CFA Exam Question of the Day

Rationale:
Choice B is correct because a simple random sample (SRS) requires that every possible sample of a given size has an equal chance of being selected, which implies that every item in the defined population has an equal and independent chance of being included in the sample. Assigning unique identifiers to each of the 4,500 ETFs and then using a random number generator to select 300 unique integers directly ensures this equal probability for each ETF in the initial population. Choice A is incorrect because by first excluding ETFs based on an expense ratio criterion, the analyst redefines the population. ETFs with an expense ratio exceeding 80 bps have no chance of being selected, violating the principle that every item in the *initial* 4,500-ETF population must have an equal chance of selection. This method constitutes a simple random sample from a *subset* of the original population, not from the initial 4,500 ETFs. Choice C is incorrect because it describes stratified random sampling, where the population is divided into subgroups (strata) and then samples are drawn from each stratum proportionally. This is not a simple random sample. Choice D is incorrect because it describes systematic random sampling, where items are selected at regular intervals from an ordered list (e.g., every 15th ETF). While it involves a random starting point, it does not give every possible sample of 300 ETFs an equal chance of being selected, and the selection of items is not fully independent in the same way as SRS.

Rationale:
Choice C is correct because for a callable bond, the most conservative estimate of its expected return is the Yield to Worst (YTW). YTW is the lower of the Yield to Maturity (YTM) and the Yield to Call (YTC). 1. **Calculate Yield to Maturity (YTM):** * N = 7 (years to maturity) * PMT = 7 (annual coupon, 7% of 100 par) * FV = 100 (par value) * PV = -105.00 (current price) * Solving for I/Y (YTM) gives approximately 6.11% or 611 basis points. 2. **Calculate Yield to Call (YTC):** * N = 3 (years to call) * PMT = 7 (annual coupon) * FV = 102.00 (call price) * PV = -105.00 (current price) * Solving for I/Y (YTC) gives approximately 5.85% or 585 basis points. 3. **Determine Yield to Worst (YTW):** * YTM (6.11%) vs. YTC (5.85%) * YTW is the lower of the two, which is 5.85% (YTC). Therefore, 585 basis points is the most conservative estimate of the bond's expected return. The other information provided, such as government bond yields, credit rating, and modified duration, are relevant for broader bond analysis but not for determining this specific yield measure. Choice A is incorrect because it represents the YTM, which is higher than YTC and thus not the Yield to Worst for this callable bond. Choice B is incorrect because it represents the Current Yield (7/105 = 6.67%), which ignores the capital loss to maturity/call and the embedded call option. Choice D is incorrect because it represents a common miscalculation of YTC, likely by using the par value (100) instead of the call price (102) as the future value (FV) in the YTC calculation (N=3, PMT=7, FV=100, PV=-105 -> I/Y approx 5.75%).

Rationale:
Choice D is correct because to minimize current period tax liability, the portfolio manager should choose the action that results in the largest tax saving or the smallest tax payment. This requires calculating the capital gain or loss for each lot and applying the appropriate short-term (held for 12 months or less) or long-term (held for more than 12 months) capital gains tax rate. 1. **Lot X (Option A):** Purchased 8 months ago at $90.00. Current price $100.00. * Capital Gain: ($100.00 - $90.00) * 1,000 shares = $10,000 (Short-term) * Tax Liability: $10,000 * 0.35 = $3,500 2. **Lot Y (Option B):** Purchased 14 months ago at $80.00. Current price $100.00. * Capital Gain: ($100.00 - $80.00) * 1,000 shares = $20,000 (Long-term) * Tax Liability: $20,000 * 0.20 = $4,000 3. **Lot Z (Option C):** Purchased 3 months ago at $105.00. Current price $100.00. * Capital Loss: ($100.00 - $105.00) * 1,000 shares = -$5,000 (Short-term) * Tax Saving: -$5,000 * 0.35 = -$1,750 4. **Lot W (Option D):** Purchased 26 months ago at $110.00. Current price $100.00. * Capital Loss: ($100.00 - $110.00) * 1,000 shares = -$10,000 (Long-term) * Tax Saving: -$10,000 * 0.20 = -$2,000 Comparing the tax impacts: Lot X results in a $3,500 tax payment, Lot Y results in a $4,000 tax payment, Lot Z results in a $1,750 tax saving, and Lot W results in a $2,000 tax saving. Selling Lot W generates the largest tax saving (or the least positive tax liability), thus most effectively minimizing the current period tax liability. The other information (beta, dividend yield, standard deviation of excess returns, analyst consensus) is extraneous noise for this specific tax-efficient disposition decision.

Rationale:
Choice D is correct because, under the CFA Institute Code of Ethics and Standards of Professional Conduct, particularly Standard III(A) Loyalty, Prudence, and Care, and Standard III(C) Suitability, investment professionals must adhere to the client's IPS as the governing document. While the investment may align with the client's overall objectives and risk tolerance (multi-step 1), the IPS does not explicitly permit this specific asset class. Therefore, the most appropriate action is to seek explicit client approval and formally amend the IPS to reflect the new investment strategy before execution (multi-step 2). This ensures transparency, client understanding, and compliance with the established mandate. Choice A and B are incorrect as they involve making the investment without prior client consent and formal IPS amendment, which constitutes a breach of the mandate and professional standards, even if documentation follows or the manager believes it's in the client's best interest. Choice C is incorrect because while it avoids a breach, it fails to act in the client's best interest by not exploring a potentially beneficial opportunity through the correct ethical and procedural channels.

Rationale:
Choice C is correct because the full (dirty) price of a bond is the sum of its quoted (clean) price and the accrued interest. First, calculate the clean price: The bond is quoted at 98.50 per 100 of par value. For a $1,000 face value bond, the clean price is 0.9850 * $1,000 = $985.00. Next, calculate the accrued interest using the 30/360 day count convention: 1. Semi-annual coupon payment = (5.00% / 2) * $1,000 = $25.00. 2. Days from last coupon (October 15, 2023) to settlement (December 15, 2023) using 30/360 convention: * October: 30 - 15 = 15 days * November: 30 days * December: 15 days * Total accrued days = 15 + 30 + 15 = 60 days. 3. Days in the current coupon period (October 15, 2023 to April 15, 2024) using 30/360 convention: 6 months * 30 days/month = 180 days. 4. Accrued Interest = (Accrued Days / Days in Coupon Period) * Semi-annual Coupon Payment = (60 / 180) * $25.00 = (1/3) * $25.00 = $8.3333... Finally, calculate the full (dirty) price: Full Price = Clean Price + Accrued Interest = $985.00 + $8.3333... = $993.33. Choice A is incorrect because it represents only the clean price, ignoring accrued interest. Choice B is incorrect because it uses an incorrect day count convention for the denominator (e.g., Actual/Actual for days in coupon period, which would be 183 days from Oct 15, 2023 to Apr 15, 2024, leading to (60/183)*$25 = $8.1967, and a dirty price of $993.20). The problem explicitly states a 30/360 convention for accrued interest. Choice D is incorrect because it adds the full semi-annual coupon payment instead of only the accrued portion.