12-0 Dollar Returns 12.1 Total dollar return = income from investment + capital gain (loss) due to change in price Example: You bought a bond for $950 1 year ago. You have received two coupons of $30 each. You can sell the bond for $975 today. What is your total dollar return? Income = = 60 Capital gain = 975 – 950 = 25 Total dollar return = = $85 LO1 © 2013 McGraw-Hill Ryerson Limited

12-1 Percentage Returns It is generally more intuitive to think in terms of percentages than dollar returns Dividend yield = income / beginning price Capital gains yield = (ending price – beginning price) / beginning price Total percentage return = dividend yield + capital gains yield LO1 © 2013 McGraw-Hill Ryerson Limited

12-2 Example – Calculating Returns You bought a stock for $35 and you received dividends of $1.25. The stock is now selling for $40. What is your dollar return? Dollar return = (40 – 35) = $6.25 What is your percentage return? Dividend yield = 1.25 / 35 = 3.57% Capital gains yield = (40 – 35) / 35 = 14.29% Total percentage return = = 17.86% LO1 © 2013 McGraw-Hill Ryerson Limited

12-3 More on Average Returns 12.5 There are many different ways of calculating returns over multiple periods Two methods are: Arithmetic Average Return Geometric Average Return LO1 © 2013 McGraw-Hill Ryerson Limited

12-4 Arithmetic vs. Geometric Average Example You invested $100 in a stock five years ago. Over the last five years, annual returns have been 15%, -8%, 12%, 18% and -11%. What is your average annual rate of return? What is your investment worth today? LO1 © 2013 McGraw-Hill Ryerson Limited

12-5 Calculating Arithmetic Average The return in an average year was 5.2%. LO1 © 2013 McGraw-Hill Ryerson Limited

12-6 What is the investment worth today? FV=$100(1+.15)(1-.08)(1+.12)(1+.18)(1-.11) FV=$ LO1 © 2013 McGraw-Hill Ryerson Limited

12-7 Calculating Geometric Average Continued What equivalent rate of return would you have to earn every year on average to achieve this same future wealth? Your average return was 4.47% each year. Notice that this is lower than the arithmetic average. This is because it includes the effects of compounding. LO1 © 2013 McGraw-Hill Ryerson Limited

12-8 Geometric Average The general formula for calculating the geometric average return is the following: LO1 © 2013 McGraw-Hill Ryerson Limited

12-9 Geometric vs. Arithmetic Average Returns LO1 INSERT NEW TABLE 12.5 HERE © 2013 McGraw-Hill Ryerson Limited