The relationship between simple return (R_t) and continuously compounded return (r_t) is given by:

1 + R_t = e^{r_t}

1 + R_t = e^{r_t}

Solving for r_t:

r_t = ln(1 + R_t)

r_t = ln(1 + R_t)

Given R_t = 15% = 0.15:

r_t = ln(1 + 0.15) = ln(1.15) = 0.1398 = 13.98%

r_t = ln(1 + 0.15) = ln(1.15) = 0.1398 = 13.98%

Therefore, the equivalent continuously compounded return is 0.1398 or 13.98%.