Question

1. A company's stock price rose 3.2% in 2011, and in 2012, it increased 77.3%.

a. Compute the geometric mean rate of return for the two-year period 2011 - 2012. (Hint: Denote an increase of 77.3% by 0.773.)

b. If someone purchased $1,000 of the company's stock at the start of 2011, what was its value at the end of 2012?

c. Over the same period, another company had a geometric mean rate of return of 9.8%. If someone purchased $1,000 of this other company's stock, how would its value compare to the value found in part (b)?

Answer 1

a)

geometric mean rate of return = ((1 + r1)(1+r2)..(1+rn))^(1/n) - 1

= sqrt((1 + 0.032)(1+0.773)) - 1

= 0.35267734512

b)

1000 * (1+0.032)(1+0.773)

= 1829.736

c)

1000 * ( 1 + 0.098)^2

= 1205.604