MBA Finance: Geometric Mean vs Arithmetic Mean of an Investment

There are still many investors and traders enjoy the thrill of fast profits from high-growth or cheap stocks by only doing a modicum of analysis.  This type of impulsive and intuitive style of trading can goad on a phase of vicissitude for the investor, especially if they have already captured profits with a paucity of research in the macroeconomic trends that increase or decrease uncertainty in the security.  This superfluous sense of certainty gives the trader a false sense of confidence and competence, along with the steadfast position of maintaining a certain investing mental model will most likely later obfuscate the trader when a long-term investor comes along and shares his or her idea in in regards to finding the value of an appropriate return of a security.

Finding returns for a particular security matter, especially for investment managers, as they must track performance for construction appropriate portfolios for their clients.  The first step in finding returns is to find out the holding-period return (HPR), which is a key measure of a stock's success for the duration of an investment period.  The calculation of HPR is as follows:

HPR = ((Ending price - Beginning price + Cash dividend) / Beginning price))

Similar to conducting a ratio analysis and finding "the story between the numbers", so too must the tyro or intermediate trader realize that there are two discrete averages must be calculated to find the "drama between the numbers".  Thus, two averages are worth learning to calculate after a portfolio has been constructed: the geometric average and the arithmetic average.

Geometric Mean

The geometric average is the single per-period return that gives the same cumulative performance as the sequence of actual returns.  This calculation of the mean for financial securities compounds the actual period-by-period returns and then finds the equivalent single per-period return.

Quarterly Rates of Return for a Mutual Fund
	1st QTR	2nd QTR	3rd QTR	4th QTR
Assets under management	1.4	1.6	2.0	0.8
Holding-period return (%)	6.0	15.0	-10.0	25.0

The geometric mean for this mutual fund would be calculated as follows:

R_c = (1 + 0.6) x (1 + .15) x (1 – 0.1) x (1 + 0.25)^1/4 – 1 = 0.1600, or 16%

Arithmetic Mean

The arithmetic mean is much simpler to calculate, but also is useful because it is the best forecast of performance in future periods,

Arithmetic mean = (6 + 15 - 10 + 25) /4 = 9%

Unlike the geometric mean, the arithmetic mean ignores compounding, but can track performance unlike the geometric mean during changes in the stock price for a given period.

Conclusion

Calculating the mean which is approbatory for calculating returns is an imperative step before making any decisions for one's mutual fund or portfolio.  These options to calculate returns will help the trader to realize there are deeper levels of learning, in contrast to following one guru or method for investing in stocks.

To learn more about MBA Aces with Blumeyer, send me a question at mblumeyer@gmail.com

Also, check out my Instagram @mblumeyer