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

Question

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	%

[su_box title="♦ Relevant knowledge" box_color="#2d6ff7" radius="1"]There are two kinds of returns: Arithmetic Returns (AR) and Geometric Returns (GR) both are used to define the historical returns of a particular stock or portfolio. The main difference between these two types of returns can be seen below:

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.

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kttutoria · Accepted Answer

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%

Joseph Davis · Answer

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%

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