In a given year, exactly half of all active fund managers beat the market index and half underperform it. Does this prove that skilled active management can reliably beat the market over time?
AYes — a 50% success rate in any single year proves skill exists in the industry
BNo — when some active managers outperform, others must underperform by the same dollar amount; after fees, the average active investor receives less than the index return
CYes — if you can identify which managers beat the market, you can capture above-index returns
DNo — active managers are legally required to match the index by regulation
The key insight is that active managers collectively ARE the market. Their aggregate holdings equal the market portfolio, so before fees, the average active manager must earn the market return — some above, some below, but averaging to the index. After fees (typically 0.5–1.5% per year for active funds vs. 0.03–0.10% for index funds), the average active manager mathematically underperforms the index. Option C fails because identifying consistently outperforming managers in advance is extremely difficult, and past outperformance does not predict future outperformance reliably.
Question 2 Multiple Choice
The primary reason index funds outperform most actively managed funds over long time horizons is:
AIndex funds take on more market risk, earning higher expected returns
BIndex fund managers are more skilled at selecting which securities to hold
CIndex funds' lower expense ratios compound into a large wealth advantage over decades, while active funds pay out a significant fraction of returns in fees
DActive funds must hold large cash reserves that drag on returns, while index funds stay fully invested
The expense ratio gap is the mechanism. A 1% annual fee advantage compounds dramatically: on $100,000 earning 7% annually, a 1% fee difference creates roughly $100,000 in additional wealth over 30 years. The index fund wins not by being smarter or taking more risk, but by taking less in fees. Option A is wrong — index funds and active funds holding similar securities have similar risk, not systematically more. Option B is backwards — the insight is that active managers cannot systematically out-select securities because they collectively are the price-setting market.
Question 3 True / False
A sufficiently skilled active fund manager can guarantee consistently above-index returns over a long investment horizon.
TTrue
FFalse
Answer: False
Even genuinely skilled managers face two headwinds that make consistent outperformance nearly impossible. First, the fee drag: a 1% annual expense ratio means they must beat the index by more than 1% every year just to break even after fees — a high bar sustained over decades. Second, market efficiency: as more capital chases skilled managers, the mispricings they exploit become harder to find. Most studies of fund performance find that past outperformance does not reliably predict future outperformance after fees, suggesting luck plays a larger role than skill in observed variation.
Question 4 True / False
Passive investing's advantage over active investing lies partly in eliminating the harmful human decisions that active strategies invite — not in adding any clever strategy.
TTrue
FFalse
Answer: True
This is a subtle but important point. Passive investing is superior not only because of lower fees but also because it removes the investor from the decision loop. Common harmful behaviors — panic-selling during downturns, chasing recent winners, switching to 'hot' active funds after strong recent performance — consistently destroy value relative to a buy-and-hold index strategy. The passive approach's power includes the behaviors it prevents, not just the expense ratio it avoids. An investor who holds an index fund but trades in and out of it based on market conditions captures little of the advantage.
Question 5 Short Answer
Why is it mathematically impossible for active managers as a group to consistently outperform the market index before fees?
Think about your answer, then reveal below.
Model answer: Active managers collectively hold the market — their combined portfolio equals the total market portfolio. Since active managers collectively own everything, their aggregate return before fees must equal the market return. When some managers outperform, others must underperform by the same amount in aggregate. Before fees, active managers as a group earn exactly the index return; after fees, they earn less. This is a mathematical identity, not an empirical claim subject to dispute.
This arithmetic of active management was formalized by William Sharpe. The insight reframes the question from 'are some active managers skilled?' (yes, probably) to 'can I identify them in advance and capture their skill after fees?' (very difficult). For most individual investors, the answer is that the expected cost of trying to identify skill — paying higher fees while searching — exceeds the expected benefit of the skill premium if found. The rational response is to accept the market return cheaply rather than pay for uncertain excess returns.