1. **Problem Statement:** We are given two sets of returns: individual security returns $R_i$ and market returns $R_m$. We need to compute the alpha ($\alpha$) and beta ($\beta$) of the security. 2. **Formulas:** - Beta ($\beta$) measures the sensitivity of the security's returns to the market returns and is given by: $$\beta = \frac{\text{Cov}(R_i, R_m)}{\text{Var}(R_m)}$$ - Alpha ($\alpha$) is the intercept of the security's return regression on the market return and is given by: $$\alpha = \bar{R_i} - \beta \bar{R_m}$$ where $\bar{R_i}$ and $\bar{R_m}$ are the means of $R_i$ and $R_m$ respectively. 3. **Calculate means:** $$\bar{R_i} = \frac{14 + 18 + 6 + 12 + 13 + 14 + 11 + 6 + 9 + 8}{10} = \frac{111}{10} = 11.1$$ $$\bar{R_m} = \frac{16 + 20 + 9 + 8 + 10 + 9 + 11 + 18 + 17 + 15}{10} = \frac{133}{10} = 13.3$$ 4. **Calculate covariance $\text{Cov}(R_i, R_m)$:** $$\text{Cov}(R_i, R_m) = \frac{1}{n} \sum_{k=1}^{n} (R_{i,k} - \bar{R_i})(R_{m,k} - \bar{R_m})$$ Calculate each term: - $(14 - 11.1)(16 - 13.3) = 2.9 \times 2.7 = 7.83$ - $(18 - 11.1)(20 - 13.3) = 6.9 \times 6.7 = 46.23$ - $(6 - 11.1)(9 - 13.3) = -5.1 \times -4.3 = 21.93$ - $(12 - 11.1)(8 - 13.3) = 0.9 \times -5.3 = -4.77$ - $(13 - 11.1)(10 - 13.3) = 1.9 \times -3.3 = -6.27$ - $(14 - 11.1)(9 - 13.3) = 2.9 \times -4.3 = -12.47$ - $(11 - 11.1)(11 - 13.3) = -0.1 \times -2.3 = 0.23$ - $(6 - 11.1)(18 - 13.3) = -5.1 \times 4.7 = -23.97$ - $(9 - 11.1)(17 - 13.3) = -2.1 \times 3.7 = -7.77$ - $(8 - 11.1)(15 - 13.3) = -3.1 \times 1.7 = -5.27$ Sum: $7.83 + 46.23 + 21.93 - 4.77 - 6.27 - 12.47 + 0.23 - 23.97 - 7.77 - 5.27 = 15.67$ Divide by $n=10$: $$\text{Cov}(R_i, R_m) = \frac{15.67}{10} = 1.567$$ 5. **Calculate variance $\text{Var}(R_m)$:** $$\text{Var}(R_m) = \frac{1}{n} \sum_{k=1}^n (R_{m,k} - \bar{R_m})^2$$ Calculate each term: - $(16 - 13.3)^2 = 2.7^2 = 7.29$ - $(20 - 13.3)^2 = 6.7^2 = 44.89$ - $(9 - 13.3)^2 = (-4.3)^2 = 18.49$ - $(8 - 13.3)^2 = (-5.3)^2 = 28.09$ - $(10 - 13.3)^2 = (-3.3)^2 = 10.89$ - $(9 - 13.3)^2 = 18.49$ - $(11 - 13.3)^2 = (-2.3)^2 = 5.29$ - $(18 - 13.3)^2 = 4.7^2 = 22.09$ - $(17 - 13.3)^2 = 3.7^2 = 13.69$ - $(15 - 13.3)^2 = 1.7^2 = 2.89$ Sum: $7.29 + 44.89 + 18.49 + 28.09 + 10.89 + 18.49 + 5.29 + 22.09 + 13.69 + 2.89 = 171.10$ Divide by $n=10$: $$\text{Var}(R_m) = \frac{171.10}{10} = 17.11$$ 6. **Calculate beta ($\beta$):** $$\beta = \frac{1.567}{17.11} \approx 0.0916$$ 7. **Calculate alpha ($\alpha$):** $$\alpha = 11.1 - 0.0916 \times 13.3 = 11.1 - 1.217 = 9.883$$ **Final answers:** $$\boxed{\beta \approx 0.092, \quad \alpha \approx 9.88}$$