Question

1a. You’ve observed the following returns on Boca Inc’s stock over the past five years: 7 percent, ?13 percent, 21 percent, 34 percent, and 15 percent. What was the arithmetic average return on Crash-n-Burn’s stock over this five-year period? What was the variance of Crash-n-Burn’s returns over this period? The standard deviation?

1b. A stock has had the following year-end prices and dividends:

Year	Price	Dividend
1	$51.50	-
2	59.32	$0.65
3	64.13	0.70
4	57.86	0.77
5	65.19	0.86
6	74.86	0.95

What are the arithmetic and geometric returns for the stock?

Answer 1

Answer 1 (A)

You've observed the following returns on crash-n-Burn Computer's stock over the past five years: 7 percent, 13 Percent, 21 percent, 34 percent, and 15 percent.

What was the arithmetic average return on Crash-n-Burn's stock over this five year Period?

Average =    µ = 7 percent + 13 Percent + 21 percent + 34 percent +15 percent / 5

                       µ = 0.7+0.13+0.21+0.34+0.15 / 5

                       µ = 1.41

                      µ = 4.38 Percent

Answer 1 (B)

Stock return = (P₁ – P₀) + D/ P₀

P₀ = Initial stock price

P₀ = Period ending stock price

D = Dividend paid

Return for year 1, R₁ = ($ 59.32 - $ 51.50) + $ 0.65/$ 51.50 = $ 7.82 + $ 0.65/$ 51.50

                              = $ 8.47/$ 51.50 = 0.164466019 or 16.45 %

Return for year 2, R₂ = ($ 64.13 - $ 59.32) + $ 0.70/$ 59.32 = $ 4.81 + $ 0.70/$ 59.32

                                      = $ 5.51/$ 59.32 = 0.092886042 or 9.29 %

Return for year 3, R₃ = ($ 57.86 - $ 64.13) + $ 0.77/$ 64.13 = - $ 6.27 + $ 0.77/$ 64.13

                                      = - $ 5.5/$ 64.13 = -0.085763293 or -8.58 %

Return for year 4, R₄ = ($ 65.19 - $ 57.86) + $ 0.86/$ 57.86 = $ 7.33 + $ 0.86/$ 57.86

                                      = $ 8.19 /$ 57.86 = 0.141548566 or 14.15 %

Return for year 5, R₅ = ($ 74.86 - $ 65.19) + $ 0.95/$ 65.19 = $ 9.67 + $ 0.95/$ 65.19

                                      = $ 10.62/ $ 65.19 = 0.162908422 or 16.29 %

Arithmetic average return = (R₁ + R₂ + R₃ + R₄ + R₅)/5

= 0.164466019 + 0.092886042 -0.085763293 + 0.141548566 + 0.162908422

= 0.476045755/5 = 0.095209151 or 9.52 %

Geometric average return = (1 + R₁) (1 + R₂) (1+ R₃) (1+ R₄) (1+ R₅)^1/5 -1

= [(1+0.164466019) (1+0.092886042) (1 - 0.085763293) (1+0.141548566) (1+0.162908422)] ^1/5- 1

= [(1.164466019) (1.092886042) (0.914236707) (1.141548566) (1.162908422)] ^1/5- 1

= (1.544543918)^1/5 – 1 = 1.090837482 – 1 = 0.090837482 or 9.08 %