The Geometric Mean?
The Geometric Means Calculate the average of items used to evaluate investment or portfolio performance. The technical term is “the nth root product of n numbers.” When working with percentages, utilize the geometric mean, while the usual arithmetic mean works with the values themselves.
Geometric Mean Formula and Calculation
μgeometric=[(1+R1)(1+R2)…(1+Rn)]1/n−1
where:
R1…Rn represents asset returns or other observations for averaging.
To compute compound interest using the geometric mean of an investment’s return, multiply $10,000 by 10% to get $1,000 in year one. The new primary is $11,000 in year two, and 10% is $1,100. Also, the new principle is $11,000 + $1,100, or $12,100.
The new principal is $12,100 in year three, and 10% is $1,210. After 25 years, $10,000 becomes $108,347.06 or $98,347.05 more than the initial investment. Shortcut: multiply the current principal by one plus the interest rate, then raise the factor to the number of years compounded. To calculate, multiply $10,000 by (1+0.1) 25 to get $108,347.06.
Understanding Geometric Mean
Calculated using the products of terms, the geometric mean (also known as compounded annual growth rate or time-weighted rate of return) is the average rate of return. That means what? The geometric mean multiplies many numbers and raises them to the 1/nth power.
Using the geometric mean to calculate portfolio performance is crucial due to its ability to account for compounding effects.
Geometric mean computation is easy with 2 and 8. I am multiplying two by eight, which yields four as the square root (½ power), as there are only two numbers. Calculating without a calculator or computer software is more arduous when several numbers exist.
Critical compounding and geometric mean become more applicable with larger time horizons.
The geometric mean’s key value is that it concentrates solely on return numbers and provides an “apples-to-apples” comparison of two investment alternatives over many periods. Unlike the essential average arithmetic mean, geometric means are always somewhat smaller.
Example of Geometric Mean
If you obtain 10% interest on $10,000 for 25 years, you get $1,000 in interest, or $25,000. This ignores interest. The calculation implies you only earn interest on the $10,000, not the $1,000 added annually. Investors get compound interest in the form of interest on interest, computed using the geometric mean.
Analysts may compute the return on an interest-bearing investment using the geometric mean. Portfolio managers recommend reinvesting dividends and earnings for this reason.
We employ the geometric mean in cash flow computations for present and future values. The geometric mean return is for compounding investments. Instead of $25,000 on a primary interest investment, the investor makes $108,347.06 on compound interest.
The geometric mean represents compound interest or return, while the arithmetic mean represents simple interest.
Excel: How to Find Geometric Means
Excel’s shorthand for geometric mean is “=GEOMEAN.” Enter the function into a cell and list the numbers (or cells with numbers) to calculate the geometric mean.
Can You Calculate the Geometric Mean With Negative Values?
Calculating a geometric mean with negative integers is impossible.
How Do You Find Two Numbers’ Geometric Mean?
Multiply two integers and take the square root to find their geometric mean.
The Verdict
The computed geometric mean is a statistical tool that can help assess investment portfolio performance. It can help investors assess their portfolios and make modifications.
Conclusion
- Geometric means are the average return rates of values obtained by multiplying terms.
- The geometric mean is best for serially correlated series, like investment portfolios.
- Bond yields, stock returns, and market risk premiums affect most financial returns.
- Since year-over-year compounding smooths the average, the geometric average gives a more accurate return measurement for volatile data.
