Question

Year	Price	Dvidened
1	$73.18
2	77.98	1.15
3	69.13	1.25
4	84.65	1.36
5	91.37	1.47
6	103.66	1.6

What is the geometric and arithmetic returns for the stock?

Please show working?

Answer 1

Year 1 - Year 2:

Rate of Return, r1 = (Ending Price + Dividend - Beginning Price) / Beginning Price
Rate of Return, r1 = ($77.98 + $1.15 - $73.18) / $73.18
Rate of Return, r1 = 0.0813

Year 2 - Year 3:

Rate of Return, r2 = (Ending Price + Dividend - Beginning Price) / Beginning Price
Rate of Return, r2 = ($69.13 + $1.25 - $77.98) / $77.98
Rate of Return, r2 = -0.0975

Year 3 - Year 4:

Rate of Return, r3 = (Ending Price + Dividend - Beginning Price) / Beginning Price
Rate of Return, r3 = ($84.65 + $1.36 - $69.13) / $69.13
Rate of Return, r3 = 0.2442

Year 4 - Year 5:

Rate of Return, r4 = (Ending Price + Dividend - Beginning Price) / Beginning Price
Rate of Return, r4 = ($91.37 + $1.47 - $84.65) / $84.64
Rate of Return, r4 = 0.0968

Year 5 - Year 6:

Rate of Return, r5 = (Ending Price + Dividend - Beginning Price) / Beginning Price
Rate of Return, r5 = ($103.66 + $1.60 - $91.37) / $91.37
Rate of Return, r5 = 0.1520

Arithmetic Return = [r1 + r2 + r3 + r4 + r5] / 5
Arithmetic Return = [0.0813 + (-0.0975) + 0.2442 + 0.0968 + 0.1520] / 5
Arithmetic Return = 0.4768 / 5
Arithmetic Return = 0.0954 or 9.54%

Geometric Return = [(1+r1) * (1+r2) * (1+r3) * (1+r4) * (1+r5)]^(1/5) - 1
Geometric Return = [(1+0.0813) * (1-0.0975) * (1+0.2442) * (1+0.0968) * (1+0.1520)]^(1/5) - 1
Geometric Return = 1.534135^(1/5) - 1
Geometric Return = 1.0894 - 1
Geometric Return = 0.0894 or 8.94%