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 $-0.7$