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Arithmetic and Compounded Average Returns
When optimizing the allocation of assets in an investment portfolio the goal is that they will produce a certain average annual return in addition to doing so with a minimum variation about this average. There are two ways in which returns can be evaluated, as an Arithmetic Average or as a Compound Average. These two can be significantly different from each other and the consequences of this difference to the value of a portfolio can grow significantly with time.
Examples:
An example of an Arithmetic Average return is as follows: An asset class produces annual returns over a three year period of +8%, -5% , and +12%, the Arithmetic Average return is:
(8 –5 +12) /3 =5.00%
The Compounded Average annual return is a bit more complicated to calculate. For this same example it is:
(((1 +8/100) x (1 +5/100) x (1 +12/100) )1/3 –1 ) x100 =4.74%
The Arithmetic Average is higher because it unfairly weights percentage gains equally with percentage losses. If one asset class experiences a50% loss in any one year then a50% gain the next year will not entirely recoup the earlier loss but will in fact recoup only one half that loss. The Arithmetic Average return of the two years is zero but there is still an overall loss over the two years as shown by the Compound Average return which in this case would be -13.4%. It actually takes a100% gain to recover from a50% loss. In this way, a Compounded Average return actually numerically weights losses more heavily than gains.
In general, the Arithmetic Average will be greater than or equal to the Compounded Average with the difference between the two averages positively related to the Arithmetic Average standard deviation of the data. In the following approximation formula the variance is the standard deviation squared.
Compound Average = Arithmetic Average-variance/(2*(1+Arithmetic Average))
An ideal compounding rate would be unbiased in the weighting of gains and losses. For short investment horizons the Arithmetic Average is closer to this ideal and is a better measure for predicting what is more likely to occur in a single time period. A Compounded Average on the other hand is more representative for what is likely to occur over many time periods in terms of the long term accumulation of wealth.
Compound annual return n = root selling price / purchase price -1 *100%
= Compound annual return is used to measure long-term investments (more than one year)
the arithmetic mean is a set of financial returns divided by the number of periods for these financial returns
Average Arithmetic Mean is computed by dividing the difference of total amount at some future date and original deposit amount by the original deposit.
Compound Rate is the rate of return by which a deposit grows annually.
In my opinion, average arithmetic mean should be greater as it includes effect of interest cumulated from year to year.
Venkitaraman explained all very well.
An arithmetic average is the sum of a series of numbers divided by the count of that series of numbers.
Compound Annual Return- the rate of return which, if compounded over the years covered by the performance history, would yield the cumulative gain or loss actually achieved by the trading program during that period.
I would say arithmetic average is higher.
I agree with mr georgesi assistant
agree with venkitaraman
with full respect
I agree with some of the answers provided.
Who preceded me do good answers I agree with them.
Great question. But I'm not sure what do you mean by "Arithmetic average"?
What I know is either "Arithmetic mean" or "Average", and they are different.
