Question: The arithmetic average continuously compounded or log gross discrete return (AALGDR) on the ASX200 accumulation index over the 24 years from 31 Dec 1992 to
The arithmetic average continuously compounded or log gross discrete return (AALGDR) on the ASX200 accumulation index over the 24 years from 31 Dec 1992 to 31 Dec 2016 is 9.49% pa. The arithmetic standard deviation (SDLGDR) is 16.92 percentage points pa. Assume that the log gross discrete returns are normally distributed and that the above estimates are true population statistics, not sample statistics, so there is no standard error in the sample mean or standard deviation estimates. Also assume that the standardised normal Z-statistic corresponding to a one-tail probability of 97.5% is exactly 1.96. You have a $1 million fund that replicates the ASX200 accumulation index.
Which of the following forecast continuously compounded returns (LGDR) over the next 9 years is NOT correct? Over the next 9 years the:
(a) 97.5th percentile continuously compounded return is 383.9% per 9 years.
(b) Mean continuously compounded return is 85.4% per 9 years.
(c) Median continuously compounded return is 85.4% per 9 years.
(d) Mode continuously compounded return is 85.4% per 9 years.
(e) 2.5th percentile continuously compounded return is -14.1% per 9 years.
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