Question

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

Year	Price	Dividend
1	$85.18	---
2	$92.35	$0.55
3	$90.49	$0.75
4	$100.05	$0.90

1. What were percentage rate of returns for Year 2, Year 3, and Year 4?
2. What is the arithmetic average return for the stock?
3. What is the geometric average return for the stock?

Answer 1

Rate of Return of Year 2 =(End Price-Beginning Price+Dividend)/Beginning Price =(92.35-85.18+0.55)/85.18=9.0632%or 9.06%
Rate of Return of Year 3 =(End Price-Beginning Price+Dividend)/Beginning Price =(90.49-92.35+0.75)/92.35=-1.2019%or-1.20%
Rate of Return of Year 4 =(End Price-Beginning Price+Dividend)/Beginning Price =(100.05-90.49+0.9)/90.49=11.5593%or 11.56%

Arithmetic return =(9.0632%-1.2019%+11.5593%)/3 =6.47%
Geometric Return =((1+9.0632%)*(1-1.2019%)*(1+11.5593%))^(1/3)-1 =6.33%