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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? |

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 = 0.1580Year 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 = 0.0732Year 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 = -0.0680Year 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 = 0.1601Year 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 = 0.1838Arithmetic 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%