Answer: -0.0012

The continuously compounded return at time 4 is calculated using the formula: $$r_t = \ln P_t - \ln P_{t-1}$$ For time 4: $$r_4 = \ln P_4 - \ln P_3 = \ln(103.56) - \ln(103.68)$$ Calculating: $$\ln(103.56) \approx 4.640$$ $$\ln(103.68) \approx 4.641$$ $$r_4 \approx 4.640 - 4.641 = -0.001$$ More precisely: $$r_4 = \ln\left(\frac{103.56}{103.68}\right) = \ln(0.99884) \approx -0.00116$$ This matches option D: -0.0012 (approximately -0.0012 or -0.12%). **Why other options are incorrect:** - **A (0.81%)**: This would be a positive return, but the price decreased from 103.68 to 103.56 - **B (-0.0081)**: This is too large in magnitude (-0.81% vs the actual -0.12%) - **C (0.0091)**: This is positive and incorrect as the price decreased

Author: Nikitesh Somanthe