# Measures of Historical Rates of Return

Some people like to give up immediate possession of savings expect to receive in the future a greater amount than they gave up. What they do with the savings to make them increase over time is investment.

Specially, an investment is the current commitment of dollars for a period of time in order to derive future payments that willcompensate the invester for (1) the time the funds are committed,(2) the expected rate of inflaiton,and (3) the uncertainty of thefuture payments. The “investor” can be an individual, a government, a pension fund, or a corporation. This definition includes all types of investment, including investment by corporations in plant and equipment and investments by individuals in stocks, bonds, commodities, or real estate. In all cases, the investor is trading a known dollar amount today for some expected future stream of payments that will be greater than the current outlay.

A central question is how investors select investments that will give them their required rates of return, that is, how to choose among alternative investment assets. This selection process requires that you must understand how to measure the rate of return and the risk involved in an investment accurately.

Measures of Historical Rates of Return

The period during which you own an investment is called its holding period, and the return for that period is the holding period return (HPR). It is caculated as follows:

HPR = Ending value of investment / Beginning value of investment

This value will always be zero or greater. A value greater than 1.0 reflects an increase in your wealth. A value less than 1.0 means that you suffered an decline in wealth. A HPR of zero indicates that you lost all you money.

Investors generally evaluate returns in percentage terms on an annual basis. The percentage return is referred to as the holding period yield (HPY). The HPY is equal to the HPR minus 1.

HPY = HPR – 1

To derive an annual HPY, you compute an annual HPR and subtract 1. Annual HPR is found by:
Annual HPR = HPR exponent(1/n)
n = number of years the investment is held

Note that we made some implicit assumptions when converting the HPY to an annual basis. This annualized holding period yield computation assumes a constant annual yield for each year.

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