1a. You’ve observed the following returns on Boca Inc’s stock over the past five

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:

What are the arithmetic and geometric returns for the stock?

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

Explanation / Answer

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 %

Related Questions

Navigate

• Browse (All)
• Browse 1
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.