Closet Index Fund

An analyst is given the following information about a portfolio and its benchmark. In particular, the analyst is concerned that the portfolio is a closet index fund.1 The T-bill return chosen to represent the risk-free rate is 0.50%. Benchmark ; Portfolio Return 8.75%; 8.90% Risk 17.50% ; 17.60% Active Return 0.00% ; 0.15% Active Risk 0.00% ; 0.79% Sharpe Ratio 0.4714; 0.4773 Information Ratio N/A ; 0.1896 Which of the following three statements does not justify your belief that the portfolio is a closet index? I. The Sharpe ratio of the portfolio is close to the Sharpe ratio of the benchmark. II. The information ratio of the portfolio is relatively small. III. The active risk of the portfolio is very low. A Statement I

B Statement II C Statement III

Why is statement II the correct answer and not statement 1?

The question is a negative question.

Closet index refers to the tracking of the index very closely to a benchmark aka extreme low active risk. So close that its likely just a replication of the benchmark.

  1. Refers to sharp ratio and has nothing to do with tracking, hanse doesnt justify the portfolio is a closet.

Bumping this as still confused. Am I correct in saying that a low information ratio suggests that tracking error is disproportionately large relative to the active return on offer. This would imply that the portfolio does not mirror the benchmark in terms of its composition (and so Statement II is correct).

I’m kind of shaky on why the answer couldn’t be Statement 1. Sharpe Ratios are absolute return measures and so wouldn’t necessarily imply anything about the portfolio being a closet index, it’s simply a return (over risk free rate) vs. units of risk.