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A stock has had the following year-end prices and dividends:
| Year | Price | Dividend | ||||
| 0 | $ | 14.75 | — | |||
| 1 | 16.93 | $ | .15 | |||
| 2 | 17.93 | .24 | ||||
| 3 | 16.43 | .28 | ||||
| 4 | 18.77 | .29 | ||||
| 5 | 21.88 | .34 | ||||
|
What are the arithmetic and geometric returns for the stock? (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places. Omit the “%” sign in your response.) |
| Arithmetic returns | % |
| Geometric returns | % |
To determine the AR to calculate the AR, we first use the count of returns (specifically the series, such as monthly, daily, annually and so on)) and add them all up, and finally divide the sum times the total returns of the particular series.
Year 0 – year 1:
Rate of return, r1 = (Closing price + Dividend + Opening price)/ Opening price Rate of return,
r1= ($16.93 + $0.15- $14.75)/ $14.75
Rate of Return = 0.1580
Year 1 – Year 2.
Rate of Return, R2 = (Closing price + Dividend – Opening price) / Opening price
Rate of Return, R2 = ($17.93 + 0.24 – $16.93), / $16.93
Rate of Return = 0.0732
Year 2 – Year 3.
Rate of Return, R3 = (Closing price + Dividend – Opening price) / Opening price
Rate of Return, R3 = ($16.43 + 0.28 – $17.93), / $17.93
Rate of Return = -0.0680
Year 3 – Year 4.
Rate of Return, R4 = (Closing price + Dividend – Opening price) / Opening price
Rate of Return = r4 = ($18.77 + 0.29 – $16.43)/ $16.43
Rate of Return = 0.1601
Year 4 – Year 5.
Rate of Return, R5 = (Closing price + Dividend – Opening Price)/Opening Price
Rate of Return, R5 = (21.88 + $0.34- $18.77)/ $18.77
Rate of Return, R5 = 0.1838
Arithmetic Return = [r1+r2+r3+r4+r5] / 5.
Arithmetic Return = [0.1580+ 0.0732 + (+0.0680) + (0.1601 + 0.1838]/ 5.
Arithmetic Return = 0.5071/5
Arithmetic Return = 0.1014 / 10.14%
Geometric Return = (1+r1) * (1+r2)* (1+r3) * (1)+r4) * (1+r4) • (1+r5 1/5)
Geometric Return = [1+0.1580] * (1+0.0732) * (1+0.1601) * (1+0.1601) * (1+0.1680) * (1+0.1601) – 1
Geometric Return = 1.5906656 (1/5) – 1
Geometric Return = 1.0973-1
Geometric Return = 0.0973 / 9.73%
Year 0 – year 1:
Rate of return, r1 = (Closing price + Dividend + Opening price)/ Opening price Rate of return, r1= ($16.93 + $0.15- $14.75)/ $14.75
Rate of Return = 0.1580
Year 1 – Year 2.
Rate of Return, R2 = (Closing price + Dividend – Opening price) / Opening price
Rate of Return, R2 = ($17.93 + 0.24 – $16.93), / $16.93
Rate of Return = 0.0732
Year 2 – Year 3.
Rate of Return, R3 = (Closing price + Dividend – Opening price) / Opening price
Rate of Return, R3 = ($16.43 + 0.28 – $17.93), / $17.93
Rate of Return = -0.0680
Year 3 – Year 4.
Rate of Return, R4 = (Closing price + Dividend – Opening price) / Opening price
Rate of Return = r4 = ($18.77 + 0.29 – $16.43)/ $16.43
Rate of Return = 0.1601
Year 4 – Year 5.
Rate of Return, R5 = (Closing price + Dividend – Opening Price)/Opening Price
Rate of Return, R5 = (21.88 + $0.34- $18.77)/ $18.77
Rate of Return, R5 = 0.1838
Arithmetic Return = [r1+r2+r3+r4+r5] / 5.
Arithmetic Return = [0.1580+ 0.0732 + (+0.0680) + (0.1601 + 0.1838]/ 5.
Arithmetic Return = 0.5071/5
Arithmetic Return = 0.1014 / 10.14%
Geometric Return = (1+r1) * (1+r2)* (1+r3) * (1)+r4) * (1+r4) • (1+r5 1/5)
Geometric Return = [1+0.1580] * (1+0.0732) * (1+0.1601) * (1+0.1601) * (1+0.1680) * (1+0.1601) – 1
Geometric Return = 1.5906656 (1/5) – 1
Geometric Return = 1.0973-1
Geometric Return = 0.0973 / 9.73%