Question

Suppose you buy 100 shares of Abolishing Dividend Corporation at the beginning of year 1 for $80. Abolishing Dividend Corporation pays no dividends. The stock price at the end of year 1 is $100, $120 at the end of year 2, and $150 at the end of year 3. The stock price declines to $100 at the end of year 4, and you sell your 100 shares. For the four years, your geometric average return is

Answer 1

Answer:  5.57%

Explanation:

Geometric return = $\sqrt[n]{(1+r1)*(1+r2)*... (1 + rn)} - 1$

First year return

= $\frac{100 - 80}{80}$

= 25%

Second year return

= $\frac{120 - 100}{100}$

= 20%

Third year return

= $\frac{150 - 120}{120}$

= 25%

Fourth Year return

= $\frac{100 - 150}{150}$

= 33.3%

Geometric return = $\sqrt[n]{(1+r1)*(1+r2)*... (1 + rn)} - 1$

Geometric return = $\sqrt[4]{(1+0.25)*(1+0.2)*(1+0.25) * (1 - 0.333)} - 1$

Geometric return =  $\sqrt[4]{1.250625} - 1$

Geometric return = 5.57%