Skip to content

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

A fund in India reports annual returns relative to a benchmark over 25 years. Its average alpha is 1.2% a year with a standard error of 0.6% a year. Using a two-sided test at the 5% level (critical value 1.96) of the null that true alpha is zero, which conclusion is correct?

The t-statistic is 1.2 divided by 0.6, which equals 2.0, exceeding 1.96, so zero alpha is rejected at 5%. But if the fund was picked from many, chance or data mining could explain it, so it does not prove market inefficiency.

  1. AThe t-statistic is 2.0, so the null is rejected, but the evidence alone does not rule out data mining across many funds screenedCorrect
  2. BThe t-statistic is 0.5, so the null is not rejected
  3. CThe t-statistic is 2.0, so the market is proven strong-form inefficient
  4. DThe t-statistic is 1.2, so the null is rejected
  5. The t-statistic is 0.72, so the null is not rejected

Explanation

t = 1.2/0.6 = 2.0, which exceeds 1.96, so the null of zero alpha is rejected at 5%. However, if this fund was selected from many funds, some would show significant alpha by chance, so this does not prove inefficiency. The other t-values are miscalculated (0.5 inverts the ratio, 0.72 multiplies).

Did you get it right without looking?

One question tells you little. A timed set on Rational expectations theory and the efficient markets hypothesis shows your real accuracy, how long you take and where you lose marks.

Practise Rational expectations theory and the efficient markets hypothesisFree diagnostic mock

More Rational expectations theory and the efficient markets hypothesis questions