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07%20risk%20and%20return%20test%20bank%20problems%20solutions

# 07%20risk%20and%20return%20test%20bank%20problems%20solutions

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FNAN 301 Solutions to test bank problems – risk and return Some answers may be slightly different than provided solutions due to rounding 1. A stock had returns of 9.0%, 3.0%, -7.0%, and 7.0% over the past four years. a. What was the arithmetic mean annual return? b. What was the compound annual return? Arithmetic annual return = [9.0% + 3.0% + (-7.0%) + 7.0%] / 4 = 12.0% / 4 = 3.0% = [.090 + .030 + (-.070) + .070] / 4 = .120 / 4 = .030 = 3.0% Geometric annual return = [(1 + .090)(1 + .030)(1 – .070)(1 + .070)] 1/4 – 1 = [1.11720] 1/4 – 1 = .0281 = 2.81% 1

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FNAN 301 Solutions to test bank problems – risk and return 2. A stock had returns of 5%, 8%, -3%, 10%, and 7% over the past five years. a. What was its arithmetic average return? b. What was its geometric return? Arithmetic return = [5% + 8% + (-3%) + 10% + 7%] / 5 = 27% / 5 = 5.4% Geometric return = [(1 + .05)(1 + .08)(1 – .03)(1 + .10)(1 + .07)] 1/5 – 1 = [1.2947] 1/5 – 1 = 5.30% 2
FNAN 301 Solutions to test bank problems – risk and return 3. Over the past 4 years, McDulles stock has had the following returns: 18%, -22%, 4%, and 14%. What is the arithmetic average return of the stock over the past 4 years minus the geometric average return of the stock over the past 4 years? Note that the arithmetic average return is sometimes referred to as the arithmetic mean return and that the geometric average return is sometimes referred to as the geometric mean return or compound return. (Spring 2010, final, question 11) Arithmetic average return = [.180 + (-.220) + .040 + .140] / 4 = .140 / 4 = .035 = 3.50% Geometric average return = [(1 + .180)(1 + (-.220)(1 + .040)(1 + .140)] 1/4 – 1 = [(1.180)(0.78)(1.040)(1.140)] 1/4 – 1 = [1.09122624] 1/4 – 1 = 1.0221 – 1 = .0221 = 2.21% Arithmetic average return – geometric average return = 3.50% – 2.21% = 1.29% 3

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FNAN 301 Solutions to test bank problems – risk and return 4. A stock had returns of -23%, 12%, and -25% in each of the past three years. Over the past four years, the arithmetic average annual return for the stock was 2.0%. What was the geometric return for the stock over the past four years? Note that individual stock returns are only given for each of the past three years, but that the question asks about the geometric return over the past four years. (Summer C 2010, quiz 4, question 3) (Summer C 2010, final, question 18) (Fall 2010, quiz 4, question 8) (Fall 2010, final, question 15) To solve: 1) Find the return from 4 years ago 2) Use the returns from the past four years to get the geometric return 1) Find the return from 4 years ago Arithmetic annual return = [(r 1 ) + (r 2 ) + … + (r n )] / n Over the past 4 years, arithmetic annual return = [(r 1 ) + (r 2 ) + (r 3 ) + (r 4 )] / 4 So .020 = [(-.23) + (.12) + (-.25) + (r 4 )] / 4 So .020 × 4 = [(-.23) + (.12) + (-.25) + (r 4 )] So .080 = [(-.23) + (.12) + (-.25) + (r 4 )] = (-.36) + (r 4 ) So .080 – (-.360) = r 4 r 4 = .440 = 44.0% 2) Use the returns from the past four years to get the geometric return Geometric annual return = [(1 + r 1 )(1 + r 2 ) … (1 + r n )] 1/n – 1 Over the past four years, geometric annual return = [(1 + r 1 )(1 + r 2 )( 1 + r 3 )(1 + r 4 )] 1/4 – 1 = [(1 + (-.23))(1 + .12)(1 +(- .25))(1 + .440)] 1/4 – 1 = [(0.77)(1.12)(0.75)(1.44)] 1/4 – 1 = [0.931392] 1/4 – 1 = 0.9824 – 1 = -.0176 = -1.76% 4
FNAN 301 Solutions to test bank problems – risk and return 5. Amazon has never paid any dividends. Eleven years ago, the firm’s stock was selling for \$7.88 per share. Today the stock is priced at \$78.96. What was the compound return over the past 11 years?

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07%20risk%20and%20return%20test%20bank%20problems%20solutions

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