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Weigh up how biases affect the returns reported for illiquid assets.

FRM® Part II · Risk Management and Investment Management · Illiquid Assets · FRM2.IM.17.c

The idea

Reported returns on illiquid assets are biased, usually in a flattering direction. Smoothing arises because values come from appraisals or stale prices that adjust slowly. As a result reported volatility is understated, returns show positive autocorrelation, correlation and beta with liquid markets are understated, and the Sharpe ratio is overstated. Survivorship bias arises when funds that fail drop out of a database, so average returns of survivors overstate what an investor in the full group earned. Selection bias arises because managers choose whether to report. Backfill or instant-history bias arises when a fund joins a database and its earlier, usually good, record is added. Consequences are an apparent free lunch in diversification and too large an allocation to illiquid assets. The exam point: smoothing hides risk, while survivorship, selection and backfill inflate average return.

A practice question

From the question bank, with the reason each wrong option is wrong.

Reported returns on an asset are based on appraisals that adjust slowly to market changes. Which pair of effects does this smoothing produce?

  1. Overstated volatility and negative autocorrelation of reported returns.Why not: Reverses both effects; slow adjustment damps changes and creates positive autocorrelation.
  2. Understated average return and overstated correlation with equities.Why not: Smoothing leaves the average return roughly unchanged and understates, not overstates, correlation.
  3. Understated volatility and positive autocorrelation of reported returns. - correct
  4. Overstated volatility and positive autocorrelation of reported returns.Why not: Gets autocorrelation right but reverses the volatility effect: smoothing damps swings.

Smoothed returns spread each true move over several periods, so reported volatility, correlation and beta are too low while autocorrelation is positive.

A harder one

A hedge fund begins reporting to a database after three years of strong returns, and the database then adds those three years to its history. Which bias does this create?

  1. Survivorship bias.Why not: Survivorship concerns funds that disappear; here a successful fund enters with its history added.
  2. Backfill (instant history) bias. - correct
  3. Smoothing bias.Why not: Smoothing concerns slow-moving valuations of the assets, not how a fund enters a database.
  4. Look-through bias in the benchmark.Why not: Not a recognised bias for hedge fund databases, and unrelated to how a fund's history is added.

Managers tend to list after good performance, and the database back-fills the record. Early history is thus drawn from funds that chose to be listed, inflating average returns.

The hardest tier

A database begins with 200 funds. During the sample 40 funds close, with an average annual return of -4 percent. The 160 survivors average 10 percent a year. The survivors-only average therefore overstates the average for all 200 funds by (in percentage points):

  1. 14.0Why not: Uses the full gap between survivors and failures instead of weighting it by the 20 percent share of failures.
  2. 2.0Why not: Multiplies the failure share (0.2) by the survivors' return instead of by the gap between the two groups.
  3. 0.8Why not: Multiplies the failure share by the failures' return alone, ignoring the survivors' return.
  4. 2.8 - correct

All-fund average = 0.8 x 10 + 0.2 x (-4) = 7.2. Bias = 10 - 7.2 = 2.8, which equals 0.2 x (10 - (-4)).

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