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Computing Mean Historical Returns

Computing mean historical returns allows investors to evaluate the typical performance of a single investment or portfolio over multiple years. The arithmetic mean return is calculated by summing all annual returns and dividing by the total number of years. Alternatively, the geometric mean return finds the nth root of the product of annual returns over several years. These mean returns provide summary measures of an investment or portfolio's rate of return that can be expected over an extended period of time.

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216 views

Computing Mean Historical Returns

Computing mean historical returns allows investors to evaluate the typical performance of a single investment or portfolio over multiple years. The arithmetic mean return is calculated by summing all annual returns and dividing by the total number of years. Alternatively, the geometric mean return finds the nth root of the product of annual returns over several years. These mean returns provide summary measures of an investment or portfolio's rate of return that can be expected over an extended period of time.

Uploaded by

mubarek oumer
Copyright
© © All Rights Reserved
Available Formats
Download as DOCX, PDF, TXT or read online on Scribd
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Remember one final point: The ending value of the investment can be the result of a positive or

negative change in price for the investment alone (for example, a stock going from $20 a share to
$22 a share), income from the investment alone, or a combination of price change and
income.Ending value includes the value of everything related to the investment.

Computing Mean Historical Returns

Now that we have calculated the HPY for a single investment for a single year, we want to
consider mean rates of return for a single investment and for a portfolio of investments. Over a
number of years, a single investment will likely give high rates of return during some years and
low rates of return, or possibly negative rates of return, during others. Your analysis should
consider each of these returns, but you also want a summary figure that indicates this
investment’s typical experience, or the rate of return you should expect to receive if you owned
this investment over an extended period of time. You can derive such a summary figure by
computing the mean annual rate of return for this investment over some period of time.

Alternatively, you might want to evaluate a portfolio of investments that might include similar
investments (for example, all stocks or all bonds) or a combination of investments (for example,
stocks, bonds, and real estate). In this instance, you would calculate the mean rate of return for
this portfolio of investments for an individual year or for a number of years. Single Investment
Given a set of annual rates of return (HPYs) for an individual investment, there are two summary
measures of return performance. The first is the arithmetic mean return, the second the geometric
mean return. To find the arithmetic mean (AM), the sum (∑) of annual HPYs is divided by the
number of years (n) as follows:

AM =∑HPY/n

where:

∑HPY = the sum of annual holding period yields

An alternative computation, the geometric mean (GM), is the nth root of the product of the
HPRs for n years.
where:

the product of the annual holding period returns as follows:

( HPR1) × (HPR2) ... (HPRn)

To illustrate these alternatives, consider an investment with the following data:

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