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3 return and risk

# 3 return and risk - What Practitioners Need To Know About...

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What Practitioners Need To Know . . . About Retum and Risk 14 Mark Kritzman Windham Capital Management At first glance, return and risk may seem to be straightforward concepts. Yet closer inspection reveals nuances that can have im- portant consequences for deter- mining the appropriate method for evaluating financial results. This column reviews various measures of return and risk with an emphasis on their suitability for alternative uses. Retum Perhaps the most straightforward rate of return is the holding- period return. It equals the in- come generated by an investment plus the investment's change in price during the period the in- vestment is held, all divided by the beginning price. For example, if we purchased a share of com- mon stock for \$50.00, received a \$2.00 dividend, and sold the stock for S55.00, we would have achieved a holding-period return equal to 14.00%. In general, we can use Equation (1) to compute holding-period returns. Eq. 1 HPR = {I + E - B)/B where HPR = holding-period retum, I = income, E = ending price and B = beginning price. Holding-period returns are also referred to as periodic retums. Dollar-Weighted versus Time-Weighted Rates of Retum Now let us consider rates of re- turn over multiple holding peri- ods. Suppose that a mutual fund generated the following annual holding-period returns from 1988 through 1992: 1988 1989 1990 1991 1992 -5.00% -15.20% 3.10% 30.75% 17.65% Suppose further that we had in- vested \$75,000 in this fund by making contributions at the be- ginning of each year according to the following schedule: 1988 1989 1990 1991 1992 S5,000 \$10,000 \$15,000 \$20,000 \$25,000 By the end of 1992, our invest- ment would have grown in value to \$103,804.56. By discounting the ending value of our invest- ment and the interim cash flows back to our initial contribution, we can determine the invest- ment's dollar-weighted rate of re- turn, which is also referred to as the internal rate of return: 5000= - 10000 15000 (1 -H r) (1-H 20000 25000 103805 7 "r P, (1 -Hr)^ (1 + DWR = 14.25% We enter the interim contribu- tions as negative values, because they are analogous to negative dividend payments. Although we cannot solve directly for the dol- lar-weighted rate of return, most financial calculators and spread- sheet software have iterative algo- rithms that quickly converge to a solution. In our example, the so- lution equals 14.25%. The dollar-weigh ted rate of re- tum measures the annual rate at which our cumulative contribu- tions grow over the measurement period. However, it is not a reli- able measure of the performance of the mutual fund in which we invested, because it depends on the timing of the cash flows. Sup- pose, for example, we reversed the order of the contributions. Given this sequence of contribu- tions, our investment would have grown to a higher value— \$103,893.76. The dollar-weighted rate of return, however, would have been only 9.12%: 25000= - 10000 20000 15000 (1 + r) (1-H r)^ 5000 103894 DWR = 9.12% In order to measure the underly- ing performance of the mutual fund, we can calculate its time- weighted rate of retum. This mea- sure does not depend on the timing of cash flows.

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