Portfolio Construction — CFA Level III practice questions

An investment committee is told that a resampled (Michaud) efficient frontier portfolio 'is guaranteed to outperform a standard MVO portfolio out of sample.' This claim is BEST characterized as:

1. Accurate, because resampling directly incorporates future return realizations into the optimization
2. Accurate, because resampling always produces the true global mean-variance efficient portfolio
3. Inaccurate — resampling improves robustness and diversification relative to point-estimate MVO, but provides no guarantee of superior out-of-sample performance
4. Inaccurate, because resampled portfolios are mathematically identical to equal-weighted portfolios

Answer: C — Inaccurate — resampling improves robustness and diversification relative to point-estimate MVO, but provides no guarantee of superior out-of-sample performance

A) Resampling uses historical or simulated inputs, not future realizations — it cannot incorporate returns that have not yet occurred. B) Resampling averages across many simulated frontiers and is not guaranteed to identify the true (unobservable) efficient portfolio. C) Correct — resampling's benefit is reduced sensitivity to estimation error and more diversified weights, not a guarantee of superior realized performance, since its inputs remain estimates. D) Resampled portfolios are generally more diversified than raw MVO output, but they are not mathematically equivalent to naive equal weighting.

Currency hedging considerations:

1. Always fully hedged at 100% in the standard framework
2. Always unhedged at 0% only in the standard framework
3. Ratio between 0% and 100% via forwards or options
4. Only via currency swaps in the standard framework

Answer: C — Ratio between 0% and 100% via forwards or options

A) Full hedging ignores currency's diversification benefit. B) Zero hedge leaves full FX exposure. C) Correct — Optimal hedge depends on horizon, correlations, and cost; typically partial. D) Swaps are only one implementation.

A receive-fixed/pay-floating interest-rate swap is functionally equivalent to:

1. Being short a fixed-rate bond and long a floating-rate note, which shortens overall portfolio duration
2. Being long a fixed-rate bond and short a floating-rate note, which adds positive duration and increases sensitivity to falling interest rates
3. A pure credit derivative with no interest-rate sensitivity, since swap cash flows are notional and non-principal
4. An equity total return swap that exchanges a floating funding rate for the total return on a stock index

Answer: B — Being long a fixed-rate bond and short a floating-rate note, which adds positive duration and increases sensitivity to falling interest rates

A) This reverses the position — receiving fixed (not paying fixed) is the long-fixed-bond-like leg, which adds, rather than removes, duration. B) Correct — receiving a fixed rate while paying a floating rate mimics being long a fixed-rate bond (whose value rises as rates fall) financed by a floating-rate liability, adding positive duration to the receiving party's position. C) Interest-rate swaps carry real interest-rate sensitivity through their fixed and floating legs, even though there is no exchange of principal; they are not credit derivatives. D) This describes a distinct instrument (an equity swap), not a plain-vanilla interest-rate swap.

A fixed-income manager has an immunized portfolio duration-matched to a 7-year liability. Eighteen months pass with no interest-rate changes, and a review shows the portfolio's duration has drifted to 6.3 years while the liability's remaining duration is now 5.5 years. The NEXT appropriate action is to:

1. Take no action, since both durations have declined and therefore remain approximately matched
2. Shift the entire portfolio into cash to eliminate duration risk entirely until the liability comes due
3. Rebalance the portfolio, most likely by shortening duration through purchases of shorter-maturity bonds, to bring the portfolio's 6.3-year duration back down toward the liability's 5.5-year duration
4. Rebalance the portfolio by extending duration further through purchases of longer-maturity bonds, since restoring balance requires moving in the same direction the mismatch has been drifting

Answer: C — Rebalance the portfolio, most likely by shortening duration through purchases of shorter-maturity bonds, to bring the portfolio's 6.3-year duration back down toward the liability's 5.5-year duration

A) Both durations fell, but by different amounts, widening the gap from a matched state to a 0.8-year mismatch (6.3 vs. 5.5), so this is not approximately matched. B) Moving entirely to cash is an overreaction that would create a large negative duration mismatch relative to a 5.5-year liability, rather than correcting the existing gap. C) Correct — since the portfolio's duration (6.3 years) now exceeds the liability's duration (5.5 years), rebalancing should shorten the portfolio's duration to restore the match. D) This reverses the needed direction — extending duration further would widen, not close, the existing 0.8-year mismatch.

An investor holding a large, low-cost-basis stock position wants downside protection below a specific price level but is unwilling to pay a large upfront cash premium for that protection, and is willing to give up some upside participation above a certain price in exchange for lower net hedging cost. The BEST strategy is:

1. A protective put alone, purchasing a put option at the desired floor strike and paying the full premium in cash upfront
2. A covered call alone, writing a call option against the stock position without purchasing any downside protection
3. A long straddle, purchasing both a put and a call at the same strike to profit from volatility in either direction
4. A zero-cost (or low-cost) collar, purchasing a protective put and simultaneously writing a call to offset most or all of the put's premium, in exchange for capping upside above the call's strike

Answer: D — A zero-cost (or low-cost) collar, purchasing a protective put and simultaneously writing a call to offset most or all of the put's premium, in exchange for capping upside above the call's strike

D) Correct — a collar combines a purchased put (the downside floor) with a written call (which generates premium income to offset the put's cost), reducing or eliminating the net upfront premium in exchange for capping gains above the call's strike, precisely matching the investor's stated tradeoff. A) A standalone protective put provides the desired floor but requires paying the full option premium in cash, which the investor specifically wants to avoid. B) A covered call generates premium income and caps upside, but provides no downside floor at all, leaving the position exposed below the current price. C) A long straddle requires paying two option premiums and profits from large moves in either direction; it does not provide a downside floor tied to the stock position's own gains and is a speculative volatility play, not a protective hedge.

A US-based asset owner holds 25% in foreign equities with a 50% currency hedge ratio. The choice of HEDGE RATIO should be guided primarily by:

1. Always fully hedged at 100% in the standard framework
2. Ratio between 0% and 100% via forwards or options
3. Always unhedged at 0% only in the standard framework
4. Only via currency swaps in the standard framework

Answer: B — Ratio between 0% and 100% via forwards or options

A) Full hedging ignores currency's diversification benefit. B) Correct — Optimal hedge depends on horizon, correlations, and cost; typically partial. C) Zero hedge leaves full FX exposure. D) Swaps are only one implementation.

A passive equity manager replicating the MSCI EAFE index using full replication will MOST likely incur tracking error from:

1. Absolute value of alpha only in the standard framework
2. Beta minus one measure in the standard framework
3. Sharpe-ratio difference in the standard framework
4. Standard deviation of active return

Answer: D — Standard deviation of active return

A) Alpha is the mean, not the dispersion. B) Beta relative is a systematic measure. C) Sharpe differences aren't tracking error. D) Correct — Tracking error = stdev(portfolio return - benchmark return).

A US small-cap value manager is evaluated against the Russell 1000 Growth Index because it is the firm's 'house' benchmark used for all equity strategies. Style analysis shows the manager's returns have an R-squared of only 0.15 against this benchmark. This result BEST supports the conclusion that:

1. The manager has clearly failed to deliver risk-adjusted outperformance over the period
2. The manager's active share must be understated in the firm's reporting systems
3. The chosen benchmark is a poor fit for the manager's actual investment style, making relative-performance conclusions drawn against it unreliable
4. The manager should be terminated immediately based on the low R-squared figure alone

Answer: C — The chosen benchmark is a poor fit for the manager's actual investment style, making relative-performance conclusions drawn against it unreliable

A) A low R-squared measures benchmark fit, not whether the manager delivered risk-adjusted outperformance; this conclusion does not follow from the statistic given. B) There is no established link between R-squared against a mismatched benchmark and the accuracy of a separately calculated active share figure. C) Correct — a very low R-squared against the assigned benchmark indicates the manager's return pattern does not track that benchmark, signaling a style/benchmark mismatch that undermines the reliability of any relative-performance evaluation against it. D) A termination decision requires a full manager review, not a single benchmark-fit statistic taken in isolation.

An insurance company's fixed-income portfolio is benchmarked using a custom liability-based index rather than a standard market-value-weighted bond index. The PRIMARY reason for this choice is that a standard market index:

1. Always has a shorter duration than any insurance liability schedule, making it unusable for any comparison
2. Cannot legally be used as a benchmark by regulated insurance companies under any circumstance
3. May not reflect the specific duration, cash-flow timing, and risk profile of the insurer's actual liabilities
4. Provides a higher yield than any liability-based index, making performance comparisons misleadingly favorable

Answer: C — May not reflect the specific duration, cash-flow timing, and risk profile of the insurer's actual liabilities

A) Market-value-weighted indices vary widely in duration depending on composition; the issue isn't a universal duration mismatch but that any given standard index may not match the specific liability profile. B) There is no blanket legal prohibition on insurers using standard market indices; some do, though many prefer custom liability-based benchmarks for asset-liability management purposes. C) Correct — A liability-based custom index is constructed to mirror the insurer's own liability duration and cash-flow schedule, which a generic market-value-weighted index is not designed to do. D) Yield levels between the two types of indices are not systematically ordered in one direction; the concern is representativeness of the liability profile, not yield magnitude.

Closet indexing — an active fund whose returns substantially track its benchmark — is MOST objectionable because:

1. Passive fees for active returns in the standard framework
2. Fully independent active mandate
3. Explicit index replication in the standard framework
4. Active fees for near-benchmark returns

Answer: D — Active fees for near-benchmark returns

A) Reverses the abuse. B) High active share isn't closet indexing. C) Transparent replication is honest indexing, not closet. D) Correct — Closet indexing: high active fees hiding low active share.

How is the number of stock index futures contracts needed to fully hedge an equity portfolio's systematic risk calculated?

Contracts = (portfolio value / futures contract notional value) x portfolio beta; a portfolio with beta above 1.0 requires proportionally more contracts than one with beta of 1.0 to fully offset its greater sensitivity to the index.

Why does an insurer typically evaluate immunization or LDI performance using key rate durations in addition to a single effective duration figure?

A single effective duration only captures sensitivity to parallel shifts in the yield curve, but liabilities and hedging assets can have different exposures across the curve, so key rate durations, which measure sensitivity to rate changes at specific maturity points, are needed to detect and hedge non-parallel (twist or steepening/flattening) yield-curve risk that a single duration figure would miss.

A manager expects the yield curve to flatten, with long-term yields falling more than short-term yields. What is the most direct portfolio expression of this view?

Increase exposure to long-duration bonds and reduce exposure to short-duration bonds, since a flattening in which long yields fall more than short yields will make long-duration bonds appreciate more than short-duration bonds, profiting from the narrowing spread between long and short yields.

What is the main advantage of using an equity futures overlay to reduce net beta versus selling the underlying stocks outright?

It adjusts aggregate market exposure quickly and reversibly while preserving the underlying security selection and avoiding realized capital gains/transaction costs from selling the physical positions.