THE CITY UNIVERSITY OF NEW YORK
MSB: 710 – INVESTMENT ANALYSIS
Chapter 5: Risk and Return
Instructor: Mario A. Gonzalez Corzo, Ph.D.
Topic: The Geometric Average Return (or Time-Weighted Return)
The geometric average of quarterly returns is equal to the single-period return that would give the same cumulative performance as the sequence of actual returns. The geometric average is calculated by compounding the actual period returns and then finding the equivalent single-period return.
Sample Mutual Fund: Quarterly Returns
In the absence of Excel, for the example provided above, the geometric average quarterly return (rg) can be calculated as follows:
(1) (1 +R1) x (1+R2) x (1+R3) … (1+Rn) = (1+RG) n
Please note that in the above notation R represents the realized returns (or HPRs) for the Sample Mutual Fund.
Applying Equation (1) to the HPRs for our Sample Mutual Fund, we obtain:
(2) (1 + 0.10) x (1 + 0.25) x (1 – 0.20) x (1+0.25) = (1+RG) 4
Solving Equation (2) for RG (geometric average return), we obtain:
(3) (1.10) x (1.25) x (0.80) x (1.25) = (1+RG) 4
RG = [(1.10) x (1.25) x (0.80) x (1.25)] ¼ - 1
RG = [1.375] ¼ - 1
RG = 1.082868 – 1
RG = 0.082868
RG = 0.0829
The left-hand side of Equation (3) represents the compounded year-end value of a $1 investment earning the four quarterly returns (HPRs) generated by Sample Mutual Fund.
The right-hand side of Equation (3) is the compounded value of $1 earning the geometric average return (RG) each quarter.
The geometric average return is also known as the time weighted average return because it ignores the quarterly volatility in the funds under management.
One of the advantages of the geometric average (or time-weighted average) return is that it ignores variations in assets (or money) under management.
In practice, published data on...