Consider these two stocks: AT&T Inc. (T) and Verizon Communications Inc. (VZ). U
ID: 2654785 • Letter: C
Question
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.
1. Estimate the mean rate of return and the standard deviation of each of these assets. Moreover estimate their correlation coefficient , and their covariance.
2. Using their correlation coefficient , find the weight of each of these assets that will give an efficient portfolio with minimum variance. Deduce the return of that portfolio.
Explanation / Answer
Verizon AT&nt Date Close Returns Date Close Returns 8/12/2015 47.85 8/12/2015 34.0 8/11/2015 47.60 -0.52% 8/11/2015 34.7 1.85% 8/10/2015 47.23 -0.78% 8/10/2015 34.8 0.38% 8/7/2015 46.36 -1.84% 8/7/2015 34.2 -1.64% 8/6/2015 46.63 0.58% 8/6/2015 34.2 0.09% 8/5/2015 46.64 0.02% 8/5/2015 34.6 0.96% 8/4/2015 46.67 0.06% 8/4/2015 34.6 0.03% 8/3/2015 46.97 0.64% 8/3/2015 34.7 0.23% 7/31/2015 46.79 -0.38% 7/31/2015 34.7 0.23% 7/30/2015 46.67 -0.26% 7/30/2015 34.8 0.17% 7/29/2015 46.56 -0.24% 7/29/2015 34.7 -0.32% 7/28/2015 45.89 -1.44% 7/28/2015 34.3 -1.04% 7/27/2015 45.83 -0.13% 7/27/2015 34.3 -0.03% 7/24/2015 46.04 0.46% 7/24/2015 34.3 -0.09% 7/23/2015 46.35 0.67% 7/23/2015 33.9 -1.05% 7/22/2015 46.45 0.22% 7/22/2015 34.3 1.00% 7/21/2015 46.97 1.12% 7/21/2015 34.6 0.88% 7/20/2015 48.10 2.41% 7/20/2015 34.9 0.95% 7/17/2015 47.59 -1.06% 7/17/2015 35.0 0.32% 7/16/2015 47.83 0.50% 7/16/2015 35.2 0.43% 7/15/2015 47.33 -1.05% 7/15/2015 34.7 -1.22% 7/14/2015 47.41 0.17% 7/14/2015 35.1 1.12% 7/13/2015 47.20 -0.44% 7/13/2015 34.9 -0.68% 7/10/2015 47.00 -0.42% 7/10/2015 34.7 -0.66% 7/9/2015 46.26 -1.57% 7/9/2015 34.4 -0.75% 7/8/2015 46.58 0.69% 7/8/2015 34.8 1.16% 7/7/2015 47.25 1.44% 7/7/2015 35.8 2.82% 7/6/2015 47.04 -0.44% 7/6/2015 35.6 -0.45% 7/2/2015 47.20 0.34% 7/2/2015 35.7 0.34% 7/1/2015 47.00 -0.42% 7/1/2015 35.6 -0.45% 6/30/2015 46.61 -0.83% 6/30/2015 35.5 -0.14% 6/29/2015 46.77 0.34% 6/29/2015 35.8 0.70% 6/26/2015 47.62 1.82% 6/26/2015 36.1 0.98% 6/25/2015 47.44 -0.38% 6/25/2015 36.2 0.17% 6/24/2015 47.29 -0.32% 6/24/2015 35.8 -1.11% 6/23/2015 47.77 1.02% 6/23/2015 35.9 0.36% 6/22/2015 47.53 -0.50% 6/22/2015 35.0 -2.42% 6/19/2015 47.46 -0.15% 6/19/2015 35.0 -0.14% 6/18/2015 47.77 0.65% 6/18/2015 35.0 0.09% 6/17/2015 47.27 -1.05% 6/17/2015 34.8 -0.63% 6/16/2015 47.42 0.32% 6/16/2015 34.7 -0.37% 6/15/2015 47.00 -0.89% 6/15/2015 34.4 -0.75% 6/12/2015 47.25 0.53% 6/12/2015 34.7 0.70% 6/11/2015 47.76 1.08% 6/11/2015 34.9 0.66% 6/10/2015 47.47 -0.61% 6/10/2015 34.7 -0.46% 6/9/2015 47.34 -0.27% 6/9/2015 34.5 -0.60% 6/8/2015 47.44 0.21% 6/8/2015 34.6 0.23% 6/5/2015 47.23 -0.44% 6/5/2015 34.6 -0.06% 6/4/2015 48.10 1.84% 6/4/2015 35.3 2.02% 6/3/2015 49.08 2.04% 6/3/2015 35.0 -0.68% 6/2/2015 49.14 0.12% 6/2/2015 34.4 -1.91% 6/1/2015 49.22 0.16% 6/1/2015 34.3 -0.03% 5/29/2015 49.44 0.45% 5/29/2015 34.5 0.55% 5/28/2015 49.54 0.20% 5/28/2015 34.8 0.75% 5/27/2015 49.57 0.06% 5/27/2015 35.0 0.43% 5/26/2015 49.42 -0.30% 5/26/2015 34.7 -0.80% 5/22/2015 49.61 0.38% 5/22/2015 34.7 0.12% 5/21/2015 49.90 0.58% 5/21/2015 35.1 1.04% 5/20/2015 49.69 -0.42% 5/20/2015 34.6 -1.28% 5/19/2015 49.55 -0.28% 5/19/2015 34.4 -0.72% 5/18/2015 49.60 0.10% 5/18/2015 34.9 1.45% 5/15/2015 49.79 0.38% 5/15/2015 34.3 -1.55% 5/14/2015 49.97 0.36% 5/14/2015 34.1 -0.58% 5/13/2015 49.73 -0.48% 5/13/2015 33.9 -0.67% 5/12/2015 49.62 -0.22% 5/12/2015 33.7 -0.71% 5/11/2015 49.80 0.36% 5/11/2015 33.5 -0.51% 5/8/2015 50.14 0.68% 5/8/2015 33.7 0.60% 5/7/2015 49.73 -0.82% 5/7/2015 33.4 -0.95% 5/6/2015 49.64 -0.18% 5/6/2015 33.4 0.03% 5/5/2015 50.09 0.91% Standard deviation 5/5/2015 33.7 1.02% 5/4/2015 50.52 0.86% Variance 5/4/2015 34.5 2.40% 5/1/2015 50.41 -0.22% 5/1/2015 34.4 -0.32% 4/30/2015 50.44 0.06% No of trading days in year 4/30/2015 34.6 0.64% 4/29/2015 50.47 0.06% Annualized variance 4/29/2015 34.8 0.35% 4/28/2015 50.55 0.16% 4/28/2015 34.9 0.29% 4/27/2015 50.08 -0.93% Standard deviation 4/27/2015 34.1 -2.21% 4/24/2015 50.03 -0.10% 4/24/2015 34.0 -0.23% 4/23/2015 50.05 0.04% Mean 4/23/2015 34.2 0.65% 4/22/2015 49.57 -0.96% 4/22/2015 32.9 -4.00% 4/21/2015 49.17 -0.81% 4/21/2015 32.7 -0.61% 4/20/2015 49.38 0.43% 4/20/2015 32.8 0.52% 4/17/2015 48.90 -0.97% 4/17/2015 32.5 -0.97% 4/16/2015 49.27 0.76% 4/16/2015 32.8 0.74% 4/15/2015 49.39 0.24% 4/15/2015 32.9 0.43% 4/14/2015 49.18 -0.43% 4/14/2015 32.7 -0.61% 4/13/2015 49.04 -0.28% 4/13/2015 32.9 0.58% 4/10/2015 49.22 0.37% 4/10/2015 32.8 -0.33% 4/9/2015 49.01 -0.43% 4/9/2015 32.7 -0.24% 4/8/2015 49.13 0.24% 4/8/2015 32.7 -0.12% 4/7/2015 49.27 0.28% 4/7/2015 33.2 1.56% 4/6/2015 49.63 0.73% 4/6/2015 33.3 0.51% 4/2/2015 49.47 -0.32% 4/2/2015 33.1 -0.60% 4/1/2015 48.92 -1.11% 4/1/2015 32.9 -0.72% 3/31/2015 48.63 -0.59% 3/31/2015 32.7 -0.73% 3/30/2015 49.12 1.01% 3/30/2015 33.0 0.98% 3/27/2015 48.56 -1.14% 3/27/2015 32.8 -0.67% 3/26/2015 48.42 -0.29% 3/26/2015 32.8 0.21% 3/25/2015 48.73 0.64% 3/25/2015 32.6 -0.61% 3/24/2015 49.41 1.40% 3/24/2015 33.1 1.38% 3/23/2015 49.64 0.47% 3/23/2015 33.3 0.64% 3/20/2015 49.56 -0.16% 3/20/2015 33.2 -0.15% 3/19/2015 49.30 -0.52% 3/19/2015 33.2 -0.09% 3/18/2015 49.54 0.49% 3/18/2015 33.6 1.17% 3/17/2015 48.95 -1.19% 3/17/2015 32.9 -2.05% 3/16/2015 49.27 0.65% 3/16/2015 33.1 0.49% 3/13/2015 48.84 -0.87% 3/13/2015 32.8 -0.91% 3/12/2015 48.73 -0.23% 3/12/2015 33.1 1.13% 3/11/2015 47.68 -2.15% 3/11/2015 32.6 -1.54% 3/10/2015 47.51 -0.36% 3/10/2015 32.8 0.49% 3/9/2015 48.23 1.52% 3/9/2015 33.3 1.74% 3/6/2015 48.29 0.12% 3/6/2015 33.5 0.39% 3/5/2015 48.92 1.30% 3/5/2015 34.0 1.55% 3/4/2015 49.07 0.31% 3/4/2015 34.0 0.00% 3/3/2015 49.55 0.98% 3/3/2015 34.4 1.21% 3/2/2015 49.47 -0.16% 3/2/2015 34.6 0.67% Standard deviation (Daily) 0.79% Standard deviation (Daily) 1.02% Variance (Daily) 0.01% Variance (Daily) 0.01% No of trading days in year 250 No of trading days in year 250 Annualized variance 1.57% Annualized variance 2.59% Standard deviation Annualised 12.53% Standard deviation Annualised 16.08% Mean Daily 0.03% Mean Daily 0.02%