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FRM Part II · FRM Exam Part II · Illiquid Assets

A real estate fund reports observed appraisal returns that follow r_obs(t) = 0.6 r_true(t) + 0.4 r_obs(t-1). True returns are serially uncorrelated with variance of 100 (in %-squared terms). Using the relationship for this partial-adjustment (AR(1)) process, what is the approximate variance of observed returns?

Observed variance is about 42.9. Using the AR(1) smoothing formula, variance equals 0.6 squared times 100 divided by one minus 0.4 squared, which is 36 divided by 0.84. This is well below the true variance of 100, showing how appraisal smoothing understates risk.

  1. AApproximately 36.0
  2. BApproximately 42.9Correct
  3. CApproximately 60.0
  4. DApproximately 100.0

Explanation

For r_obs = a r_true + b r_obs(t-1) with a=0.6, b=0.4, Var(obs) = a²·Var(true)/(1−b²) = 0.36×100/(1−0.16) = 36/0.84 = 42.86. Option 36 ignores the lag term's contribution; 100 ignores smoothing.

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