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IAI Actuarial Core Principles · Economic Modelling · Rational expectations theory and the efficient markets hypothesis

A fund manager charges 1.2% a year in costs. A passive index fund returns 11% a year gross of costs with costs of 0.2%. The manager's gross return is 11.9% a year, before the 1.2% costs. Assuming returns are accurately stated, which statement is correct for an investor and consistent with a market that is efficient after costs?

The active manager nets 10.7% (11.9% less 1.2%) while the passive fund nets 10.8% (11% less 0.2%). Gross outperformance is more than eaten up by higher costs, which is consistent with markets being efficient after costs and favours passive holding.

  1. AThe active manager beats the passive fund by 0.9% net, which proves the manager has skill
  2. BThe active manager's net return is 10.7%, below the passive net return of 10.8%, consistent with efficient marketsCorrect
  3. CThe active manager's net return is 10.7%, above the passive net return of 10.8%
  4. DThe active manager's net return is 12.0%, so the active fund is preferred
  5. The two funds have identical net returns of 10.8%

Explanation

Active net return = 11.9% - 1.2% = 10.7%. Passive net = 11% - 0.2% = 10.8%. The active fund underperforms by 0.1% net, even though it slightly outperformed gross (11.9% vs 11%). Gross outperformance being absorbed by higher costs is consistent with efficiency after costs. Option 1 and 3 misstate the arithmetic.

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