The Excel workbook titled "Return.xlsx" (available on the class web page) contains monthly

returns on 4 stocks (FB: Facebook, AMZN: Amazon, MSFT: Microsoft, CMG: Chipotle) and one

month US T-bills for the period May 2012 -Sept. 2020.

1. For the 4 stocks and T-bill, calculate the following statistics using the monthly return

data/sample from 2012 to 2020: (20 points)

a. Find the arithmetic mean, variance, and standard deviation of monthly returns. Also,

state the annualized mean and standard deviation, assuming monthly compounding. (5

points)

b. Find the skewness and kurtosis of monthly returns. Also interpret the findings. (5

points)

c. Find the pair-wise covariances (in the form of a covariance matrix) for each set of

assets. (5 points)

d. Find the pair-wise correlations (in the form of a correlation matrix) for each set of

assets. (5 points)

2. Find the average monthly risk premium earned by each of the four stocks over this period

of time and the Sharpe Ratio for each of the four stocks? (Hint: A risk premium is defined

as return of an investment in excess of risk-free rate and Sharpe ratio is defined as risk

premium of an investment divided by the standard deviation of the investment. It is well

known that T-bill can be considered a proxy for risk-free investment. You have calculated

average monthly return for each stock and that for the T-bill investment. So, you have all

the information required for the calculation of average monthly risk premium for each of

the four stocks.) (5 points)

Date FB return AMZN return MSFT return CMG return T-bill return 2012/5/1 5.07% 7.25% 4.80% -8.02% 0.01% 2012/6/1 -30.19% 2.17% -3.66% -23.06% 0.00% 2012/7/1 - 16.81% 6.42% 4.58% -1.26% 0.00% 2012/8/1 19.93% 2.44% -3.44% 10.01% 0.01% 2012/9/1 -2.54% -8.43% -4.10% - 19.84% 0.01% 2012/10/1 32.64% 8.23% -6.73% 3.63% 0.01% 2012/11/1 -4.93% -0.47% 0.34% 12.77% 0.01% 2012/12/1 16.38% 5.83% 2.77% 3.21% 0.01% 2013/1/1 - 12.04% -0.46% 1.28% 3.19% 0.00% 2013/2/1 -6.13% 0.84% 2.91% 2.87% 0.00% 2013/3/1 8.56% -4.76% 15.69% 11.45% 0.00% 2013/4/1 -12.32% 6.06% 5.44% -0.60% 0.00% 2013/5/1 2.18% 3.15% -1.03% 0.93% 0.00% 2013/6/1 47.91% 8.47% -7.82% 13.15% 0.00% 2013/7/1 12.20% -6.72% 4.90% -0.99% 0.00% 2013/8/1 21.65% 11.27% -0.36% 5.05% 0.00% 2013/9/1 -0.04% 16.44% 6.40% 22.89% 0.00% 2013/10/1 -6.37% 8.13% 7.68% -0.59% 0.00% 2013/11/1 16.25% 1.31% -1.89% 1.70% 0.00% 2013/12/1 14.49% - 10.06% 1.15% 3.60% 0.00% 2014/1/1 9.41% 0.95% 1.24% 2.40% 0.00% 2014/2/1 - 12.01% -7.11% 7.00% 0.50% 0.00% 2014/3/1 -0.76% -9.58% -1.44% - 12.24% 0.00% 2014/4/1 5.89% 2.77% 1.34% 9.75% 0.00% 2014/5/1 6.30% 3.91% 1.86% 8.30% 0.00% 2014/6/1 7.97% -3.63% 3.50% 13.50% 0.00% 2014/7/1 2.99% 8.32% 5.26% 0.91% 0.00% 2014/8/1 5.64% -4.90% 2.05% -1.78% 0.00% 2014/9/1 -5.12% -5.27% 1.27% -4.29% 0.00% 2014/10/1 3.61% 10.86% 1.83% 4.02% 0.00% 2014/11/1 0.41% -8.35% -2.84% 3.15% 0.00% 2014/12/1 - 2.70% 14.24% -13.02% 3.70% 0.00% 2015/1/1 2015/2/1 2015/3/1 2015/4/1 2015/5/1 2015/6/1 2015/7/1 2015/8/1 2015/9/1 2015/10/1 2015/11/1 2015/12/1 2016/1/1 2016/2/1 2016/3/1 2016/4/1 2016/5/1 2016/6/1 2016/7/1 2016/8/1 2016/9/1 2016/10/1 2016/11/1 2016/12/1 2017/1/1 2017/2/1 2017/3/1 2017/4/1 2017/5/1 2017/6/1 2017/7/1 2017/8/1 2017/9/1 2017/10/1 2017/11/1 2017/12/1 4.03% 4.12% -4.20% 0.53% 8.31% 9.61% -4.55% 0.19% 13.43% 2.23% 0.40% 7.21% -4.71% 6.72% 3.05% 1.05% -3.81% 8.45% 1.76% 1.70% 2.12% -9.60% -2.85% 13.27% 4.01% 4.80% 5.77% 0.81% -0.32% 12.10% 1.61% -0.64% 5.38% -1.60% -0.41% 5.91% 7.23% -2.12% 13.35% 1.77% 1.13% 23.51% -4.34% -0.19% 22.27% 6.22% 1.67% -13.15% -5.87% 7.44% 11.11% 9.58% -0.99% 6.04% 1.36% 8.86% -5.67% -4.97% 2.41% 7.13% 2.62% 4.91% 4.34% 7.53% -2.68% 2.04% -0.73% -1.96% 14.97% 6.47% -0.62% 24.06% 8.54% -7.27% 19.63% -3.66% -5.78% 5.78% -6.81% 1.70% 18.93% 3.25% 2.08% -0.70% -7.64% 8.55% -9.70% 6.28% -3.45% 10.77% 1.38% 0.24% 4.03% 0.57% 3.12% 4.04% - 1.04% 2.94% 3.95% 2.02% -1.30% 5.47% 2.85% -0.37% 11.67% 1.19% 1.63% 11.07% -6.32% -2.17% -4.49% -0.94% -1.71% 22.68% -2.03% -0.95% - 11.11% -9.48% - 17.20% -5.60% 12.40% -7.50% -10.62% 4.99% -8.87% 5.27% -2.42% 2.36% - 14.81% 9.86% -4.80% 11.69% -0.64% 6.40% 6.50% 0.61% -12.83% - 17.38% - 7.87% -2.80% - 11.67% 11.95% -5.05% 12.36% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.01% 0.01% 0.02% 0.02% 0.01% 0.01% 0.02% 0.02% 0.02% 0.02% 0.02% 0.01% 0.03% 0.04% 0.04% 0.03% 0.05% 0.06% 0.06% 0.07% 0.09% 0.09% 0.09% 0.08% 0.09% 2018/1/1 2018/2/1 2018/3/1 2018/4/1 2018/5/1 2018/6/1 2018/7/1 2018/8/1 2018/9/1 2018/10/1 2018/11/1 2018/12/1 2019/1/1 2019/2/1 2019/3/1 2019/4/1 2019/5/1 2019/6/1 2019/7/1 2019/8/1 2019/9/1 2019/10/1 2019/11/1 2019/12/1 2020/1/1 2020/2/1 2020/3/1 2020/4/1 2020/5/1 2020/6/1 2020/7/1 2020/8/1 2020/9/1 -4.59% -10.39% 7.64% 11.50% 1.32% - 11.19% 1.83% -6.41% -7.70% -7.37% -6.77% 27.16% -3.14% 3.25% 16.02% -8.24% 8.75% 0.64% -4.41% -4.09% 7.62% 5.21% 1.79% -1.63% -4.68% - 13.34% 22.73% 9.96% 0.88% 11.71% 15.58% -10.68% 0.46% 4.24% -4.30% 8.21% 4.05% 4.31% 4.57% 13.24% -0.48% -20.22% 5.77% -11.13% 14.43% - 4.59% 8.59% 8.19% -7.86% 6.68% -1.42% -4.85% -2.27% 2.35% 1.36% 2.61% 8.71% -6.22% 3.50% 26.89% - 1.28% 12.96% 14.71% 9.05% -8.76% -3.58% -1.31% -2.67% 2.47% 5.69% -0.23% 7.58% 5.89% 1.82% -6.61% 3.82% -8.40% 2.82% 7.28% 5.28% 10.73% -5.30% 8.31% 1.72% 1.17% 0.85% 3.12% 5.59% 4.17% 7.95% -4.83% -2.65% 13.63% 2.25% 11.06% 0.74% 10.01% -6.74% -3.74% -1.96% 1.48% 31.02% 1.62% 0.28% 0.53% 9.57% -4.35% 1.28% 2.80% -8.75% 22.65% 14.71% 16.92% -3.14% -4.08% 11.05% 8.55% 5.39% 0.24% -7.41% 4.60% 2.85% 3.54% -10.75% -15.41% 34.25% 14.27% 4.83% 9.77% 13.43% -5.08% -3.40% 0.11% 0.11% 0.12% 0.14% 0.14% 0.14% 0.16% 0.16% 0.15% 0.19% 0.18% 0.19% 0.21% 0.18% 0.19% 0.21% 0.21% 0.18% 0.19% 0.16% 0.18% 0.15% 0.12% 0.14% 0.13% 0.12% 0.12% 0.00% 0.01% 0.01% 0.01% 0.01% 0.01% Date FB return AMZN return MSFT return CMG return T-bill return 2012/5/1 5.07% 7.25% 4.80% -8.02% 0.01% 2012/6/1 -30.19% 2.17% -3.66% -23.06% 0.00% 2012/7/1 - 16.81% 6.42% 4.58% -1.26% 0.00% 2012/8/1 19.93% 2.44% -3.44% 10.01% 0.01% 2012/9/1 -2.54% -8.43% -4.10% - 19.84% 0.01% 2012/10/1 32.64% 8.23% -6.73% 3.63% 0.01% 2012/11/1 -4.93% -0.47% 0.34% 12.77% 0.01% 2012/12/1 16.38% 5.83% 2.77% 3.21% 0.01% 2013/1/1 - 12.04% -0.46% 1.28% 3.19% 0.00% 2013/2/1 -6.13% 0.84% 2.91% 2.87% 0.00% 2013/3/1 8.56% -4.76% 15.69% 11.45% 0.00% 2013/4/1 -12.32% 6.06% 5.44% -0.60% 0.00% 2013/5/1 2.18% 3.15% -1.03% 0.93% 0.00% 2013/6/1 47.91% 8.47% -7.82% 13.15% 0.00% 2013/7/1 12.20% -6.72% 4.90% -0.99% 0.00% 2013/8/1 21.65% 11.27% -0.36% 5.05% 0.00% 2013/9/1 -0.04% 16.44% 6.40% 22.89% 0.00% 2013/10/1 -6.37% 8.13% 7.68% -0.59% 0.00% 2013/11/1 16.25% 1.31% -1.89% 1.70% 0.00% 2013/12/1 14.49% - 10.06% 1.15% 3.60% 0.00% 2014/1/1 9.41% 0.95% 1.24% 2.40% 0.00% 2014/2/1 - 12.01% -7.11% 7.00% 0.50% 0.00% 2014/3/1 -0.76% -9.58% -1.44% - 12.24% 0.00% 2014/4/1 5.89% 2.77% 1.34% 9.75% 0.00% 2014/5/1 6.30% 3.91% 1.86% 8.30% 0.00% 2014/6/1 7.97% -3.63% 3.50% 13.50% 0.00% 2014/7/1 2.99% 8.32% 5.26% 0.91% 0.00% 2014/8/1 5.64% -4.90% 2.05% -1.78% 0.00% 2014/9/1 -5.12% -5.27% 1.27% -4.29% 0.00% 2014/10/1 3.61% 10.86% 1.83% 4.02% 0.00% 2014/11/1 0.41% -8.35% -2.84% 3.15% 0.00% 2014/12/1 - 2.70% 14.24% -13.02% 3.70% 0.00% 2015/1/1 2015/2/1 2015/3/1 2015/4/1 2015/5/1 2015/6/1 2015/7/1 2015/8/1 2015/9/1 2015/10/1 2015/11/1 2015/12/1 2016/1/1 2016/2/1 2016/3/1 2016/4/1 2016/5/1 2016/6/1 2016/7/1 2016/8/1 2016/9/1 2016/10/1 2016/11/1 2016/12/1 2017/1/1 2017/2/1 2017/3/1 2017/4/1 2017/5/1 2017/6/1 2017/7/1 2017/8/1 2017/9/1 2017/10/1 2017/11/1 2017/12/1 4.03% 4.12% -4.20% 0.53% 8.31% 9.61% -4.55% 0.19% 13.43% 2.23% 0.40% 7.21% -4.71% 6.72% 3.05% 1.05% -3.81% 8.45% 1.76% 1.70% 2.12% -9.60% -2.85% 13.27% 4.01% 4.80% 5.77% 0.81% -0.32% 12.10% 1.61% -0.64% 5.38% -1.60% -0.41% 5.91% 7.23% -2.12% 13.35% 1.77% 1.13% 23.51% -4.34% -0.19% 22.27% 6.22% 1.67% -13.15% -5.87% 7.44% 11.11% 9.58% -0.99% 6.04% 1.36% 8.86% -5.67% -4.97% 2.41% 7.13% 2.62% 4.91% 4.34% 7.53% -2.68% 2.04% -0.73% -1.96% 14.97% 6.47% -0.62% 24.06% 8.54% -7.27% 19.63% -3.66% -5.78% 5.78% -6.81% 1.70% 18.93% 3.25% 2.08% -0.70% -7.64% 8.55% -9.70% 6.28% -3.45% 10.77% 1.38% 0.24% 4.03% 0.57% 3.12% 4.04% - 1.04% 2.94% 3.95% 2.02% -1.30% 5.47% 2.85% -0.37% 11.67% 1.19% 1.63% 11.07% -6.32% -2.17% -4.49% -0.94% -1.71% 22.68% -2.03% -0.95% - 11.11% -9.48% - 17.20% -5.60% 12.40% -7.50% -10.62% 4.99% -8.87% 5.27% -2.42% 2.36% - 14.81% 9.86% -4.80% 11.69% -0.64% 6.40% 6.50% 0.61% -12.83% - 17.38% - 7.87% -2.80% - 11.67% 11.95% -5.05% 12.36% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.01% 0.01% 0.02% 0.02% 0.01% 0.01% 0.02% 0.02% 0.02% 0.02% 0.02% 0.01% 0.03% 0.04% 0.04% 0.03% 0.05% 0.06% 0.06% 0.07% 0.09% 0.09% 0.09% 0.08% 0.09% 2018/1/1 2018/2/1 2018/3/1 2018/4/1 2018/5/1 2018/6/1 2018/7/1 2018/8/1 2018/9/1 2018/10/1 2018/11/1 2018/12/1 2019/1/1 2019/2/1 2019/3/1 2019/4/1 2019/5/1 2019/6/1 2019/7/1 2019/8/1 2019/9/1 2019/10/1 2019/11/1 2019/12/1 2020/1/1 2020/2/1 2020/3/1 2020/4/1 2020/5/1 2020/6/1 2020/7/1 2020/8/1 2020/9/1 -4.59% -10.39% 7.64% 11.50% 1.32% - 11.19% 1.83% -6.41% -7.70% -7.37% -6.77% 27.16% -3.14% 3.25% 16.02% -8.24% 8.75% 0.64% -4.41% -4.09% 7.62% 5.21% 1.79% -1.63% -4.68% - 13.34% 22.73% 9.96% 0.88% 11.71% 15.58% -10.68% 0.46% 4.24% -4.30% 8.21% 4.05% 4.31% 4.57% 13.24% -0.48% -20.22% 5.77% -11.13% 14.43% - 4.59% 8.59% 8.19% -7.86% 6.68% -1.42% -4.85% -2.27% 2.35% 1.36% 2.61% 8.71% -6.22% 3.50% 26.89% - 1.28% 12.96% 14.71% 9.05% -8.76% -3.58% -1.31% -2.67% 2.47% 5.69% -0.23% 7.58% 5.89% 1.82% -6.61% 3.82% -8.40% 2.82% 7.28% 5.28% 10.73% -5.30% 8.31% 1.72% 1.17% 0.85% 3.12% 5.59% 4.17% 7.95% -4.83% -2.65% 13.63% 2.25% 11.06% 0.74% 10.01% -6.74% -3.74% -1.96% 1.48% 31.02% 1.62% 0.28% 0.53% 9.57% -4.35% 1.28% 2.80% -8.75% 22.65% 14.71% 16.92% -3.14% -4.08% 11.05% 8.55% 5.39% 0.24% -7.41% 4.60% 2.85% 3.54% -10.75% -15.41% 34.25% 14.27% 4.83% 9.77% 13.43% -5.08% -3.40% 0.11% 0.11% 0.12% 0.14% 0.14% 0.14% 0.16% 0.16% 0.15% 0.19% 0.18% 0.19% 0.21% 0.18% 0.19% 0.21% 0.21% 0.18% 0.19% 0.16% 0.18% 0.15% 0.12% 0.14% 0.13% 0.12% 0.12% 0.00% 0.01% 0.01% 0.01% 0.01% 0.01%