Question

A stock has had the following year-end prices and dividends: Year Price Dividend 1 $ 43.43 - 2 48.41 $ .69 3 57.33 .72 4 45.41 .80 5 52.33 .85 6 61.41 .93 What are the arithmetic and geometric average returns for the stock?

Answer 1

Answer and Explanation:

Average return = (Closing Price + Dividend - Opening Price) / Opening Price

For 1st year:

0 Return

For 2nd year:

($48.41 + $0.69 - $43.43) / $43.43  = 0.130

For 3rd year

 ($57.33 + $0.72 - $48.41) / $48.41 = 0.199

For 4th year:

($45.41 + $0.80 - $57.33) / $57.33  = -0.194

For 5th year

($52.33 + $0.85 - $45.41) / $45.41 = 0.171

For 6th year

($61.41 + $0.93 - $52.33) / $52.33 = 0.191

Arithmetic Return = Sum of all return / Total number of return

= [0.130 + 0.199 + (-0.194) + 0.171 + 0.191] / 5

Arithmetic Return = 9.96% $Geometric Return = [(1+r1)(1+r2)(1+r3)(1+r4)(1+r5)] ^ {(1/5)}-1$

$Geometric Return = [1.52445]^{(1/5) }-1$

Geometric Return = 1.0880 - 1

Geometric Return = 0.0880 = 8.80%