In a volatility-weighted approach, we adjust historical returns to account for changes in volatility over time. This method ensures that the adjusted returns reflect the current volatility environment, which is crucial for accurate risk assessment. The formula for the volatility-adjusted return is:

$$r^*_{t,i} = \left(\frac{\sigma_{T,i}}{\sigma_{t,i}}\right) r_{t,i}$$

where:

• $r^*_{t,i}$ is the volatility-adjusted return.
• $\sigma_{T,i}$ is the current volatility estimate.
• $\sigma_{t,i}$ is the historical volatility estimate at time t.
• $r_{t,i}$ is the historical return at time t.

$$\therefore r^*_{t,i} = \left(\frac{0.015}{0.020}\right) 0.05 = 0.0375$$