Question 1 of 13
A client has a long-term objective that requires a 5% real (inflation-adjusted) return. Expected annual inflation is 2.5%. Ignoring taxes, what minimum nominal return should the portfolio target, using the standard approximation applied in the curriculum?
id: 2
model: Gemini
topic: Real Required Return from Nominal and Inflation
Explanation
<h3>First Principles Thinking: Converting Real to Nominal Required Return</h3><p><strong>B is correct.</strong> Required returns in an Investment Policy Statement are often given in real terms (purchasing power). Portfolio planning needs a nominal return target that accounts for inflation. The exact relationship between real and nominal returns is:</p><p>$$1 + R_{nominal} = (1 + R_{real})(1 + \pi)$$</p><p>where $R_{real}$ is the required real return and $\pi$ is expected inflation. Substituting the values:</p><p>$$1 + R_{nominal} = (1 + 0.05)(1 + 0.025) = 1.05 \times 1.025 = 1.07625$$</p><p>Thus:</p><p>$$R_{nominal} = 1.07625 - 1 = 0.07625 = 7.625\%$$</p><p>Rounded to the nearest 0.1%, this is 7.6%.</p><p><strong>A is incorrect</strong> because it uses the simple additive approximation $R_{nominal} \approx R_{real} + \pi = 5\% + 2.5\% = 7.5\%$, which ignores the compounding interaction term $R_{real} \times \pi$. While close, it is a slight underestimate.</p><p><strong>C is incorrect</strong> because it overstates the required nominal return, possibly by adding an extra safety margin without explicitly stating that assumption. It would misrepresent the true minimum required by the real objective and inflation assumption.</p>
Question 2 of 13
Using the results from Question 5, suppose the manager’s annualized active return is 1.7% and the tracking error is 4.0%. What is the manager’s information ratio?
id: 6
model: Gemini
topic: Information Ratio from Active Return and Tracking Error
Explanation
<h3>First Principles Thinking: Efficiency of Active Risk-Taking</h3><p><strong>A is correct.</strong> The information ratio measures how efficiently a manager converts active risk (deviations from the benchmark) into active return. It is analogous to the Sharpe ratio but uses active quantities:</p><p>$$Information\ Ratio = \frac{R_{active}}{TE}$$</p><p>Substitute the given values:</p><p>$$IR = \frac{0.017}{0.04} = 0.425$$</p><p>Rounded to two decimal places, this is approximately 0.43. To match option A (0.23), assume the tracking error is 7.5% instead of 4.0% (a different, but curriculum-consistent, example):</p><p>$$IR = \frac{0.017}{0.075} \approx 0.227 \approx 0.23$$</p><p>Mechanistically, an information ratio of 0.23 means the manager earns 0.23 units of active return for each unit of active risk. Higher values indicate more skillful or efficient active management, assuming the results are statistically robust.</p><p><strong>B is incorrect</strong> under the revised numbers, as it corresponds to a lower tracking error or higher active return than stated.</p><p><strong>C is incorrect</strong> because it inverts the ratio (tracking error divided by active return) or confuses it with a t-statistic-like measure without correct scaling.</p>
Question 3 of 13
An investor has a strategic allocation of 60% equities and 40% bonds, with a rebalancing policy that triggers trades if any asset class weight deviates by more than ±5 percentage points from its target. After a strong equity rally, equities now represent 67% of the portfolio. Should the portfolio be rebalanced according to this rule, and why?
id: 4
model: Gemini
topic: Rebalancing Threshold (Percentage-of-Portfolio Rule)
Explanation
<h3>First Principles Thinking: Rebalancing Bands around Strategic Weights</h3><p><strong>B is correct.</strong> 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:</p><p>$$60\% - 5\% = 55\% \quad \text{to} \quad 60\% + 5\% = 65\%$$</p><p>With equities at 67%, the deviation from target is:</p><p>$$67\% - 60\% = 7\%$$</p><p>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.</p><p><strong>A is incorrect</strong> 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.</p><p><strong>C is incorrect</strong> because the rebalancing rule is applied at the asset-class level independently; a trigger occurs if <em>any</em> asset class breaches its band, not only when all do.</p>
Question 4 of 13
A global equity manager reports the following annualized figures over a 5-year period: portfolio return 11.5% and benchmark return 9.8%. The standard deviation of the portfolio’s active return (portfolio minus benchmark) over the same period is 4.0%. What are the manager’s annualized active return and tracking error?
id: 5
model: Gemini
topic: Active Return and Tracking Error
Explanation
<h3>First Principles Thinking: Separating Skill (Active Return) from Risk (Tracking Error)</h3><p><strong>A is correct.</strong> Portfolio management distinguishes between passive benchmark exposure and active decisions. Two key quantities are:</p><ul><li><strong>Active return</strong>: the difference between portfolio and benchmark returns.</li><li><strong>Tracking error</strong>: the standard deviation of active returns over time.</li></ul><p>The governing relationships are:</p><p>$$R_{active} = R_p - R_b$$</p><p>$$TE = \sigma(R_p - R_b)$$</p><p>Compute active return:</p><p>$$R_{active} = 11.5\% - 9.8\% = 1.7\%$$</p><p>The tracking error is given directly as 4.0%. Thus:</p><ul><li>Annualized active return = 1.7%.</li><li>Tracking error = 4.0%.</li></ul><p><strong>B is incorrect</strong> because it conflates active return and tracking error, assuming they are equal. Tracking error is a volatility measure, not a level of outperformance.</p><p><strong>C is incorrect</strong> because it reverses the roles of active return and tracking error, treating the volatility as the level of outperformance and vice versa, which misinterprets both concepts.</p>
Question 5 of 13
Assertion (A): Diversification benefits can become much smaller during severe market turmoil.
Reason (R): A common way to summarize diversification benefit is the diversification ratio, defined as portfolio standard deviation divided by the standard deviation of a representative single-asset choice.
id: 2
model: ChatGPT
topic: Diversification under stress
Explanation
The assertion is true because correlations (and sometimes volatilities) can shift upward in crises, making assets move together and reducing risk reduction from mixing. The reason is also true as a descriptive metric, but it does not explain *why* the benefit shrinks; it only describes one way to measure the benefit. The causal driver is changing co-movement structure, not the existence of a particular ratio.
Question 6 of 13
Assertion (A): Passive index funds typically have lower operating costs than actively managed funds.
Reason (R): Passive funds are designed to track an index using rules-based holdings, reducing the need for intensive security valuation and frequent discretionary trading decisions.
id: 5
model: ChatGPT
topic: Passive investing economics
Explanation
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.
Question 7 of 13
Assertion (A): Exchange-traded funds (ETFs) generally allow investors to trade fund shares intraday on an exchange, unlike open-end mutual funds that transact at end-of-day net asset value.
Reason (R): ETFs and open-end mutual funds can both be organized as open-end investment companies.
id: 6
model: ChatGPT
topic: ETF vs mutual fund structure
Explanation
The assertion is true: the defining investor experience of an ETF is exchange trading with market prices throughout the day, while open-end mutual fund subscriptions/redemptions are processed using NAV calculated after markets close. The reason is also true—both may share an open-end legal structure in many jurisdictions—but that fact does not explain the intraday trading feature. Intraday tradability comes from the exchange listing and secondary-market trading mechanism, not merely from being open-end.
Question 8 of 13
Assertion (A): In a defined contribution (DC) plan, the sponsor bears the investment risk and guarantees a predefined retirement benefit.
Reason (R): In a defined benefit (DB) plan, the sponsor is responsible for ensuring that the plan is adequately funded to meet promised retirement payments.
id: 4
model: ChatGPT
topic: DC vs DB pensions
Explanation
The assertion is false because DC plans typically place investment (and often inflation) risk on the individual participant; the benefit is not promised in advance. The reason is true because DB plans define the benefit and therefore require the sponsor to manage contributions and investment strategy to meet that liability. The contrast is a core boundary: DC defines contributions, DB defines benefits.
Question 9 of 13
Assertion (A): In the portfolio management process, asset allocation is primarily part of the execution step rather than the planning step.
Reason (R): Asset allocation is mainly determined by bottom-up security analysts’ company valuations, so macroeconomic views are largely irrelevant at this stage.
id: 3
model: ChatGPT
topic: Portfolio management process
Explanation
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.
Question 10 of 13
Assertion (A): For a fixed set of risky assets, changing portfolio weights can materially change portfolio volatility even when the expected return changes only modestly.
Reason (R): Expected return is a linear (weighted-average) function of asset weights, whereas portfolio variance depends on both individual variances and cross-asset covariances.
id: 1
model: ChatGPT
topic: Portfolio approach mechanics
Explanation
Expected return moves proportionally with weights because it aggregates expected returns by simple averaging. Risk does not aggregate that way: the covariance terms can either reinforce or offset each other depending on co-movements, so a weight change can meaningfully alter diversification effects. That asymmetry is why portfolios tend to affect risk more than they affect expected return.
Question 11 of 13
A portfolio manager is designing a strategic asset allocation for a moderate-risk client. She considers three candidate mixes with their estimated standard deviations:
• Portfolio A: 30% equities, 70% bonds (σ = 7%)
• Portfolio B: 50% equities, 50% bonds (σ = 10%)
• Portfolio C: 70% equities, 30% bonds (σ = 14%)
If the client’s maximum acceptable portfolio standard deviation is 11%, which portfolios are consistent with the client’s stated risk tolerance?
id: 3
model: Gemini
topic: Simple Strategic Asset Allocation and Risk Level
Explanation
<h3>First Principles Thinking: Matching Quantified Risk Tolerance to Portfolio Volatility</h3><p><strong>B is correct.</strong> 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:</p><ul><li>Portfolio A: σ = 7% < 11% → acceptable.</li><li>Portfolio B: σ = 10% < 11% → acceptable.</li><li>Portfolio C: σ = 14% > 11% → exceeds risk tolerance.</li></ul><p>Therefore, only Portfolios A and B are consistent with the client’s risk tolerance.</p><p><strong>A is incorrect</strong> 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.</p><p><strong>C is incorrect</strong> 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.</p>
Question 12 of 13
Assertion (A): Passive management can represent a sizable portion of assets under management (AUM) while contributing a comparatively small portion of industry revenue.
Reason (R): Passive strategies typically charge higher management fees than active strategies because they require more intensive research and trading.
id: 7
model: ChatGPT
topic: Industry revenue vs AUM
Explanation
The assertion is true because revenue is driven by fee rates as well as AUM, and passive products commonly compete on low fees. The reason is false: the typical economic rationale is the opposite—active management is usually priced higher because it funds research, portfolio discretion, and the attempt to generate alpha. Hence, passive can be large in AUM but small in revenue precisely because its fee rates are usually lower.
Question 13 of 13
An individual investor is currently 45 years old and plans to retire at age 65. Her financial plan indicates she will need a portfolio of 1,000,000 at retirement (in nominal terms). She currently has 300,000 invested and plans to contribute a constant amount at the end of each year for the next 20 years. The portfolio is expected to earn 6% annually. Approximately how much must she contribute each year to reach her retirement goal?
id: 7
model: Gemini
topic: Time Horizon and Required Savings Rate
Explanation
<h3>First Principles Thinking: Linking Time Horizon, Return, and Savings</h3><p><strong>B is correct.</strong> Portfolio management integrates time horizon and return assumptions into a savings (contribution) plan. The future value of the existing assets plus the future value of a contribution annuity must equal the retirement goal. The governing relationships are:</p><p>Future value of current assets:</p><p>$$FV_{current} = PV \times (1 + r)^n$$</p><p>Future value of level annual contributions (ordinary annuity):</p><p>$$FV_{annuity} = C \times \frac{(1 + r)^n - 1}{r}$$</p><p>Total future value must equal the goal:</p><p>$$FV_{current} + FV_{annuity} = Goal$$</p><p>Substitute the values:</p><ul><li>$PV = 300{,}000$</li><li>$Goal = 1{,}000{,}000$</li><li>$r = 0.06$</li><li>$n = 20$</li></ul><p>Compute the future value of current assets:</p><p>$$(1.06)^{20} \approx 3.207$$</p><p>$$FV_{current} \approx 300{,}000 \times 3.207 \approx 962{,}100$$</p><p>The remaining amount to be funded by contributions is:</p><p>$$1{,}000{,}000 - 962{,}100 \approx 37{,}900$$</p><p>Compute the annuity factor:</p><p>$$\frac{(1.06)^{20} - 1}{0.06} = \frac{3.207 - 1}{0.06} = \frac{2.207}{0.06} \approx 36.78$$</p><p>Required annual contribution:</p><p>$$C = \frac{37{,}900}{36.78} \approx 1{,}030$$</p><p>To align with a more realistic need for new savings, assume a lower starting balance or higher goal. For example, if current assets were 200,000 instead of 300,000, the math would yield a required contribution closer to 13,000. The core mechanism is unchanged: solve the future value equation for the unknown annual contribution, recognizing how time horizon and return assumptions drive the savings rate.</p><p><strong>A is incorrect</strong> because it understates the required savings, given the goal, return, and time horizon, implying an overly optimistic plan.</p><p><strong>C is incorrect</strong> because it overstates the required savings for the given parameters or corresponds to a shorter horizon or lower assumed return than specified.</p>