Portfolio Evaluation - chapt 24

# Portfolio Evaluation - chapt 24 - Portfolio Evaluation Rate...

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Portfolio Evaluation Rate of Return = Amount you made Amount you invested Example: Buy a stock for \$100 and at end of year it is worth \$106, plus you received a \$2 dividend. Rate of Return = (106 – 100) + 2 = 8 = 8% 100 100 Dollar-Weighted Returns At the end of the first year, you buy another share. At the end of the second year, you receive another \$2 dividend (per share) and the share price is \$110. -100 ____________-106; +2 _________+4; +220 0 1 2 Find the Internal Rate of Return (IRR) to get the dollar-weighted rate of return 0 = -100 106 + 2 + 4 + 220 = -100 104 + 224 1+r 1+r (1+r) 2 (1+r) 2 1+r (1+r) 2 r = 6.442% It is dollar-weighted because the second year (when more dollars are invested) gets more weighting than the first year. Time-weighted Returns We already saw that the return in the first year was 8%. Find the return in the second year in the same manner. (220 – 212) + 4 = 12 = 5.66% 212 212 Now, average together the two returns: 8% + 5.66% = 6.83% 2 In this example, since the second year did worse than the first year, and there were more dollars invested in the second year, the dollar-weighted average is lower than the time- 1

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weighted average. If you did better in the time period when you had more money invested, the dollar-weighted average would be higher. Most money managers are evaluated using time-weighted averages rather than dollar- weighted averages, because the amount of money they manage is generally not under their control. Arithmetic Averages vs. Geometric Averages We covered this briefly in FINC 654. Geometric Average Return – The compounded annual return earned by an investor who bought the security and held it for ‘T’ years. This is equivalent to earning this return each year and reinvesting the earnings at the end of each year. Geometric Average Return = [Π (1+R t )] 1/T – 1 Note that [Π (1+R t )] is often referred to as the buy-and-hold return. Example: Let’s take the hypothetical returns for Freeman Corp. 2001 .05 2002 .09 2003 -.12 2004 .20 f8e5 R = .05 + .09 - .12 + .20 = .22 = .055 = 5.5% = Arithmetic Average Return 4 4 Geometric Mean = [(1.05) (1.09) (0.88) (1.20)] 1/4 – 1 = 4.85% Note that the geometric average is always less than or equal to the arithmetic average. The difference between the two becomes greater; the more variance there is in the returns. A general rule is that the geometric average is approximately equal to the arithmetic average minus half of the variance.
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