Measures of Historical Rates of Return

When you are evaluating alternative investments for inclusion in your portfolio, you will often become paring investments with widely different prices or lives. As an example, you might want to compare a $10 stock that pays no dividends to a stock selling for $150 that pays dividends of $5 a year. To properly evaluate these two investments, you must accurately compare their histor-ical rates of returns. A proper measurement of the rates of return is the purpose of this section.  When we invest, we defer current consumption in order to add to our wealth so that we can consume more in the future. Therefore, when we talk about a return on an investment, we are concerned with the change in wealth resulting from this investment. This change in wealth can be either due to cash inflows, such as interest or dividends, or caused by a change in the price of the asset (positive or negative).If you commit $200 to an investment at the beginning of the year and you get back $220 at the end of the year, what is your return for the period? 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). In this example, the HPR is 1.10, calculated as follows:

HPR = Ending Value of Investment/Beginning Value of Investment

= 220/200 = 1.10

This value will always be zero or greater—that is, it can never be a negative value. A value greater than1.0 reflects an increase in your wealth, which means that you received a positive rate of return during the period. A value less than 1.0 means that you suffered a decline in wealth, which indicates that you had a negative return during the period. An HPR of zero indicates that you lost all your money.  Although HPR helps us express the change in value of an investment, investors generally evaluate returns in percentage terms on an annual basis.  This conversion to annual percentage rates makes it easier to directly compare alternative investments that have markedly different characteristics. The first step in converting an HPR to an annual percentage rate is to derive a percentage return, referred to as the holding period yield (HPY). The HPY is equal to the HPR minus 1.

1.2                          HPY =HPR – 1

In our example:

HPY =1.10 – 1 =0.10=10%

To derive an annualHPY,you compute an annualHPR and subtract 1. Annual HPR is found by:➤

1.3                          Annual HPR =HPR1/n

where:

n=number of years the investment is held Consider an investment that cost $250 and is worth $350 after being held for two years: