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.

hey Repe,

I think what they are trying to say is that given that closet index funds very closely perform the same as their benchmark, the return for both the benchmark and the fund would be the same. So if you calculate the shape ratio for both the fund and the benchmark, they will turn out to be the same.

The information ratio of a closet fund is usually close to 0 and usually, its active risk is very low because they don’t do much to beat the benchmark. They are more like replicating the benchmark.

Hope it helps.

Actually statement 1 does justify that the portfolio is a closet fund, because the sharpe ratio is very close to the benchmark.

Lots of portfolios that don’t track the benchmark can have a Sharpe ratio that’s close to that of the benchmark.

As a simple example, a portfolio that’s 50% benchmark and 50% risk-free will do so. So will one that’s 150% benchmark and −50% risk-free.

The question is quite confusing just based on what’s provided in the curriculum. All three would justify a closet index fund.

Taken directly from the curriculum:

"closet index fund” (a fund that advertises itself as being actively managed but is actually close to being an index fund) will have a Sharpe ratio that is close to the benchmark because the excess return and volatility will be similar to the benchmark. However, the closet index fund will have a small amount of active risk, although positive by definition like any volatility estimate. While there may be little active risk, the information ratio of a closet index fund will likely be close to zero or slightly negative if value added cannot overcome the management fees

The point is that while this is true, its converse isn’t.