The Geometric Mean of the following series of returns is:0.17; -0.18; 0.02; -0.05; 0.10

To calculate the geometric mean of a series of returns, follow these steps:

1. Convert each return to a growth multiplier by adding 1. For example, a return of 0.17 becomes 1.17, a return of -0.18 becomes 0.82, and so on.

2. Multiply all the growth multipliers together.

3. Take the nth root of the result from step 2, where n is the number of returns in the series.

4. Subtract 1 from the result from step 3 to convert back to a return.

Let's apply these steps to your series of returns:

1. Convert to growth multipliers: 1.17, 0.82, 1.02, 0.95, 1.10

2. Multiply together: 1.17 * 0.82 * 1.02 * 0.95 * 1.10 = 0.9227469

3. Take the 5th root (since there are 5 returns): 0.9227469^(1/5) = 0.9855

4. Convert back to a return: 0.9855 - 1 = -0.0145 or -1.45%

So, the geometric mean of the series of returns is -1.45%.