Consider these two stocks: AT&T Inc. (T) and Verizon Communications Inc. (VZ). Use the daily adjusted closing prices from March 1, 2015 to August 12, 2015 as historical data.
- Estimate the mean rate of return and the standard deviation of each of these assets. Moreover estimate their correlation coefficient ρ, and their covariance.
- Using their correlation coefficient ρ, find the weight of each of these assets that will give an efficient portfolio with minimum variance. Deduce the return of that portfolio.
The rate of return of stock $AT \& T$ is
$$ r_t^T=\frac{PCA_t^T-PCA_{t-1}^T}{PCA_{t-1}^T} $$
T is the index name of $AT \& T$. t is the index for the $t^{th}$ day.
PCA is the close price adjusted for dividends and splits.
The standard deviation of the rate of return of $AT \& T$ is
$$\sigma^T =\sqrt{\frac1n \times \sum_{t=1}^n \left( r_t^T-\mu^T \right) ^2 }$$
with $\mu^T= \frac1n\sum_{t=1}^n r_t^T$