Question

From January 2017 through December 2019 the manager of "Australia's Best" mutual fund did really well in timing the market. The manager was able to earn a holding period return of 32%, beating the market by 12% over the same period. After 3 years of strong performance, investors took notice and invested millions of dollars in the fund at the start of 2020 , doubling the funds under management in a very short time. Unfortunately, the fund manager wasn't so lucky since the start of 2020, earning an HPR of only 1% returns from January 2020 till now, underperforming the market by 7%. You calculated the arithmetic, geometric, and dollar-weighted average returns for the fund. Which return is the lowest? Geometric average return Insufficient information to determine Dollar-weighted return Arithmetic average return

Answer 1

the lowest return among the arithmetic average return and the geometric average return is the arithmetic average return of 16.5%.

Step-by-step explanation:

Based on the information provided, we can determine the lowest return among the arithmetic average return, geometric average return, and dollar-weighted return.

The arithmetic average return is the simple average of the annual returns over the specified period. In this case, the arithmetic average return for the fund would be (32% + 1%)/2 = 16.5%.

The geometric average return, also known as the compound average growth rate, takes into account the compounding effect of returns over time. It is calculated by taking the nth root of the product of (1 + R1)(1 + R2)...(1 + Rn) - 1, where R1, R2, ..., Rn are the individual annual returns. Since we only have two returns (32% and 1%), we can calculate the geometric average return as (1 + 0.32)^(1/2) - 1 = 0.173 or 17.3%.

The dollar-weighted return considers the timing and magnitude of cash flows into and out of the fund. However, the information provided does not include details on the specific cash flows or investment amounts, so we cannot calculate the dollar-weighted return.

Therefore, based on the information given, the lowest return among the arithmetic average return and the geometric average return is the arithmetic average return of 16.5%.