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Beta Coefficients

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Beta Coefficients


1. **State the problem:** We need to find the Beta coefficient for AKC and BLC companies given their standard deviations and correlation coefficients with the market portfolio. 2. **Recall the formula for Beta:** $$\beta = \rho_{i,m} \times \frac{\sigma_i}{\sigma_m}$$ where $\rho_{i,m}$ is the correlation coefficient between the stock and the market, $\sigma_i$ is the standard deviation of the stock returns, and $\sigma_m$ is the standard deviation of the market returns. 3. **Given data:** - For AKC: $\sigma_{AKC} = 0.45$, $\rho_{AKC,m} = +0.75$ - For BLC: $\sigma_{BLC} = 0.035$, $\rho_{BLC,m} = -0.5$ - Market portfolio: $\sigma_m = 0.025$ 4. **Calculate Beta for AKC:** $$\beta_{AKC} = 0.75 \times \frac{0.45}{0.025} = 0.75 \times 18 = 13.5$$ 5. **Calculate Beta for BLC:** $$\beta_{BLC} = -0.5 \times \frac{0.035}{0.025} = -0.5 \times 1.4 = -0.7$$ **Final answers:** - Beta coefficient for AKC Company is $13.5$ - Beta coefficient for BLC Company is $-0.7$