# Geometric Mean Maximization

First, when investing it is important to distinguish between geometric returns and arithmetic returns.  Geometric mean returns measure the average rate at which investment returns compound over a given period of time.  The geometric or compound return represents the return that is achieved through reinvestment whereas the arithmetic return is simply the average of a series of returns over a given period of time.  The geometric mean will always be equal to or less than the arithmetic mean.  There are a couple of reasons why the geometric mean is important in the context of retirement finances.  First, for most people financial planning for retirement involves taking a sum of money and both: a) making it last, and; b) turning it into income.  The compounding effects reflected in geometric mean returns are the primary driver of the terminal wealth that is the basis of retirement finances.  Second, the volatility of returns is the key factor in the difference between geometric returns and arithmetic returns (see the definition for volatility drag).  Consider, for example, the person who invests \$100 and has a 100 percent return during year 1 followed by a 50 percent loss during year 2.  This person’s arithmetic return is 25 percent, while the geometric return over the same period is actually zero (start with \$100, double to \$200 after the first year, then back to \$100 after the 50 percent loss during the second year).  Which return is more relevant for the person who will be spending whatever money is there at the end of the investing period? Also note how hazardous volatility is to compound performance (again, see the definition for volatility drag).  Geometric mean maximization is simply a focus on maximizing the geometric mean or the growth rate of money that is invested.  Geometric mean maximization should be considered highly relevant to anyone who is concerned about the amount of actual funds available after a period of saving and investing.

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