Question

Assume the annual return for the lowest turnover portfolio is 19% and the annual return for the highest turnover portfolio is 10%. If you invest $105,000 and have the highest turnover, how much lower will the value of your portfolio be at the end of 10 years than if you had had the lowest turnover?

Answer 1

The value of the portfolio with the highest turnover will be $316,155 lower than that of the lowest turnover portfolio after 10 years, after calculating the future value using the compound interest formula.

To calculate the difference in value between the lowest turnover portfolio and the highest turnover portfolio after 10 years, we need to use the formula for compound interest. We will first calculate the future value of both portfolios separately and then find the difference between them.

Lowest Turnover Portfolio:

Future Value (FV) = $105,000 × (1 + 0.19)^10

FV for Lowest Turnover = $105,000 × (1.19)^10

FV for Lowest Turnover ≈ $105,000 × 5.604

FV for Lowest Turnover ≈ $588,420

Highest Turnover Portfolio:

FV = $105,000 × (1 + 0.10)^10

FV for Highest Turnover = $105,000 × (1.10)^10

FV for Highest Turnover ≈ $105,000 × 2.593

FV for Highest Turnover ≈ $272,265

Difference in Value:

Difference = FV for Lowest Turnover - FV for Highest Turnover

Difference ≈ $588,420 - $272,265

Difference ≈ $316,155

The value of the portfolio with the highest turnover will be $316,155 lower than the portfolio with the lowest turnover after 10 years.