Over a 4-year period, a portfolio has returns of 10%, −2%, 18%, and −12%. The geometric mean return across the period is closest to:

To calculate the geometric mean return, we first need to convert each year's return into a multiplicative factor. We do this by adding 1 to each return (expressed as a decimal).

For the first year, the return is 10%, so the factor is 1 + 0.10 = 1.10. For the second year, the return is -2%, so the factor is 1 - 0.02 = 0.98. For the third year, the return is 18%, so the factor is 1 + 0.18 = 1.18. For the fourth year, the return is -12%, so the factor is 1 - 0.12 = 0.88.

Next, we multiply these factors together: 1.10 * 0.98 * 1.18 * 0.88 = 1.121736.

The geometric mean is the fourth root of this product (since there are 4 years), minus 1 (to convert back from a factor to a return).

The fourth root of 1.121736 is approximately 1.0286.

Subtracting 1 gives us 0.0286, or 2.86%.

So, the geometric mean return over the 4-year period is approximately 2.86%.