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