The continuously compounded rate of return is calculated using the formula: r = ln(S₁ / S₀), where S₀ is the initial value and S₁ is the final value.

Given:

• Initial value (S₀) = 127,350
• Final value (S₁) = 108,427
• Time period = 1 year

Calculation: r = ln(108,427 / 127,350) r = ln(0.8515) r = -0.1609

Converting to percentage: r = -0.1609 × 100% = -16.09%

Therefore, the continuously compounded rate of return is -16.09%.

Key Concept: Continuously compounded returns use the natural logarithm of the ratio of ending to beginning values, which is different from discrete compounding where we use (S₁/S₀)^(1/t) - 1.