With the financial data given

A. Calculate the return, variance, and sharpe ratio for a portfolio constructed of 60% (SPY index) /40 % (TNX index) ytd. Compare to a portfolio constructed of 40% (SPY index) /40 % (TNX index) / 20% (VIX) ytd.

B. Calculate the covariance of VIX and SPY Index. Calculate the covariance of VIX and TNX.

C. Explain the results this data.xlsx

\begin{tabular}{|r|r|r|r|} \hline 9/16/22 & 385.559998 & 26.299999 & 3.265 \\ \hline 9/19/22 & 388.549988 & 25.76 & 3.193 \\ \hline 9/20/22 & 384.089996 & 27.16 & 3.34 \\ \hline 9/21/22 & 377.390015 & 27.99 & 3.265 \\ \hline 9/22/22 & 374.220001 & 27.35 & 3.292 \\ \hline 9/23/22 & 367.950012 & 29.92 & 3.321 \\ \hline 9/26/22 & 364.309998 & 32.259998 & 3.362 \\ \hline 9/27/22 & 363.380005 & 32.599998 & 3.422 \\ \hline 9/28/22 & 370.529999 & 30.18 & 3.412 \\ \hline 9/29/22 & 362.790009 & 31.84 & 3.459 \\ \hline 9/30/22 & 357.179993 & 31.620001 & 3.448 \\ \hline 10/3/22 & 366.609985 & 30.1 & 3.49 \\ \hline 10/4/22 & 377.970001 & 29.07 & 3.651 \\ \hline 10/5/22 & 377.089996 & 28.549999 & 3.617 \\ \hline 10/6/22 & 373.200012 & 30.52 & 3.759 \\ \hline 10/7/22 & 362.790009 & 31.360001 & 3.826 \\ \hline 10/10/22 & 360.019989 & 32.450001 & 3.883 \\ \hline 10/11/22 & 357.73999 & 33.630001 & 3.888 \\ \hline 10/12/22 & 356.559998 & 33.57 & 3.939 \\ \hline 10/13/22 & 365.970001 & 31.940001 & 3.902 \\ \hline 10/14/22 & 358.665009 & 32.790001 & 3.952 \\ \hline \end{tabular} \begin{tabular}{|r|r|r|r|} \hline 6/14/22 & 373.869995 & 32.689999 & 2.844 \\ \hline 6/15/22 & 379.200012 & 29.620001 & 2.931 \\ \hline 6/16/22 & 366.649994 & 32.950001 & 2.913 \\ \hline 6/17/22 & 365.859985 & 31.129999 & 2.957 \\ \hline 6/21/22 & 375.070007 & 30.190001 & 3.038 \\ \hline 6/22/22 & 374.390015 & 28.950001 & 2.972 \\ \hline 6/23/22 & 378.059998 & 29.049999 & 3.029 \\ \hline 6/24/22 & 390.079987 & 27.23 & 3.044 \\ \hline 6/27/22 & 388.589996 & 26.950001 & 3.156 \\ \hline 6/28/22 & 380.649994 & 28.360001 & 3.366 \\ \hline 6/29/22 & 380.339996 & 28.16 & 3.483 \\ \hline 6/30/22 & 377.25 & 28.709999 & 3.395 \\ \hline 7/1/22 & 381.23999 & 26.700001 & 3.307 \\ \hline 7/5/22 & 381.959991 & 27.540001 & 3.239 \\ \hline 7/6/22 & 383.25 & 26.73 & 3.307 \\ \hline 7/7/22 & 388.98999 & 26.08 & 3.156 \\ \hline 7/8/22 & 388.670013 & 24.639999 & 3.068 \\ \hline 7/11/22 & 384.230011 & 26.17 & 3.125 \\ \hline 7/12/22 & 380.829987 & 27.290001 & 3.194 \\ \hline 7/13/22 & 378.829987 & 26.82 & 3.206 \\ \hline 7/14/22 & 377.910004 & 26.4 & 3.093 \\ \hline 7/15/22 & 385.130005 & 24.23 & 2.972 \\ \hline 7/18/22 & 381.950012 & 25.299999 & 2.889 \\ \hline 7/19/22 & 392.269989 & 24.5 & 2.809 \\ \hline 7/20/22 & 394.769989 & 23.879999 & 2.913 \\ \hline 7/21/22 & 398.790009 & 23.110001 & 3.008 \\ \hline 7/22/22 & 395.089996 & 23.030001 & 3.101 \\ \hline 7/25/22 & 395.570007 & 23.360001 & 2.991 \\ \hline 7/26/22 & 390.890015 & 24.690001 & 2.958 \\ \hline 7/27/22 & 401.040009 & 23.24 & 2.904 \\ \hline 7/28/22 & 406.070007 & 22.33 & 2.96 \\ \hline \end{tabular} \begin{tabular}{|r|r|r|r|} \hline 7/29/22 & 411.98999 & 21.33 & 2.93 \\ \hline 8/1/22 & 410.769989 & 22.84 & 2.96 \\ \hline 8/2/22 & 408.059998 & 23.93 & 3.019 \\ \hline 8/3/22 & 414.450012 & 21.950001 & 3.036 \\ \hline 8/4/22 & 414.170013 & 21.440001 & 2.91 \\ \hline 8/5/22 & 413.470001 & 21.15 & 2.783 \\ \hline 8/8/22 & 412.98999 & 21.290001 & 2.82 \\ \hline 8/9/22 & 411.350006 & 21.77 & 2.787 \\ \hline 8/10/22 & 419.98999 & 19.74 & 2.734 \\ \hline 8/11/22 & 419.98999 & 20.200001 & 2.681 \\ \hline 8/12/22 & 427.100006 & 19.530001 & 2.642 \\ \hline 8/15/22 & 428.859985 & 19.950001 & 2.606 \\ \hline 8/16/22 & 429.700012 & 19.690001 & 2.741 \\ \hline 8/17/22 & 426.649994 & 19.9 & 2.748 \\ \hline 8/18/22 & 427.890015 & 19.559999 & 2.676 \\ \hline 8/19/22 & 422.140015 & 20.6 & 2.84 \\ \hline 8/22/22 & 413.350006 & 23.799999 & 2.765 \\ \hline 8/23/22 & 412.350006 & 24.110001 & 2.797 \\ \hline 8/24/22 & 413.670013 & 22.82 & 2.786 \\ \hline 9/14/22 & 394.600006 & 26.16 & 3.11 \\ \hline 8/25/22 & 419.51001 & 21.780001 & 2.888 \\ \hline 8/26/22 & 405.309998 & 25.559999 & 2.849 \\ \hline 8/29/22 & 402.630005 & 26.209999 & 2.791 \\ \hline 8/30/22 & 398.209991 & 26.209999 & 2.824 \\ \hline 8/31/22 & 395.179993 & 25.870001 & 2.893 \\ \hline 9/1/22 & 396.420013 & 25.559999 & 2.88 \\ \hline 9/2/22 & 392.23999 & 25.469999 & 2.989 \\ \hline 9/6/22 & 390.76001 & 26.91 & 3.037 \\ \hline 9/7/22 & 397.779999 & 24.639999 & 3.054 \\ \hline 9/8/22 & 400.380005 & 23.610001 & 3.106 \\ \hline 9/9/22 & 406.600006 & 22.790001 & 3.026 \\ \hline 9/210.970001 & 23.870001 & 3.035 \\ \hline \end{tabular} \begin{tabular}{|r|r|r|r|} \hline 9/9/22 & 406.600006 & 22.790001 & 3.026 \\ \hline 9/12/22 & 410.970001 & 23.870001 & 3.035 \\ \hline 9/13/22 & 393.100006 & 27.27 & 3.11 \\ \hline 9/14/22 & 394.600006 & 26.16 & 3.11 \\ \hline 9/15/22 & 390.119995 & 26.27 & 3.133 \\ \hline 9/16/22 & 385.559998 & 26.299999 & 3.265 \\ \hline 9/19/22 & 388.549988 & 25.76 & 3.193 \\ \hline 9/20/22 & 384.089996 & 27.16 & 3.34 \\ \hline 9/21/22 & 377.390015 & 27.99 & 3.265 \\ \hline 9/22/22 & 374.220001 & 27.35 & 3.292 \\ \hline 9/23/22 & 367.950012 & 29.92 & 3.321 \\ \hline 9/26/22 & 364.309998 & 32.259998 & 3.362 \\ \hline 9/27/22 & 363.380005 & 32.599998 & 3.422 \\ \hline 9/28/22 & 370.529999 & 30.18 & 3.412 \\ \hline 9/29/22 & 362.790009 & 31.84 & 3.459 \\ \hline 9/30/22 & 357.179993 & 31.620001 & 3.448 \\ \hline 10/3/22 & 366.609985 & 30.1 & 3.49 \\ \hline 10/4/22 & 377.970001 & 29.07 & 3.651 \\ \hline 10/5/22 & 377.089996 & 28.549999 & 3.617 \\ \hline 10/6/22 & 373.200012 & 30.52 & 3.759 \\ \hline 10/7/22 & 362.790009 & 31.360001 & 3.826 \\ \hline 10/10/22 & 360.019989 & 32.450001 & 3.883 \\ \hline 10/11/22 & 357.73999 & 33.630001 & 3.888 \\ \hline 10/12/22 & 356.559998 & 33.57 & 3.939 \\ \hline 10/13/22 & 365.970001 & 31.940001 & 3.902 \\ \hline 10/14/22 & 358.665009 & 32.790001 & 3.952 \\ \hline \end{tabular} \begin{tabular}{|r|r|r|r|} \hline 4/25/22 & 428.51001 & 27.02 & 2.713 \\ \hline 4/26/22 & 416.100006 & 33.52 & 2.78 \\ \hline 4/27/22 & 417.269989 & 31.6 & 2.725 \\ \hline 4/28/22 & 427.809998 & 29.99 & 2.687 \\ \hline 4/29/22 & 412 & 33.400002 & 2.828 \\ \hline 5/2/22 & 414.480011 & 32.34 & 2.862 \\ \hline 5/3/22 & 416.380005 & 29.25 & 2.913 \\ \hline 5/4/22 & 429.059998 & 25.42 & 2.84 \\ \hline 5/5/22 & 413.809998 & 31.200001 & 2.917 \\ \hline 5/6/22 & 411.339996 & 30.190001 & 2.906 \\ \hline 5/9/22 & 398.170013 & 34.75 & 2.826 \\ \hline 5/10/22 & 399.089996 & 32.990002 & 2.772 \\ \hline 5/11/22 & 392.75 & 32.560001 & 2.818 \\ \hline 5/12/22 & 392.339996 & 31.77 & 2.863 \\ \hline 5/13/22 & 401.720001 & 28.870001 & 2.887 \\ \hline 6/9/22 & 401.440002 & 26.09 & 2.749 \\ \hline 5/16/22 & 400.089996 & 27.469999 & 2.996 \\ \hline 5/17/22 & 408.320007 & 26.1 & 2.96 \\ \hline 5/18/22 & 391.859985 & 30.959999 & 2.917 \\ \hline 5/19/22 & 389.459991 & 29.35 & 3.066 \\ \hline 5/20/22 & 389.630005 & 29.43 & 3.123 \\ \hline 5/23/22 & 396.920013 & 28.48 & 3.079 \\ \hline 5/24/22 & 393.890015 & 29.450001 & 2.993 \\ \hline 5/25/22 & 397.369995 & 28.370001 & 2.921 \\ \hline 5/26/22 & 405.309998 & 27.5 & 2.817 \\ \hline 5/27/22 & 415.26001 & 25.719999 & 2.935 \\ \hline 5/31/22 & 412.929993 & 26.190001 & 2.877 \\ \hline 6/1/22 & 409.589996 & 25.690001 & 2.968 \\ \hline 6/2/22 & 417.390015 & 24.719999 & 2.886 \\ \hline 6/22 & 410.540009 & 24.790001 & 2.855 \\ \hline 6 \end{tabular} \begin{tabular}{|r|r|r|r|} \hline 9/16/22 & 385.559998 & 26.299999 & 3.265 \\ \hline 9/19/22 & 388.549988 & 25.76 & 3.193 \\ \hline 9/20/22 & 384.089996 & 27.16 & 3.34 \\ \hline 9/21/22 & 377.390015 & 27.99 & 3.265 \\ \hline 9/22/22 & 374.220001 & 27.35 & 3.292 \\ \hline 9/23/22 & 367.950012 & 29.92 & 3.321 \\ \hline 9/26/22 & 364.309998 & 32.259998 & 3.362 \\ \hline 9/27/22 & 363.380005 & 32.599998 & 3.422 \\ \hline 9/28/22 & 370.529999 & 30.18 & 3.412 \\ \hline 9/29/22 & 362.790009 & 31.84 & 3.459 \\ \hline 9/30/22 & 357.179993 & 31.620001 & 3.448 \\ \hline 10/3/22 & 366.609985 & 30.1 & 3.49 \\ \hline 10/4/22 & 377.970001 & 29.07 & 3.651 \\ \hline 10/5/22 & 377.089996 & 28.549999 & 3.617 \\ \hline 10/6/22 & 373.200012 & 30.52 & 3.759 \\ \hline 10/7/22 & 362.790009 & 31.360001 & 3.826 \\ \hline 10/10/22 & 360.019989 & 32.450001 & 3.883 \\ \hline 10/11/22 & 357.73999 & 33.630001 & 3.888 \\ \hline 10/12/22 & 356.559998 & 33.57 & 3.939 \\ \hline 10/13/22 & 365.970001 & 31.940001 & 3.902 \\ \hline 10/14/22 & 358.665009 & 32.790001 & 3.952 \\ \hline \end{tabular} \begin{tabular}{|r|r|r|r|} \hline 6/14/22 & 373.869995 & 32.689999 & 2.844 \\ \hline 6/15/22 & 379.200012 & 29.620001 & 2.931 \\ \hline 6/16/22 & 366.649994 & 32.950001 & 2.913 \\ \hline 6/17/22 & 365.859985 & 31.129999 & 2.957 \\ \hline 6/21/22 & 375.070007 & 30.190001 & 3.038 \\ \hline 6/22/22 & 374.390015 & 28.950001 & 2.972 \\ \hline 6/23/22 & 378.059998 & 29.049999 & 3.029 \\ \hline 6/24/22 & 390.079987 & 27.23 & 3.044 \\ \hline 6/27/22 & 388.589996 & 26.950001 & 3.156 \\ \hline 6/28/22 & 380.649994 & 28.360001 & 3.366 \\ \hline 6/29/22 & 380.339996 & 28.16 & 3.483 \\ \hline 6/30/22 & 377.25 & 28.709999 & 3.395 \\ \hline 7/1/22 & 381.23999 & 26.700001 & 3.307 \\ \hline 7/5/22 & 381.959991 & 27.540001 & 3.239 \\ \hline 7/6/22 & 383.25 & 26.73 & 3.307 \\ \hline 7/7/22 & 388.98999 & 26.08 & 3.156 \\ \hline 7/8/22 & 388.670013 & 24.639999 & 3.068 \\ \hline 7/11/22 & 384.230011 & 26.17 & 3.125 \\ \hline 7/12/22 & 380.829987 & 27.290001 & 3.194 \\ \hline 7/13/22 & 378.829987 & 26.82 & 3.206 \\ \hline 7/14/22 & 377.910004 & 26.4 & 3.093 \\ \hline 7/15/22 & 385.130005 & 24.23 & 2.972 \\ \hline 7/18/22 & 381.950012 & 25.299999 & 2.889 \\ \hline 7/19/22 & 392.269989 & 24.5 & 2.809 \\ \hline 7/20/22 & 394.769989 & 23.879999 & 2.913 \\ \hline 7/21/22 & 398.790009 & 23.110001 & 3.008 \\ \hline 7/22/22 & 395.089996 & 23.030001 & 3.101 \\ \hline 7/25/22 & 395.570007 & 23.360001 & 2.991 \\ \hline 7/26/22 & 390.890015 & 24.690001 & 2.958 \\ \hline 7/27/22 & 401.040009 & 23.24 & 2.904 \\ \hline 7/28/22 & 406.070007 & 22.33 & 2.96 \\ \hline \end{tabular} \begin{tabular}{|r|r|r|r|} \hline 7/29/22 & 411.98999 & 21.33 & 2.93 \\ \hline 8/1/22 & 410.769989 & 22.84 & 2.96 \\ \hline 8/2/22 & 408.059998 & 23.93 & 3.019 \\ \hline 8/3/22 & 414.450012 & 21.950001 & 3.036 \\ \hline 8/4/22 & 414.170013 & 21.440001 & 2.91 \\ \hline 8/5/22 & 413.470001 & 21.15 & 2.783 \\ \hline 8/8/22 & 412.98999 & 21.290001 & 2.82 \\ \hline 8/9/22 & 411.350006 & 21.77 & 2.787 \\ \hline 8/10/22 & 419.98999 & 19.74 & 2.734 \\ \hline 8/11/22 & 419.98999 & 20.200001 & 2.681 \\ \hline 8/12/22 & 427.100006 & 19.530001 & 2.642 \\ \hline 8/15/22 & 428.859985 & 19.950001 & 2.606 \\ \hline 8/16/22 & 429.700012 & 19.690001 & 2.741 \\ \hline 8/17/22 & 426.649994 & 19.9 & 2.748 \\ \hline 8/18/22 & 427.890015 & 19.559999 & 2.676 \\ \hline 8/19/22 & 422.140015 & 20.6 & 2.84 \\ \hline 8/22/22 & 413.350006 & 23.799999 & 2.765 \\ \hline 8/23/22 & 412.350006 & 24.110001 & 2.797 \\ \hline 8/24/22 & 413.670013 & 22.82 & 2.786 \\ \hline 9/14/22 & 394.600006 & 26.16 & 3.11 \\ \hline 8/25/22 & 419.51001 & 21.780001 & 2.888 \\ \hline 8/26/22 & 405.309998 & 25.559999 & 2.849 \\ \hline 8/29/22 & 402.630005 & 26.209999 & 2.791 \\ \hline 8/30/22 & 398.209991 & 26.209999 & 2.824 \\ \hline 8/31/22 & 395.179993 & 25.870001 & 2.893 \\ \hline 9/1/22 & 396.420013 & 25.559999 & 2.88 \\ \hline 9/2/22 & 392.23999 & 25.469999 & 2.989 \\ \hline 9/6/22 & 390.76001 & 26.91 & 3.037 \\ \hline 9/7/22 & 397.779999 & 24.639999 & 3.054 \\ \hline 9/8/22 & 400.380005 & 23.610001 & 3.106 \\ \hline 9/9/22 & 406.600006 & 22.790001 & 3.026 \\ \hline 9/210.970001 & 23.870001 & 3.035 \\ \hline \end{tabular} \begin{tabular}{|r|r|r|r|} \hline 9/9/22 & 406.600006 & 22.790001 & 3.026 \\ \hline 9/12/22 & 410.970001 & 23.870001 & 3.035 \\ \hline 9/13/22 & 393.100006 & 27.27 & 3.11 \\ \hline 9/14/22 & 394.600006 & 26.16 & 3.11 \\ \hline 9/15/22 & 390.119995 & 26.27 & 3.133 \\ \hline 9/16/22 & 385.559998 & 26.299999 & 3.265 \\ \hline 9/19/22 & 388.549988 & 25.76 & 3.193 \\ \hline 9/20/22 & 384.089996 & 27.16 & 3.34 \\ \hline 9/21/22 & 377.390015 & 27.99 & 3.265 \\ \hline 9/22/22 & 374.220001 & 27.35 & 3.292 \\ \hline 9/23/22 & 367.950012 & 29.92 & 3.321 \\ \hline 9/26/22 & 364.309998 & 32.259998 & 3.362 \\ \hline 9/27/22 & 363.380005 & 32.599998 & 3.422 \\ \hline 9/28/22 & 370.529999 & 30.18 & 3.412 \\ \hline 9/29/22 & 362.790009 & 31.84 & 3.459 \\ \hline 9/30/22 & 357.179993 & 31.620001 & 3.448 \\ \hline 10/3/22 & 366.609985 & 30.1 & 3.49 \\ \hline 10/4/22 & 377.970001 & 29.07 & 3.651 \\ \hline 10/5/22 & 377.089996 & 28.549999 & 3.617 \\ \hline 10/6/22 & 373.200012 & 30.52 & 3.759 \\ \hline 10/7/22 & 362.790009 & 31.360001 & 3.826 \\ \hline 10/10/22 & 360.019989 & 32.450001 & 3.883 \\ \hline 10/11/22 & 357.73999 & 33.630001 & 3.888 \\ \hline 10/12/22 & 356.559998 & 33.57 & 3.939 \\ \hline 10/13/22 & 365.970001 & 31.940001 & 3.902 \\ \hline 10/14/22 & 358.665009 & 32.790001 & 3.952 \\ \hline \end{tabular} \begin{tabular}{|r|r|r|r|} \hline 4/25/22 & 428.51001 & 27.02 & 2.713 \\ \hline 4/26/22 & 416.100006 & 33.52 & 2.78 \\ \hline 4/27/22 & 417.269989 & 31.6 & 2.725 \\ \hline 4/28/22 & 427.809998 & 29.99 & 2.687 \\ \hline 4/29/22 & 412 & 33.400002 & 2.828 \\ \hline 5/2/22 & 414.480011 & 32.34 & 2.862 \\ \hline 5/3/22 & 416.380005 & 29.25 & 2.913 \\ \hline 5/4/22 & 429.059998 & 25.42 & 2.84 \\ \hline 5/5/22 & 413.809998 & 31.200001 & 2.917 \\ \hline 5/6/22 & 411.339996 & 30.190001 & 2.906 \\ \hline 5/9/22 & 398.170013 & 34.75 & 2.826 \\ \hline 5/10/22 & 399.089996 & 32.990002 & 2.772 \\ \hline 5/11/22 & 392.75 & 32.560001 & 2.818 \\ \hline 5/12/22 & 392.339996 & 31.77 & 2.863 \\ \hline 5/13/22 & 401.720001 & 28.870001 & 2.887 \\ \hline 6/9/22 & 401.440002 & 26.09 & 2.749 \\ \hline 5/16/22 & 400.089996 & 27.469999 & 2.996 \\ \hline 5/17/22 & 408.320007 & 26.1 & 2.96 \\ \hline 5/18/22 & 391.859985 & 30.959999 & 2.917 \\ \hline 5/19/22 & 389.459991 & 29.35 & 3.066 \\ \hline 5/20/22 & 389.630005 & 29.43 & 3.123 \\ \hline 5/23/22 & 396.920013 & 28.48 & 3.079 \\ \hline 5/24/22 & 393.890015 & 29.450001 & 2.993 \\ \hline 5/25/22 & 397.369995 & 28.370001 & 2.921 \\ \hline 5/26/22 & 405.309998 & 27.5 & 2.817 \\ \hline 5/27/22 & 415.26001 & 25.719999 & 2.935 \\ \hline 5/31/22 & 412.929993 & 26.190001 & 2.877 \\ \hline 6/1/22 & 409.589996 & 25.690001 & 2.968 \\ \hline 6/2/22 & 417.390015 & 24.719999 & 2.886 \\ \hline 6/22 & 410.540009 & 24.790001 & 2.855 \\ \hline 6 \end{tabular}