalent yield is approximated by multiplying the 30/360 yield by $365/360$. Thus, USD 3.20\% \times 365/360 = 3.244\%$, about 3.24%. Option B ignores the day-count restatement. Option A moves in the wrong direction.

First Principles Thinking: Decomposition of Portfolio Risk with Many Assets

B is correct. Assertion A is true: as stated in the CFA Curriculum, when N becomes large, the first term ($\bar{\sigma}^2/N$) becomes smaller and smaller, implying that the contribution of one asset's variance to portfolio variance gradually becomes negligible. Reason R is also true — the formula accurately reflects the portfolio variance decomposition shown in the CFA Curriculum. However, the Assertion specifically states "identical variances and identical pairwise correlations" while the Reason presents the more general formula using average variance and average covariance with equal weights. The formula in R applies to any equally weighted portfolio regardless of whether individual variances and correlations are identical. Therefore, R is true but is the general case, not the specific causal explanation for the identical-variance-and-correlation scenario described in A, where the more specific formula $\sigma_p = \sqrt{\sigma^2/N + ((N-1)/N)\rho\sigma^2}$ applies.

Option A is incorrect because R presents the general average-based formula rather than the specific formula for identical variances and correlations that directly explains Assertion A.

Option D is incorrect because Assertion A is true according to the CFA Curriculum.

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.

The CML plots portfolios combining the risk-free asset with the market portfolio—the tangency point on the efficient frontier. The reason correctly identifies why CML restriction exists: total risk equals systematic risk only for fully diversified (efficient) portfolios where σ²(nonsystematic) = 0. The SML, using beta (systematic risk), applies to any security. This causality—efficient portfolios having zero diversifiable risk—directly explains CML's domain limitation.

Event-driven returns come from catalysts: a merger closing, a restructuring plan, a liquidation recovery—so (1) is true. Because outcomes hinge on specific transactions and counterparties, risk is idiosyncratic and not fully diversified away by market hedges (2). Legal/regulatory approval, financing, shareholder votes, and court decisions can determine whether the event occurs and at what terms, so (4) is true. Statement (3) is false: that describes global macro; event-driven is micro/catalyst-driven.

First Principles Thinking

Pricing an FRN involves comparing what the bond pays vs. what the market requires.

1. Numerator (Cash Flows): The bond pays Reference Rate + Quoted Margin (QM = +120 bps). 2. Denominator (Discount Rate): The market requires Reference Rate + Discount Margin (DM = +150 bps). 3. Comparison: The bond is paying 120 bps over the index, but investors demand 150 bps over the index. The bond is paying less than the required rate of return. 4. Result: When the coupon rate (QM) is lower than the required yield (DM), the price must adjust downward to boost the effective return. Therefore, the bond trades at a discount.

First Principles Thinking: Physical Constraints

D is correct. Assertion (A) is False: Short-run supply for commodities is notoriously *inelastic*. You cannot speed up a biological harvest or build a mine overnight. Reason (R) is True: It accurately describes the physical reality (lead times, growth cycles) that causes the inelasticity. Because A is False and R is True, D is the correct choice.

A, B, and C are incorrect because the premise in A is false.

First Principles Thinking: Interest Rate Parity

B is correct. For a currency futures or forward contract with continuous compounding:
$$ F_0 = S_0 e^{(r_{dc} - r_{fc})T} $$

Here, \( S_0 = 1.3000 \), \( r_{dc} = 0.02 \), \( r_{fc} = 0.04 \), and \( T=1 \):
$$ F_0 = 1.3000e^{(0.02 - 0.04)} = 1.3000e^{-0.02} \approx 1.2743 $$

A is incorrect because it swaps the domestic and foreign rates.

C is incorrect because it uses discrete compounding rather than the continuous compounding specified in the stem.

A is true by construction: effective duration can be decomposed into the sum of partial (key rate) sensitivities when the key-rate framework is used. R is also true, but it describes what key rate duration measures (shaping risk) rather than why the key rate durations must add up to effective duration (the additive decomposition implied by the definitions).

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.

First Principles Thinking: Tail Risk and Convexity

A is correct. This demonstrates the 'Convexity Bias'.
Futures (Short): Payoff is linear. $Gain = \text{Notional} \times \Delta Rate \times Time$. The cash is received daily (no discounting).
FRA (Long): Payoff is $ \frac{\text{Notional} \times \Delta Rate \times Time}{1 + (Rate \times Time)} $.
Mechanism: As rates ($R$) rise, the denominator in the FRA formula increases, dampening the payoff. The Futures contract does not have this denominator effect. Therefore, for a large rate increase, the Futures payoff (undiscounted) > FRA payoff (discounted).

B is incorrect. The FRA payoff is concave (dampened) relative to rates.
C is incorrect due to the daily settlement vs term settlement difference.

First Principles Thinking: Types of Public Offerings

B is correct. A **seasoned security** is one that an issuer has already issued. If the issuer sells additional units of a previously issued security, this is called a **seasoned offering** (sometimes called a secondary offering). Both IPOs and seasoned offerings take place in the primary market .

A is incorrect: An **Initial Public Offering (IPO)** (or placing) is when the issuer sells a security to the public for the *first* time .

C is incorrect: A private placement is a sale to a small group of qualified investors on an unregulated basis, not necessarily a sale to the public of previously issued securities.

First Principles Thinking: Price-Yield Relationship

B is correct. From the fundamental inverse relationship between bond prices and yields, when yields rise, prices fall: \( P = \sum CF_t / (1+y)^t \). Higher y (discount rate) reduces present value of all cash flows. If the investor sells at the new lower price, they realize a capital loss relative to the purchase price. For example, buying at par (100) when yields are 5%, then selling after yields rise to 6%, the bond trades below par—say 95—creating a 5-point capital loss. This is pure price risk: the mark-to-market loss from adverse rate movements. This principle is fundamental to understanding bond investing: holding period shorter than maturity exposes investors to price risk from yield changes.

A is incorrect because capital gains occur when prices rise, which happens when yields fall, not rise. The question specifies rising rates, which causes falling prices. A capital gain would require selling at a price above purchase price, impossible when rates have risen and pushed prices down. This answer reverses the price-yield relationship.

C is incorrect because "no capital gain or loss" only occurs if: (1) the bond is held to maturity (redemption at par eliminates price risk), or (2) yields remain unchanged so the sale price equals the constant-yield trajectory. The question specifies rising rates and sale before maturity, guaranteeing a price change. Even if the bond was bought at a discount, rising rates push the price further below the trajectory, creating a mark-to-market loss relative to the expected path.