1. **Problem Statement:** Calculate the return and risk (standard deviation) of each stock ALI, TEN, and BOC from 2016 to 2024. 2. **Formula for Return:** The annual return $R_t$ for year $t$ is calculated as $$R_t = \frac{P_t - P_{t-1}}{P_{t-1}}$$ where $P_t$ is the price at year $t$ and $P_{t-1}$ is the price at the previous year. 3. **Formula for Risk (Standard Deviation):** The risk is the standard deviation of the returns: $$\sigma = \sqrt{\frac{1}{n-1} \sum_{t=1}^n (R_t - \bar{R})^2}$$ where $\bar{R}$ is the mean return and $n$ is the number of returns. 4. **Calculate Returns for Each Stock:** - For ALI: Calculate returns from 2017 to 2024 using prices from 2016 to 2023. - For TEN: Similarly calculate returns. - For BOC: Similarly calculate returns. 5. **Example Calculation for ALI Returns:** $$R_{2017} = \frac{63.8 - 60}{60} = 0.0633$$ $$R_{2018} = \frac{66 - 63.8}{63.8} = 0.0345$$ ... and so on for all years. 6. **Calculate Mean Return $\bar{R}$ for Each Stock:** Sum all returns and divide by number of returns (8 years). 7. **Calculate Standard Deviation $\sigma$ for Each Stock:** Use the formula above with the returns and mean return. 8. **Summary of Returns and Risks:** - ALI: Mean return $\bar{R}_{ALI}$ and standard deviation $\sigma_{ALI}$ - TEN: Mean return $\bar{R}_{TEN}$ and standard deviation $\sigma_{TEN}$ - BOC: Mean return $\bar{R}_{BOC}$ and standard deviation $\sigma_{BOC}$ **Final numerical results:** - ALI returns: [0.0633, 0.0345, 0.1682, -0.0635, 0.0964, 0.0762, -0.1774, 0.05] - ALI mean return $\bar{R}_{ALI} = 0.0379$ - ALI standard deviation $\sigma_{ALI} \approx 0.096$ - TEN returns: [0.1533, 0.0145, -0.0714, 0.04, 0.0686, 0.1385, -0.0273, -0.14] - TEN mean return $\bar{R}_{TEN} = 0.0229$ - TEN standard deviation $\sigma_{TEN} \approx 0.091$ - BOC returns: [-0.1321, 0.0741, 0.1797, 0.2292, 0.0158, -0.067, -0.025, 0.0486] - BOC mean return $\bar{R}_{BOC} = 0.0332$ - BOC standard deviation $\sigma_{BOC} \approx 0.111$ These calculations provide the return and risk for each stock based on the given data.