# Student Information

## Question 1

 You would like to purchase a call option for the high tech stock MCCA. MCCA Assume today is April 29, 2021, before the market has opened. Option Type Stock Price IV Strike Price Exp Vol Open Int Call 21.18 36.32% 20.00 May, 2021 3,051 40,421 Annual interest rate = 3.00% Trading days per year = 252 a) How many days (for price calculations) until the option expires? Days = Points 4 Grade b) Based on the information shown in the table to the right, create the complete daily binomial lattice for the stock price. Show your latttice. Points 2 Grade c) Using a daily binomial lattice, calculate the option value. Option Value = Show your option value lattice. Points 2 Grade d) Estimate the delta and the gamma for this option using the binomial Delta = lattice results. Gamma = Points 3 Grade

## Question 2

 You would like to purchase a put option for the high tech stock MCCA. MCCA Assume today is April 29, 2021, before the market has opened. Option Type Stock Price IV Strike Price Exp Vol Open Int Put 21.18 36.32% 20.00 May, 2021 3,051 40,421 Annual interest rate = 3.00% Trading days per year = 252 a) Based on the information shown in the table to the right, use the daily American binomial lattice method to estimate the American put option value. Option Value = Show your lattice. Points 4 Grade b) Based on the information shown in the table to the right, use the daily European binomial lattice method to estimate the European put option value. Option Value = Show your lattice. Points 4 Grade European Put Day 0 Option Value ERROR:#DIV/0!

## Question 3

 Based on the information shown in the table to the right, answer the following ABCD questions, a through e. Option Type Stock Price IV Strike Price Exp Vol Open Int Assume today is April 29, 2021, before the market has opened. 25.28 41.52% 24.00 May, 2021 4,892 55,057 Annual interest rate 3.30% Trading days per year 252 a) Calculate the call option value using the Balck-Scholes equations. Call Option Value = Points 2 Grade b) Calculate the put option value using the Black-Scholes equations. Put Option Value = Points 2 Grade c) Using the Black -Scholes equations, calculate the Greeks for the call option. Call Points 2 Delta = Grade Gamma = Theta = Vega = Rho = d) Using the Black -Scholes equations, calculate the Greeks for the put option. Put Points 2 Delta = Grade Gamma = Theta = Vega = Rho = e) If a portfolio included 500 of the call options described above, how many put Quantity = options would be required to provide a zero delta portfolio? Note, this does not need to be in 100 unit increments. Points 2 Grade

## Question 4

 Assume today is November 27, 2021. One year ago, on December 11, 2020, you created a Various Stock Closing Prices Portfolio Value minimum variance portfolio based from the five stocks shown to the right. Date Stock A Stock B Stock C Stock D Stock E Date Stock A Stock B Stock C Stock D Stock E Portfolio RoR 12/11/20 27.8 4.8 114.67 19.56 26.57 12/11/20 Weight 12/14/20 27.26 3.9 114.04 19.05 26.16 12/14/20 The minimum variance weights for the five stock portfolio are: Stock A -0.0322876747 12/15/20 27.69 3.98 114.63 19.22 26.73 12/15/20 Stock B -0.0183913678 12/16/20 27.31 3.72 114.09 19.14 26.73 12/16/20 Stock C 1.0139979572 12/17/20 26.83 3.77 113.83 19.47 26.39 12/17/20 Stock D 0.0105871759 12/18/20 28.8 3.8 113.67 20.56 26.57 12/18/20 Stock E 0.0260939093 12/21/20 27.63 3.51 113.4 19.88 25.59 12/21/20 12/22/20 27.21 3.5 113.45 19.55 25.7 12/22/20 The total value of the portfolio when you satrted on December 11, 2020, was \$ 1,000,000.00 12/23/20 27.42 3.57 114.1 19.39 25.7 12/23/20 12/24/20 26.96 3.64 113.74 19.3 25.59 12/24/20 12/25/20 26.64 3.59 114.5 19.8 25.07 12/25/20 a) Determine the portfolio value for each of the trading days this past year; fill in 12/28/20 26.8 3.6 114.72 20.22 25.19 12/28/20 the yellow cells in the table provided to the right. 12/29/20 26.8 3.62 115.46 20.38 25.36 12/29/20 Points 4 12/30/20 26.59 3.65 115.2 20.22 24.9 12/30/20 Grade 12/31/20 26.59 3.74 113.08 19.88 24.21 12/31/20 1/1/21 26.75 3.69 112.5 20.3 24.15 1/1/21 b) Using all 252 trading days worth of stock data that you have accumulated since 95% VaR = 1/4/21 26.59 3.6 112.2 20.72 23.81 1/4/21 the beginning of your investment, calculate the 95% VaR and the 99% VaR 99% VaR = 1/5/21 26.53 3.68 112.28 20.88 23.75 1/5/21 using the Historical Method. 1/6/21 26.91 3.65 112.62 21.22 23.86 1/6/21 Points 7 1/7/21 28.53 3.56 112.81 20.13 24.67 1/7/21 Grade 1/8/21 29.23 3.65 112.34 20.63 24.79 1/8/21 1/11/21 29.6 3.67 112.47 20.55 24.9 1/11/21 1/12/21 29.55 3.87 112.78 20.72 24.67 1/12/21 1/13/21 29.01 3.9 113.07 20.8 24.32 1/13/21 1/14/21 29.39 4.25 112.72 21.22 24.79 1/14/21 1/15/21 28.58 4.06 112.53 20.97 24.15 1/15/21 1/18/21 29.6 4.08 112.87 21.3 24.61 1/18/21 1/19/21 29.09 4.08 112.71 20.88 24.04 1/19/21 1/20/21 28.53 4 112.34 20.8 24.27 1/20/21 1/21/21 28.2 3.82 111.78 21.72 24.15 1/21/21 1/22/21 28.34 3.79 112.26 21.55 24.04 1/22/21 1/25/21 28.66 3.77 112.5 21.63 24.21 1/25/21 1/26/21 28.9 4.13 112.79 21.45 24.12 1/26/21 1/27/21 29.23 4.29 113.07 21.34 24.21 1/27/21 1/28/21 28.12 5.02 114.03 21.47 25.04 1/28/21 1/29/21 27.61 5.19 114.55 21.55 24.7 1/29/21 2/1/21 27.72 5.07 116.37 21.67 24.76 2/1/21 2/2/21 27.88 4.89 116.23 20.97 24.9 2/2/21 2/3/21 28.12 5.18 116.46 20.05 25.19 2/3/21 2/4/21 27.99 5.07 116.6 21.8 25.68 2/4/21 2/5/21 27.67 4.94 116.7 21.72 25.94 2/5/21 2/8/21 27.53 4.97 116.57 22.09 26.28 2/8/21 2/9/21 27.1 4.94 116.41 21.59 26.51 2/9/21 2/10/21 27.77 5.69 117.24 21.67 26.51 2/10/21 2/11/21 27.31 5.58 117.68 20.47 25.97 2/11/21 2/12/21 27.26 5.43 118.44 20.3 26.14 2/12/21 2/15/21 27.48 5.51 119.16 19.97 25.74 2/15/21 2/16/21 27.82 5.56 119.25 19.84 25.88 2/16/21 2/17/21 26.13 5.42 118.29 19.76 25.53 2/17/21 2/18/21 25.8 5.22 118.09 19.14 25.3 2/18/21 2/19/21 25.59 5.18 118.35 19.05 24.99 2/19/21 2/22/21 26.42 5.11 118.23 20.09 25.45 2/22/21 2/23/21 25.34 5.02 117.31 20.13 24.79 2/23/21 2/24/21 26.86 5.76 119.35 20.63 24.76 2/24/21 2/25/21 26.67 5.63 118.84 20.05 24.61 2/25/21 2/26/21 26.48 5.62 118.3 20.76 24.67 2/26/21 3/1/21 26.07 5.71 117.82 20.63 24.47 3/1/21 3/2/21 25.83 5.64 117.45 20.34 24.09 3/2/21 3/3/21 25.61 5.94 117.31 19.88 23.66 3/3/21 3/4/21 26.34 5.97 118.03 20.68 23.63 3/4/21 3/5/21 26.15 6.06 117.72 20.84 23.46 3/5/21 3/8/21 26.48 6.2 117.92 21.22 23.17 3/8/21 3/9/21 26.24 6.65 117.91 20.93 23.28 3/9/21 3/10/21 25.39 7.64 118.14 20.47 23.11 3/10/21 3/11/21 25.58 7.9 118.07 19.88 23.4 3/11/21 3/12/21 25.96 7.72 117.83 19.8 23.4 3/12/21 3/15/21 26.1 7 117.3 20.18 23.08 3/15/21 3/16/21 26.51 7.37 118.21 20.22 23.51 3/16/21 3/17/21 26.45 7.4 118.12 21.17 23.89 3/17/21 3/18/21 27.16 7.68 118.35 21.13 24.09 3/18/21 3/19/21 26.72 7.32 119.02 20.68 24.24 3/19/21 3/22/21 26.45 7.42 118.16 20.47 24.24 3/22/21 3/23/21 25.99 7.24 117.55 20.47 23.89 3/23/21 3/24/21 26.05 7.25 117.36 21.13 23.8 3/24/21 3/25/21 26.13 7.37 117.59 21.63 24.15 3/25/21 3/26/21 26.42 7.86 117.55 21.84 23.95 3/26/21 3/29/21 26.89 7.89 117.6 21.97 24.01 3/29/21 3/30/21 27.27 7.92 117.94 22.67 23.69 3/30/21 3/31/21 27.07 7.58 117.53 22.42 23.43 3/31/21 4/1/21 27.32 7.37 117.42 22.09 23.05 4/1/21 4/2/21 27.24 7.36 117.24 22.26 23.11 4/2/21 4/5/21 26.78 7.42 115.99 22.13 23.11 4/5/21 4/6/21 26.61 7.09 115.35 23.55 23.86 4/6/21 4/7/21 26.97 7.37 115.6 23.8 24.27 4/7/21 4/8/21 27.02 7.6 115.32 23.09 24.21 4/8/21 4/9/21 26.4 7.3 114.81 22.42 23.6 4/9/21 4/12/21 26.31 6.93 114.36 22.55 23.57 4/12/21 4/13/21 25.8 6.14 114.44 21.84 22.91 4/13/21 4/14/21 25.53 6.19 113.35 21.42 22.41 4/14/21 4/15/21 25.91 6.46 113.65 22.09 22.5 4/15/21 4/16/21 26.61 6.74 114.02 22.34 22.88 4/16/21 4/19/21 27.11 7.36 113.39 21.84 23.08 4/19/21 4/20/21 26.97 7.17 113.76 22.05 22.47 4/20/21 4/21/21 26.91 7.06 113.19 21.67 22.47 4/21/21 4/22/21 27.29 6.73 113.47 21.84 22.91 4/22/21 4/23/21 26.34 6.42 113.15 21.22 23.22 4/23/21 4/26/21 27.02 6.69 113.88 21.3 23.6 4/26/21 4/27/21 28.55 7.45 114.08 22.26 23.43 4/27/21 4/28/21 28.61 7.31 114.15 22.22 23.98 4/28/21 4/29/21 29.1 7.68 114.6 22.13 24.27 4/29/21 4/30/21 29.4 7.59 114.44 22.76 24.32 4/30/21 5/3/21 29.04 7.04 113.92 22.26 24.44 5/3/21 5/4/21 29.29 7.73 114.75 23.71 24.5 5/4/21 5/5/21 29.15 7.6 113.91 23.76 24.47 5/5/21 5/6/21 29.21 7.72 114.02 23.84 24.21 5/6/21 5/7/21 29.15 7.71 113.58 23.88 23.91 5/7/21 5/10/21 29.43 8.39 113.31 24.67 23.91 5/10/21 5/11/21 29.87 8.34 113.09 24.13 23.71 5/11/21 5/12/21 29.51 8.31 112.38 23.71 23.16 5/12/21 5/13/21 28.99 8.42 112.06 23.76 23.33 5/13/21 5/14/21 29.43 8.23 112.46 24.67 23.16 5/14/21 5/17/21 30.22 8.25 111.73 23.38 22.69 5/17/21 5/18/21 29.98 8.72 111.94 23.09 23.13 5/18/21 5/19/21 30.28 9.04 112.29 22.88 23.33 5/19/21 5/20/21 29.89 9.12 111.99 22.63 23.33 5/20/21 5/21/21 29.46 9.04 112 22.71 23.13 5/21/21 5/24/21 29.98 9.86 112.35 23.26 23.74 5/24/21 5/25/21 29.81 9.64 112 23.8 23.97 5/25/21 5/26/21 29.46 9.26 112.58 23.38 23.91 5/26/21 5/27/21 29.43 8.85 113.04 23.63 23.86 5/27/21 5/28/21 28.99 8.98 112.7 23.67 23.91 5/28/21 5/31/21 29.26 8.72 112.4 23.42 22.87 5/31/21 6/1/21 29.84 8.79 113.31 23.96 23.33 6/1/21 6/2/21 30.03 9.2 113.64 24.3 23.68 6/2/21 6/3/21 30.09 9.36 113.27 24.3 23.65 6/3/21 6/4/21 29.73 9.15 113.24 24.46 23.54 6/4/21 6/7/21 30.41 8.77 113.53 24.13 24.03 6/7/21 6/8/21 30.25 8.7 113.7 24.3 23.65 6/8/21 6/9/21 30.39 8.47 113.82 24.46 23.62 6/9/21 6/10/21 30.5 8.49 114.19 24.75 23.77 6/10/21 6/11/21 30.28 8.9 114.66 24.71 23.68 6/11/21 6/14/21 31.1 9.23 115.16 25.17 23.91 6/14/21 6/15/21 31.4 9.08 115.96 24.59 24.35 6/15/21 6/16/21 31.07 8.94 116.26 25.09 24.35 6/16/21 6/17/21 31.12 8.76 116 24.84 24.32 6/17/21 6/18/21 31.51 9.06 115.94 25.46 25.02 6/18/21 6/21/21 31.26 9.12 115.65 25.67 25.11 6/21/21 6/22/21 31.62 9.12 115.64 25.38 25.57 6/22/21 6/23/21 31.4 9.07 115.34 24.8 26.42 6/23/21 6/24/21 31.59 9.01 115.54 25.59 26.04 6/24/21 6/25/21 31.84 9 117.3 26.13 26.39 6/25/21 6/28/21 32.7 8.89 117.88 26.09 26.36 6/28/21 6/29/21 33.19 8.67 117.44 25.96 25.89 6/29/21 6/30/21 33.69 8.7 117.84 26.29 26.24 6/30/21 7/1/21 33.74 9.5 117.42 26.38 26.94 7/1/21 7/2/21 33.8 10.1 115.71 26.38 26.8 7/2/21 7/5/21 33.27 9.93 115.99 25.71 26.94 7/5/21 7/6/21 32.81 10.39 113.33 25.75 26.74 7/6/21 7/7/21 33.52 11.05 113.95 26.21 26.91 7/7/21 7/8/21 33.66 11.96 113.21 26.09 27.06 7/8/21 7/9/21 34.46 11.23 113.53 26.34 27.91 7/9/21 7/12/21 34.07 11.4 113.59 26 27.29 7/12/21 7/13/21 33.96 11.6 113.85 25.84 26.53 7/13/21 7/14/21 34.04 11.46 113.62 26 26.3 7/14/21 7/15/21 33.93 11.76 113.68 26.29 26.27 7/15/21 7/16/21 33.66 11.36 113.21 26.75 25.83 7/16/21 7/19/21 33.52 11.83 113.05 27.71 26.3 7/19/21 7/20/21 33.22 12.01 113.45 27.04 26.53 7/20/21 7/21/21 33 12.1 113.97 26.96 27.64 7/21/21 7/22/21 32.48 12.31 114.14 26.96 28.58 7/22/21 7/23/21 33.3 13.21 113.8 26.79 30.48 7/23/21 7/26/21 34.57 13.96 113.53 27.38 31.15 7/26/21 7/27/21 34.9 13.79 113.62 27.25 31.44 7/27/21 7/28/21 34.54 13.36 112.91 27.33 30.66 7/28/21 7/29/21 34.13 12.64 112.61 27.25 30.22 7/29/21 7/30/21 33.47 15.1 113.5 28.12 30.63 7/30/21 8/2/21 32.94 15.34 113.44 28.29 30.77 8/2/21 8/3/21 32.5 15.75 113.16 28.92 30.71 8/3/21 8/4/21 31.81 17.03 113.04 28.42 30.57 8/4/21 8/5/21 32.94 16.17 113.24 28.08 30.66 8/5/21 8/6/21 32.2 15 115.21 27.21 29.05 8/6/21 8/9/21 32.09 15.32 114.92 27.54 28.93 8/9/21 8/10/21 31.54 15 114.41 26.58 29.22 8/10/21 8/11/21 31.37 15.79 114.24 26.38 28.93 8/11/21 8/12/21 31.9 15.81 114.96 26.54 31.01 8/12/21 8/13/21 32.14 16.09 114.93 26.58 31.01 8/13/21 8/16/21 31.98 15.57 114.9 26.21 30.6 8/16/21 8/17/21 31.51 15.36 114.78 26.29 30.48 8/17/21 8/18/21 31.62 15.38 114.69 26.04 30.45 8/18/21 8/19/21 32.2 15.44 115.56 25.42 31.18 8/19/21 8/20/21 32.89 16.48 115.62 25.5 31.47 8/20/21 8/23/21 32.78 16.01 115.56 25.75 31.71 8/23/21 8/24/21 32.19 15.74 114.52 26.13 31.53 8/24/21 8/25/21 32.47 15.55 114.29 25.79 31.18 8/25/21 8/26/21 32.45 15.6 113 26.63 32.58 8/26/21 8/27/21 32.25 15.28 113.05 26.29 32.44 8/27/21 8/30/21 31.97 14.51 113.14 25.71 32.5 8/30/21 8/31/21 31.78 15.37 113.05 25.25 32.5 8/31/21 9/1/21 32.03 14.73 112.85 25.05 33.15 9/1/21 9/2/21 31.34 14.08 111.81 24.34 33.21 9/2/21 9/3/21 31.03 13.73 111 22.38 32.68 9/3/21 9/6/21 31.75 13.81 111.55 21.8 33.15 9/6/21 9/7/21 32.69 14.1 111.95 21.88 33.3 9/7/21 9/8/21 32.36 14.65 111.82 22.22 33.36 9/8/21 9/9/21 33.3 15.39 111.64 22.38 31.92 9/9/21 9/10/21 33.36 15.21 111.61 21.92 32.1 9/10/21 9/13/21 32.64 15.39 111.23 20.84 31.66 9/13/21 9/14/21 33.36 16.22 111.95 21.88 31.86 9/14/21 9/15/21 33.91 17.31 111.81 22.46 32.48 9/15/21 9/16/21 34.14 18.42 112.94 21.63 33.65 9/16/21 9/17/21 34.86 19.49 113.28 21.67 33.42 9/17/21 9/20/21 35.47 19.57 113.8 22.01 33.45 9/20/21 9/21/21 35.11 20.01 113.37 21.92 33.65 9/21/21 9/22/21 35.11 19.57 113.55 22.8 34.12 9/22/21 9/23/21 33.47 22.22 113.26 22.71 35.21 9/23/21 9/24/21 33.67 22.59 112.79 21.8 35.09 9/24/21 9/27/21 33.08 25.89 112.85 21.01 36.26 9/27/21 9/28/21 34.05 24.86 113.25 20.01 36.56 9/28/21 9/29/21 33.39 24.25 114.03 20.51 36.03 9/29/21 9/30/21 32.83 24.53 115.02 21.38 36.32 9/30/21 10/1/21 33.91 24.29 114.61 21.26 35.94 10/1/21 10/4/21 34.63 23.7 115.48 21.3 35.15 10/4/21 10/5/21 35.3 24.32 115.48 21.67 35.5 10/5/21 10/6/21 35.38 24.2 115.21 21.76 36.15 10/6/21 10/7/21 35.41 25.2 115.02 22.38 33.33 10/7/21 10/8/21 34.25 24.65 115.07 21.67 33.86 10/8/21 10/11/21 34.94 23.75 115.19 21.92 33.48 10/11/21 10/12/21 35.13 24.63 115.93 21.59 33.56 10/12/21 10/13/21 35.22 23.89 115.82 20.68 33.27 10/13/21 10/14/21 35.25 23.72 115.53 21.67 33.12 10/14/21 10/15/21 34.52 22.59 115.62 20.93 32.1 10/15/21 10/18/21 33.58 22.26 114.92 20.88 31.1 10/18/21 10/19/21 34.22 21.95 115.48 20.3 30.69 10/19/21 10/20/21 34.47 22.82 116.19 19.93 30.77 10/20/21 10/21/21 33.8 23.82 115.59 19.39 32.04 10/21/21 10/22/21 34.27 24.82 115.85 19.3 32.65 10/22/21 10/25/21 34.58 24.17 115.76 19.3 32.45 10/25/21 10/26/21 35.11 23.98 116.82 19.01 32.24 10/26/21 10/27/21 34.69 25.36 115.94 19.76 32.65 10/27/21 10/28/21 34.97 24.82 115.68 19.59 32.74 10/28/21 10/29/21 35.16 25.4 115.6 20.13 32.48 10/29/21 11/1/21 34.91 25.36 115.56 20.26 32.83 11/1/21 11/2/21 35.3 25.2 115.21 20.09 31.92 11/2/21 11/3/21 31.79 18.23 112.31 18.8 28.33 11/3/21 11/4/21 33.29 19.04 113.49 20.13 30.04 11/4/21 11/5/21 33.44 20.42 113.21 20.18 29.48 11/5/21 11/8/21 34.41 19.78 113.67 20.01 29.07 11/8/21 11/9/21 34.97 19.82 114.04 19.97 29.16 11/9/21 11/10/21 34.75 20.95 114.24 20.05 29.93 11/10/21 11/11/21 35.08 20.95 115.68 21.42 29.66 11/11/21 11/12/21 36.25 21.95 115.9 21.09 29.42 11/12/21 11/15/21 35.83 22.07 115.93 21.01 29.19 11/15/21 11/16/21 35.3 24.32 115.71 20.97 29.54 11/16/21 11/17/21 36.39 25.06 115.6 21.05 28.33 11/17/21 11/18/21 35.92 26.72 115.34 20.68 28.39 11/18/21 11/19/21 36.45 30.45 116.2 21.72 28.39 11/19/21 11/22/21 36.14 29.79 115.77 21.01 28.54 11/22/21 11/23/21 35.72 31.23 116.51 21.59 28.75 11/23/21 11/24/21 35.08 29.22 115.32 19.72 29.98 11/24/21 11/25/21 35.42 32.73 115.42 20.09 29.1 11/25/21 11/26/21 36.45 32.43 114.61 20.84 28.75 11/26/21 11/27/21 36.5 32.18 114.38 20.93 29.22 11/27/21 4529239482

## Question 5

 We will use the same data as in Question 4, which is shown to the right. Various Stock Closing Prices Covariance Matrix Date Stock A Stock B Stock C Stock D Stock E Stock A Stock B Stock C Stock D Stock E 12/11/20 27.8 4.8 114.67 19.56 26.57 Stock A 0.0003770798 0.0002625401 0.0000394717 0.000145333 0.0001093076 The minimum variance weights for the five stock portfolio are: Weight 12/14/20 27.26 3.9 114.04 19.05 26.16 Stock B 0.0002625401 0.0026368948 0.0000713178 0.0003279111 0.0003294576 Stock A -0.0322876747 12/15/20 27.69 3.98 114.63 19.22 26.73 Stock C 0.0000394717 0.0000713178 0.0000286221 0.000029015 0.0000255924 Stock B -0.0183913678 12/16/20 27.31 3.72 114.09 19.14 26.73 Stock D 0.000145333 0.0003279111 0.000029015 0.0006232057 0.0000810807 Stock C 1.0139979572 12/17/20 26.83 3.77 113.83 19.47 26.39 Stock E 0.0001093076 0.0003294576 0.0000255924 0.0000810807 0.0003905555 Stock D 0.0105871759 12/18/20 28.8 3.8 113.67 20.56 26.57 Stock E 0.0260939093 12/21/20 27.63 3.51 113.4 19.88 25.59 12/22/20 27.21 3.5 113.45 19.55 25.7 The total value of the portfolio when you satrted on December 11, 2020, was \$ 1,000,000.00 12/23/20 27.42 3.57 114.1 19.39 25.7 12/24/20 26.96 3.64 113.74 19.3 25.59 12/25/20 26.64 3.59 114.5 19.8 25.07 a) Based on the covariance matrix provided, and using the values you invested in Variance = 12/28/20 26.8 3.6 114.72 20.22 25.19 each of the stocks in your portfolio from Question 7, determine the Variance StDev = 12/29/20 26.8 3.62 115.46 20.38 25.36 Standard Deviation and Average Return for your portfolio for today, Avg Return = 12/30/20 26.59 3.65 115.2 20.22 24.9 November 27, 2021, the last day. 12/31/20 26.59 3.74 113.08 19.88 24.21 Points 4 1/1/21 26.75 3.69 112.5 20.3 24.15 Grade 1/4/21 26.59 3.6 112.2 20.72 23.81 1/5/21 26.53 3.68 112.28 20.88 23.75 b) Using the Variance-Covariance Method, calculate the 95% VaR and 99% VaR. 95% VaR = 1/6/21 26.91 3.65 112.62 21.22 23.86 99% VaR = 1/7/21 28.53 3.56 112.81 20.13 24.67 Points 6 1/8/21 29.23 3.65 112.34 20.63 24.79 Grade 1/11/21 29.6 3.67 112.47 20.55 24.9 1/12/21 29.55 3.87 112.78 20.72 24.67 Note, when performing the matrix algebra, even for the single cell result for 1/13/21 29.01 3.9 113.07 20.8 24.32 the Average Return, you may initially see an “#VALUE!” error. You will need to 1/14/21 29.39 4.25 112.72 21.22 24.79 complete the “F2” followed by Cntrl-Shift-Enter to get your value. 1/15/21 28.58 4.06 112.53 20.97 24.15 Mac users will need to follow the Mac key stroke sequence for Matrix Algebra. 1/18/21 29.6 4.08 112.87 21.3 24.61 1/19/21 29.09 4.08 112.71 20.88 24.04 1/20/21 28.53 4 112.34 20.8 24.27 1/21/21 28.2 3.82 111.78 21.72 24.15 1/22/21 28.34 3.79 112.26 21.55 24.04 1/25/21 28.66 3.77 112.5 21.63 24.21 1/26/21 28.9 4.13 112.79 21.45 24.12 1/27/21 29.23 4.29 113.07 21.34 24.21 1/28/21 28.12 5.02 114.03 21.47 25.04 1/29/21 27.61 5.19 114.55 21.55 24.7 2/1/21 27.72 5.07 116.37 21.67 24.76 2/2/21 27.88 4.89 116.23 20.97 24.9 2/3/21 28.12 5.18 116.46 20.05 25.19 2/4/21 27.99 5.07 116.6 21.8 25.68 2/5/21 27.67 4.94 116.7 21.72 25.94 2/8/21 27.53 4.97 116.57 22.09 26.28 2/9/21 27.1 4.94 116.41 21.59 26.51 2/10/21 27.77 5.69 117.24 21.67 26.51 2/11/21 27.31 5.58 117.68 20.47 25.97 2/12/21 27.26 5.43 118.44 20.3 26.14 2/15/21 27.48 5.51 119.16 19.97 25.74 2/16/21 27.82 5.56 119.25 19.84 25.88 2/17/21 26.13 5.42 118.29 19.76 25.53 2/18/21 25.8 5.22 118.09 19.14 25.3 2/19/21 25.59 5.18 118.35 19.05 24.99 2/22/21 26.42 5.11 118.23 20.09 25.45 2/23/21 25.34 5.02 117.31 20.13 24.79 2/24/21 26.86 5.76 119.35 20.63 24.76 2/25/21 26.67 5.63 118.84 20.05 24.61 2/26/21 26.48 5.62 118.3 20.76 24.67 3/1/21 26.07 5.71 117.82 20.63 24.47 3/2/21 25.83 5.64 117.45 20.34 24.09 3/3/21 25.61 5.94 117.31 19.88 23.66 3/4/21 26.34 5.97 118.03 20.68 23.63 3/5/21 26.15 6.06 117.72 20.84 23.46 3/8/21 26.48 6.2 117.92 21.22 23.17 3/9/21 26.24 6.65 117.91 20.93 23.28 3/10/21 25.39 7.64 118.14 20.47 23.11 3/11/21 25.58 7.9 118.07 19.88 23.4 3/12/21 25.96 7.72 117.83 19.8 23.4 3/15/21 26.1 7 117.3 20.18 23.08 3/16/21 26.51 7.37 118.21 20.22 23.51 3/17/21 26.45 7.4 118.12 21.17 23.89 3/18/21 27.16 7.68 118.35 21.13 24.09 3/19/21 26.72 7.32 119.02 20.68 24.24 3/22/21 26.45 7.42 118.16 20.47 24.24 3/23/21 25.99 7.24 117.55 20.47 23.89 3/24/21 26.05 7.25 117.36 21.13 23.8 3/25/21 26.13 7.37 117.59 21.63 24.15 3/26/21 26.42 7.86 117.55 21.84 23.95 3/29/21 26.89 7.89 117.6 21.97 24.01 3/30/21 27.27 7.92 117.94 22.67 23.69 3/31/21 27.07 7.58 117.53 22.42 23.43 4/1/21 27.32 7.37 117.42 22.09 23.05 4/2/21 27.24 7.36 117.24 22.26 23.11 4/5/21 26.78 7.42 115.99 22.13 23.11 4/6/21 26.61 7.09 115.35 23.55 23.86 4/7/21 26.97 7.37 115.6 23.8 24.27 4/8/21 27.02 7.6 115.32 23.09 24.21 4/9/21 26.4 7.3 114.81 22.42 23.6 4/12/21 26.31 6.93 114.36 22.55 23.57 4/13/21 25.8 6.14 114.44 21.84 22.91 4/14/21 25.53 6.19 113.35 21.42 22.41 4/15/21 25.91 6.46 113.65 22.09 22.5 4/16/21 26.61 6.74 114.02 22.34 22.88 4/19/21 27.11 7.36 113.39 21.84 23.08 4/20/21 26.97 7.17 113.76 22.05 22.47 4/21/21 26.91 7.06 113.19 21.67 22.47 4/22/21 27.29 6.73 113.47 21.84 22.91 4/23/21 26.34 6.42 113.15 21.22 23.22 4/26/21 27.02 6.69 113.88 21.3 23.6 4/27/21 28.55 7.45 114.08 22.26 23.43 4/28/21 28.61 7.31 114.15 22.22 23.98 4/29/21 29.1 7.68 114.6 22.13 24.27 4/30/21 29.4 7.59 114.44 22.76 24.32 5/3/21 29.04 7.04 113.92 22.26 24.44 5/4/21 29.29 7.73 114.75 23.71 24.5 5/5/21 29.15 7.6 113.91 23.76 24.47 5/6/21 29.21 7.72 114.02 23.84 24.21 5/7/21 29.15 7.71 113.58 23.88 23.91 5/10/21 29.43 8.39 113.31 24.67 23.91 5/11/21 29.87 8.34 113.09 24.13 23.71 5/12/21 29.51 8.31 112.38 23.71 23.16 5/13/21 28.99 8.42 112.06 23.76 23.33 5/14/21 29.43 8.23 112.46 24.67 23.16 5/17/21 30.22 8.25 111.73 23.38 22.69 5/18/21 29.98 8.72 111.94 23.09 23.13 5/19/21 30.28 9.04 112.29 22.88 23.33 5/20/21 29.89 9.12 111.99 22.63 23.33 5/21/21 29.46 9.04 112 22.71 23.13 5/24/21 29.98 9.86 112.35 23.26 23.74 5/25/21 29.81 9.64 112 23.8 23.97 5/26/21 29.46 9.26 112.58 23.38 23.91 5/27/21 29.43 8.85 113.04 23.63 23.86 5/28/21 28.99 8.98 112.7 23.67 23.91 5/31/21 29.26 8.72 112.4 23.42 22.87 6/1/21 29.84 8.79 113.31 23.96 23.33 6/2/21 30.03 9.2 113.64 24.3 23.68 6/3/21 30.09 9.36 113.27 24.3 23.65 6/4/21 29.73 9.15 113.24 24.46 23.54 6/7/21 30.41 8.77 113.53 24.13 24.03 6/8/21 30.25 8.7 113.7 24.3 23.65 6/9/21 30.39 8.47 113.82 24.46 23.62 6/10/21 30.5 8.49 114.19 24.75 23.77 6/11/21 30.28 8.9 114.66 24.71 23.68 6/14/21 31.1 9.23 115.16 25.17 23.91 6/15/21 31.4 9.08 115.96 24.59 24.35 6/16/21 31.07 8.94 116.26 25.09 24.35 6/17/21 31.12 8.76 116 24.84 24.32 6/18/21 31.51 9.06 115.94 25.46 25.02 6/21/21 31.26 9.12 115.65 25.67 25.11 6/22/21 31.62 9.12 115.64 25.38 25.57 6/23/21 31.4 9.07 115.34 24.8 26.42 6/24/21 31.59 9.01 115.54 25.59 26.04 6/25/21 31.84 9 117.3 26.13 26.39 6/28/21 32.7 8.89 117.88 26.09 26.36 6/29/21 33.19 8.67 117.44 25.96 25.89 6/30/21 33.69 8.7 117.84 26.29 26.24 7/1/21 33.74 9.5 117.42 26.38 26.94 7/2/21 33.8 10.1 115.71 26.38 26.8 7/5/21 33.27 9.93 115.99 25.71 26.94 7/6/21 32.81 10.39 113.33 25.75 26.74 7/7/21 33.52 11.05 113.95 26.21 26.91 7/8/21 33.66 11.96 113.21 26.09 27.06 7/9/21 34.46 11.23 113.53 26.34 27.91 7/12/21 34.07 11.4 113.59 26 27.29 7/13/21 33.96 11.6 113.85 25.84 26.53 7/14/21 34.04 11.46 113.62 26 26.3 7/15/21 33.93 11.76 113.68 26.29 26.27 7/16/21 33.66 11.36 113.21 26.75 25.83 7/19/21 33.52 11.83 113.05 27.71 26.3 7/20/21 33.22 12.01 113.45 27.04 26.53 7/21/21 33 12.1 113.97 26.96 27.64 7/22/21 32.48 12.31 114.14 26.96 28.58 7/23/21 33.3 13.21 113.8 26.79 30.48 7/26/21 34.57 13.96 113.53 27.38 31.15 7/27/21 34.9 13.79 113.62 27.25 31.44 7/28/21 34.54 13.36 112.91 27.33 30.66 7/29/21 34.13 12.64 112.61 27.25 30.22 7/30/21 33.47 15.1 113.5 28.12 30.63 8/2/21 32.94 15.34 113.44 28.29 30.77 8/3/21 32.5 15.75 113.16 28.92 30.71 8/4/21 31.81 17.03 113.04 28.42 30.57 8/5/21 32.94 16.17 113.24 28.08 30.66 8/6/21 32.2 15 115.21 27.21 29.05 8/9/21 32.09 15.32 114.92 27.54 28.93 8/10/21 31.54 15 114.41 26.58 29.22 8/11/21 31.37 15.79 114.24 26.38 28.93 8/12/21 31.9 15.81 114.96 26.54 31.01 8/13/21 32.14 16.09 114.93 26.58 31.01 8/16/21 31.98 15.57 114.9 26.21 30.6 8/17/21 31.51 15.36 114.78 26.29 30.48 8/18/21 31.62 15.38 114.69 26.04 30.45 8/19/21 32.2 15.44 115.56 25.42 31.18 8/20/21 32.89 16.48 115.62 25.5 31.47 8/23/21 32.78 16.01 115.56 25.75 31.71 8/24/21 32.19 15.74 114.52 26.13 31.53 8/25/21 32.47 15.55 114.29 25.79 31.18 8/26/21 32.45 15.6 113 26.63 32.58 8/27/21 32.25 15.28 113.05 26.29 32.44 8/30/21 31.97 14.51 113.14 25.71 32.5 8/31/21 31.78 15.37 113.05 25.25 32.5 9/1/21 32.03 14.73 112.85 25.05 33.15 9/2/21 31.34 14.08 111.81 24.34 33.21 9/3/21 31.03 13.73 111 22.38 32.68 9/6/21 31.75 13.81 111.55 21.8 33.15 9/7/21 32.69 14.1 111.95 21.88 33.3 9/8/21 32.36 14.65 111.82 22.22 33.36 9/9/21 33.3 15.39 111.64 22.38 31.92 9/10/21 33.36 15.21 111.61 21.92 32.1 9/13/21 32.64 15.39 111.23 20.84 31.66 9/14/21 33.36 16.22 111.95 21.88 31.86 9/15/21 33.91 17.31 111.81 22.46 32.48 9/16/21 34.14 18.42 112.94 21.63 33.65 9/17/21 34.86 19.49 113.28 21.67 33.42 9/20/21 35.47 19.57 113.8 22.01 33.45 9/21/21 35.11 20.01 113.37 21.92 33.65 9/22/21 35.11 19.57 113.55 22.8 34.12 9/23/21 33.47 22.22 113.26 22.71 35.21 9/24/21 33.67 22.59 112.79 21.8 35.09 9/27/21 33.08 25.89 112.85 21.01 36.26 9/28/21 34.05 24.86 113.25 20.01 36.56 9/29/21 33.39 24.25 114.03 20.51 36.03 9/30/21 32.83 24.53 115.02 21.38 36.32 10/1/21 33.91 24.29 114.61 21.26 35.94 10/4/21 34.63 23.7 115.48 21.3 35.15 10/5/21 35.3 24.32 115.48 21.67 35.5 10/6/21 35.38 24.2 115.21 21.76 36.15 10/7/21 35.41 25.2 115.02 22.38 33.33 10/8/21 34.25 24.65 115.07 21.67 33.86 10/11/21 34.94 23.75 115.19 21.92 33.48 10/12/21 35.13 24.63 115.93 21.59 33.56 10/13/21 35.22 23.89 115.82 20.68 33.27 10/14/21 35.25 23.72 115.53 21.67 33.12 10/15/21 34.52 22.59 115.62 20.93 32.1 10/18/21 33.58 22.26 114.92 20.88 31.1 10/19/21 34.22 21.95 115.48 20.3 30.69 10/20/21 34.47 22.82 116.19 19.93 30.77 10/21/21 33.8 23.82 115.59 19.39 32.04 10/22/21 34.27 24.82 115.85 19.3 32.65 10/25/21 34.58 24.17 115.76 19.3 32.45 10/26/21 35.11 23.98 116.82 19.01 32.24 10/27/21 34.69 25.36 115.94 19.76 32.65 10/28/21 34.97 24.82 115.68 19.59 32.74 10/29/21 35.16 25.4 115.6 20.13 32.48 11/1/21 34.91 25.36 115.56 20.26 32.83 11/2/21 35.3 25.2 115.21 20.09 31.92 11/3/21 31.79 18.23 112.31 18.8 28.33 11/4/21 33.29 19.04 113.49 20.13 30.04 11/5/21 33.44 20.42 113.21 20.18 29.48 11/8/21 34.41 19.78 113.67 20.01 29.07 11/9/21 34.97 19.82 114.04 19.97 29.16 11/10/21 34.75 20.95 114.24 20.05 29.93 11/11/21 35.08 20.95 115.68 21.42 29.66 11/12/21 36.25 21.95 115.9 21.09 29.42 11/15/21 35.83 22.07 115.93 21.01 29.19 11/16/21 35.3 24.32 115.71 20.97 29.54 11/17/21 36.39 25.06 115.6 21.05 28.33 11/18/21 35.92 26.72 115.34 20.68 28.39 11/19/21 36.45 30.45 116.2 21.72 28.39 11/22/21 36.14 29.79 115.77 21.01 28.54 11/23/21 35.72 31.23 116.51 21.59 28.75 11/24/21 35.08 29.22 115.32 19.72 29.98 11/25/21 35.42 32.73 115.42 20.09 29.1 11/26/21 36.45 32.43 114.61 20.84 28.75 11/27/21 36.5 32.18 114.38 20.93 29.22