Free CFP Exam Investment Planning Practice Questions

The arithmetic mean return is calculated by summing all period returns and dividing by the number of periods: (20% + (-10%) + 15%) / 3 = 25% / 3 = 8.33%. The arithmetic mean is the simple average and tends to overstate the compound growth rate when returns are volatile. The geometric mean (which accounts for compounding) would be lower than 8.33% due to the volatility of returns.

Tax-loss harvesting is most beneficial for investors who have realized capital gains in taxable accounts because the harvested losses can offset those gains, reducing the current-year tax liability. The strategy involves selling depreciated securities to realize losses and reinvesting in similar (but not substantially identical) securities to maintain market exposure. Investors holding all assets in tax-deferred accounts (A) gain no benefit because gains and losses in these accounts have no current tax impact. Investors in the lowest bracket with no capital gains (C) have minimal tax savings opportunity. Municipal bond investors (B) already receive tax-exempt income and typically would not need to harvest losses from those holdings.

A is correct. The minimum variance portfolio weight for Asset A is: wA = (σB² - Cov(A,B)) / (σA² + σB² - 2·Cov(A,B)). First, Cov(A,B) = ρ·σA·σB = 0.25 × 0.40 × 0.20 = 0.02. Then: wA = (0.04 - 0.02) / (0.16 + 0.04 - 2×0.02) = 0.02 / 0.16 = 0.125, or 12.5%. The minimum variance portfolio heavily favors the lower-volatility asset when one asset is much riskier than the other.
Choice B is incorrect because 30% overstates the allocation to the higher-volatility asset, which would increase portfolio variance beyond the minimum.
Choice C is incorrect because equal weighting does not minimize variance unless the two assets have identical standard deviations and specific correlation conditions are met.
Choice D is incorrect because 20% overweights Asset A relative to the optimal minimum variance allocation of 12.5%, resulting in higher portfolio variance.