From the year-end prices and dividends below, compute the arithmetic and geometr

ID: 2616468 • Letter: F

Question

From the year-end prices and dividends below, compute the arithmetic and geometric average returns for the stock. Hint: compute the holding period returns first (there will only be 5 holding period returns). be olding period returns) Period Dividend Holding Period Return Stock Price $43.15 48.13 57.05 45.13 52.05 61.13 $.45 .49 .55 62 68 4 Arithmetic Average Geometric Average

Explanation / Answer

Period

Stock price

Dividend

Holding period return

$ 43.15

$ 48.13

$ 0.45

12.58 %

$ 57.05

$ 0.49

19.55 %

$ 45.13

$ 0.55

-19.93 %

$ 52.05

$ 0.62

16.71 %

$ 61.13

$ 0.68

18.75 %

Arithmetic Average

9.53 %

Geometric Average

8.35 %

Explanation:

Formula for Holding Period Return (HPR) is:

HPR = Income + (End of Period Value – Initial Value)/ Initial Value

EOY 1 HRP:

HRP r1 = $ 0.45 + ($ 48.13 - $ 43.15)/ $ 43.15

= ($ 0.45 + $ 4.98)/$ 43.15

= $ 5.43/$ 43.15

= 0.125840093 or 12.48 %

EOY 2 HRP:

HRP r2 = $ 0.49 + ($ 57.05 - $ 48.13)/ $ 48.13

= ($ 0.49 + $ 8.92)/$ 48.13

= $ 9.41/$ 48.13

= 0.195512155 or 19.55 %

EOY 3 HRP:

HRP r3 = $ 0.55 + ($ 45.13 - $ 57.05)/ $ 57.05

= ($ 0.55 - $ 11.92)/$ 57.05

= - $ 11.73/$ 57.05

= - 0.199298861 or - 19.93 %

EOY 4 HRP:

HRP r4 = $ 0.62 + ($ 52.05 - $ 45.13)/ $ 45.13

= ($ 0.62 - $ 6.92)/$ 45.13

= $ 7.54/$ 45.13

= 0.167072901 or 16.71 %

EOY 5 HRP:

HRP r5 = $ 0.68 + ($ 61.13 - $ 52.05)/ $ 52.05

= ($ 0.68 - $ 9.08)/$ 52.05

= $ 9.76/$ 52.05

= 0.187512008 or 18.75 %

Arithmetic Average Return = (r1 + r2 + r3 + r4 + r5)/5

= (0.125840093 + 0.195512155 - 0.199298861 + 0.167072901 + 0.187512008)/5

= 0.476638295/5 = 0.095327659 or 9.53 %

Geometric Average Return = [(1+ r1) x (1+ r2) x (1+ r3) x (1+ r4) x (1+ r5)] 1/5 -1

=[(1+ 0.125840093)x (1 + 0.195512155) x (1- 0.199298861) x (1+0.167072901) x (1+0.187512008)] 1/5 -1

= [(1.125840093) x (1.195512155) x (0.800701139) x (1.167072901) x (1.187512008)] 1/5 -1

= (1.493609776)1/5 -1

= 1.08354619 – 1 = 0.08354619 or 8.35 %