Question

Please answer Part (b) only -- SHOW YOUR work

Part (a) Calculate the geometric mean rate of return for the following quarterly SP500 returns:

3.20%, 2.5%, -1.55%, 4.32%, -3.25%, 0.55%

ANSWER = 0.93 %

part (b) What is the continuously compounded rate of return that produces the same cumulative return as in part (a)?

1. 5.69 %
2. 5.77 %
3. 5.55 %
4. 5.35 %
5. 4.06 %

Answer 1

Geometric Average = 0.93%

Cumulative Return = (1.0093)6 - 1 = 5.71%

Calculating Continuous Compounding rate,

1 + r = er

Using log,

r = log(1 + r)/log(e)

r = log(1.0571)/log(e)

r = 5.55%