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).
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 AverageExplanation / Answer
Period
Stock price
Dividend
Holding period return
1
$ 43.15
2
$ 48.13
$ 0.45
12.58 %
3
$ 57.05
$ 0.49
19.55 %
4
$ 45.13
$ 0.55
-19.93 %
5
$ 52.05
$ 0.62
16.71 %
6
$ 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 %
Period
Stock price
Dividend
Holding period return
1
$ 43.15
2
$ 48.13
$ 0.45
12.58 %
3
$ 57.05
$ 0.49
19.55 %
4
$ 45.13
$ 0.55
-19.93 %
5
$ 52.05
$ 0.62
16.71 %
6
$ 61.13
$ 0.68
18.75 %
Arithmetic Average
9.53 %
Geometric Average
8.35 %
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