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This means that an investment of $100 that yields an arithmetic return of 50% followed by an arithmetic return of −50% will result in $75, while an investment of $100 that yields a logarithmic return of 50% followed by a logarithmic return of −50% will come back to $100. Logarithmic return is also called the continuously compounded return.
The Törnqvist or Törnqvist-Theil index is the geometric average of the n price relatives of the current to base period prices (for n goods) weighted by the arithmetic average of the value shares for the two periods. [16] [17]
The Brinson model performance attribution can be described as "arithmetic attribution" in the sense that it describes the difference between the portfolio return and the benchmark return. For example, if the portfolio return was 21%, and the benchmark return was 10%, arithmetic attribution would explain 11% of value added. [11]
If this instantaneous return is received continuously for one period, then the initial value P t-1 will grow to = during that period. See also continuous compounding . Since this analysis did not adjust for the effects of inflation on the purchasing power of P t , RS and RC are referred to as nominal rates of return .
[2] [3] This is not literally a tax in the sense of a levy imposed by a government, but the mathematical difference between geometric averages compared to arithmetic averages. This difference resembles a tax due to the mathematics which impose a lower compound return when returns vary over time, compared to a simple sum of returns.
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The real return on investment is what you earn after returns are adjusted for inflation and taxes. Nominal returns, on the other hand, don't account for those deductions. Understanding …
The information ratio is often annualized. While it is then common for the numerator to be calculated as the arithmetic difference between the annualized portfolio return and the annualized benchmark return, this is an approximation because the annualization of an arithmetic difference between terms is not the arithmetic difference of the annualized terms. [6]