12-1

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 = 30 + 30 = 60• Capital gain = 975 – 950 = 25• Total dollar return = 60 + 25 = $85

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12-2

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

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12-3

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 = 1.25 + (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 = 3.57 + 14.29 = 17.86%

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12-4

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

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12-5

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?

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12-6

Calculating Arithmetic Average

5.2 R

5

)11(1812)8(15 Return Average Arithmetic

A

AR

• The return in an average year was 5.2%.

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12-7

What is the investment worth today?

• FV=$100(1+.15)(1-.08)(1+.12)(1+.18)(1-.11)• FV=$124.44

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12-8

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.

%47.4

12444.1

)1(100$44.124$

51

5

G

G

G

R

R

R

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12-9

Geometric Average

• The general formula for calculating the geometric average return is the following:

1R1...R1R1 Return Average Geometric1

T21 T

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12-10

Geometric vs. Arithmetic Average Returns 1957-2011

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© 2013 McGraw-Hill Ryerson Limited