A hedge fund has reported a Sharpe ratio of 2.5 for five consecutive years by systematically selling out-of-the-money put options (collecting premiums when markets are calm). Why might this Sharpe ratio be misleading?
AOptions strategies are exempt from CAPM analysis, making the Sharpe ratio inapplicable
BThe Sharpe ratio uses beta in the denominator, which options strategies artificially inflate
CThe strategy exhibits low measured volatility but carries large tail risk — rare catastrophic losses that don't appear in historical standard deviation until they occur
DA Sharpe ratio above 2.0 is mathematically impossible with normal return distributions
Selling options generates steady income with low observed volatility — until a crash materializes and the short puts are deeply in-the-money. The Sharpe ratio uses historical standard deviation (σ) in the denominator, which is low during calm periods. This inflates the ratio right up until a catastrophic loss event, which is precisely when the strategy's true risk reveals itself. This is a classic example of the Sharpe ratio's limitation: it implicitly assumes normally distributed returns and misses strategies with negative skewness and fat left tails. Option B is wrong — the Sharpe ratio uses σ, not beta.
Question 2 Multiple Choice
Two managers each run a sub-portfolio within a large diversified pension fund. Manager A: Sharpe ratio 0.6, Treynor ratio 0.10. Manager B: Sharpe ratio 0.9, Treynor ratio 0.06. Which manager added more value to the pension fund?
AManager B — a higher Sharpe ratio always indicates better risk-adjusted performance
BManager A — the Treynor ratio is the correct measure for sub-portfolios, and Manager A's is higher
CThey are equivalent — both ratios must agree for a valid comparison
DCannot determine without knowing their Jensen's alphas relative to the fund's benchmark
When a portfolio is one component of a larger diversified holding, idiosyncratic risk diversifies away in context. Only systematic risk (beta) matters for evaluating that sub-portfolio's contribution. The Treynor ratio uses beta in the denominator for exactly this reason. Manager A's higher Treynor ratio means they delivered more excess return per unit of systematic risk — the relevant measure. Manager B's higher Sharpe ratio reflects lower total volatility, but that idiosyncratic volatility is irrelevant when it's a sleeve within a diversified fund. Choosing the wrong measure leads to rewarding the wrong manager.
Question 3 True / False
A fund reporting positive Jensen's alpha relative to a CAPM benchmark has definitively demonstrated manager skill.
TTrue
FFalse
Answer: False
Positive CAPM alpha is necessary but not sufficient evidence of skill. It may instead reflect exposure to well-known priced factors — size (small-cap premium), value (HML), momentum, or profitability — that the one-factor CAPM benchmark doesn't capture. A strategy that simply buys small-cap value stocks would show positive CAPM alpha in many periods, but that alpha disappears when evaluated against a Fama-French multi-factor model. True alpha requires that excess returns persist after accounting for all known systematic risk factors, and even then, it could reflect luck over the evaluation period.
Question 4 True / False
The Treynor ratio is more appropriate than the Sharpe ratio for evaluating a sub-portfolio within a larger diversified fund, because only systematic risk (beta) is relevant in that context.
TTrue
FFalse
Answer: True
This is the key contextual principle for choosing between these measures. The Sharpe ratio is appropriate when the portfolio in question represents the investor's entire wealth — there is no larger portfolio to absorb its idiosyncratic risk. When the portfolio is a sleeve within a larger diversified fund, the fund-level diversification eliminates idiosyncratic volatility, leaving only systematic risk as the relevant cost. The Treynor ratio correctly charges only for that remaining systematic risk. Using Sharpe in this context penalizes managers whose portfolios happen to be more volatile even if that volatility adds no systematic risk.
Question 5 Short Answer
Why might a fund that shows positive Jensen's alpha versus a simple market-beta benchmark show zero or negative alpha when evaluated against a Fama-French multi-factor model?
Think about your answer, then reveal below.
Model answer: CAPM uses only market beta to predict expected return. If the fund loads heavily on known priced factors — small-cap stocks (size premium), cheap stocks (value premium), or past winners (momentum premium) — those factor exposures generate returns that CAPM incorrectly attributes to skill. When the Fama-French model explicitly controls for size, value, and momentum factors, those returns are correctly identified as compensation for systematic factor risk, not alpha. Only the residual return unexplained by all known factors counts as true alpha.
This is why professional performance attribution increasingly decomposes returns into factor exposures versus residual alpha. The practical implication is that apparent alpha against a simple benchmark invites the question: 'What systematic risk is this strategy exposed to that my benchmark doesn't capture?' If the answer is 'exposure to size and value,' the manager hasn't generated alpha — they've constructed a factor portfolio without disclosing it as such.