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11 Dec 2019

The purpose of this exercise consists in computing a VaR measure for a $1 million trading portfolio of an investment bank. The portfolio is composed of $300,000 of Emera (EMA) stock, $200,000 of Clearwater Seafoods (CLR) stock and $500,000 of Royal Bank (RY) stock. The file 2017_prices.xlsx (that can be downloaded from Brightspace) contains daily historical closing prices over the last year (2017) for the three stocks. (The prices have already been adjusted for splits or dividends.)

1) Calculate the daily (logarithmic/geometric) returns for each of the stocks over the sample period. Using “Tools/Data Analysis/Descriptive statistics” calculate the mean, standard deviation, kurtosis, and skewness for each of the historical distributions of returns. Based on these statistics, do the historical distributions of returns of the three stocks look like the normal distribution? (explain)

2) Using “Tools/Data Analysis/Histogram” visually inspect the historical distribution of returns of each of the stocks. Do they resemble to the normal distribution?

3) What are the VaRs (1.5%,1 day) and VaRs(1.5%, 20 days) at the end of 2017 of the investments in each of the stocks if they were held separately and assuming a normal distribution of daily returns? Answer using the parametric method for computing the VaR with the standard deviations obtained in 1), and the function “normsinv” for deriving the value of the standard normal deviate (alpha) corresponding to the chosen confidence level.

4) By assuming a normal distribution for the daily returns, what is the portfolio VaR(1.5%,1 day) at the end of 2017? (Use “Tools/Data analysis/Correlation” to compute the correlations of the daily returns of the three stocks.) What can you say if you compare the portfolio VaR with the sum of the VaRs obtained in 3)?

5) Compute the historical VaR (1.5%,1-day) at the end of 2017 of the position on the RY stock. Compare and interpret the differences between the VaR(1.5%,1-day) estimates from the two different VaR models for the position in the RY stock.

6) Compute the Monte Carlo VaR (1.5%,1-day) at the end of 2017 of the position in the RY stock assuming a normal distribution of returns and 5,000 simulations. Compare

and interpret the differences between the VaR(1.5%,1-day) estimates from the three different VaR models for the position in the RY stock. (You can use either Excel or @Risk available in the Bloomberg Lab or trial student version).

7) For the RY stock, compute the standard deviation of its returns for each day using the returns from the previous 20 trading days. Compute the VaR(1.5%,1 day) for each day using the standard deviation of returns for 20 previous days (thus, you obtain a dynamic VaR). Plot the bank’s daily returns together with each day VaR and compute the number of times the daily return exceeded the VaR (remember that the VaR corresponds to a loss). Is the result coherent with the confidence level you use for computing the VaR?

8) What is the portfolio VaR(1.5%,1 day) at the end of 2017 using the historical simulation approach rather than by assuming normal distributions as in 4)? (Hint: Rank the daily portfolio returns using for example the function “sort” or use a function for finding a percentile.)

Name ROYAL BANK OF CANADA EMERA CLEARWATER SEAFOODS
2017/1/2 90.87 45.39 11.65
2017/1/3 91.5 45.19 11.35
2017/1/4 92.84 45.59 10.57
2017/1/5 92.82 45.59 10.5
2017/1/6 92.72 45.43 10.48
2017/1/9 92.52 45.42 10.43
2017/1/10 92.97 45.28 10.13
2017/1/11 93.89 45.22 10.36
2017/1/12 93.75 45.28 10.22
2017/1/13 94.5 45.37 10.3
2017/1/16 94.27 45.65 10.37
2017/1/17 93.58 45.79 10.22
2017/1/18 93.29 45.76 10.35
2017/1/19 93.28 45.88 10.35
2017/1/20 94.17 45.99 10.47
2017/1/23 94.09 45.66 10.5
2017/1/24 93.38 45.68 10.55
2017/1/25 93.99 46.11 10.51
2017/1/26 94.36 46.12 10.73
2017/1/27 94.47 45.94 10.73
2017/1/30 94.06 44.88 10.32
2017/1/31 93.56 45.44 10.12
2017/2/1 93.69 44.95 10.11
2017/2/2 93.76 45.2 10.11
2017/2/3 94.6 45.22 10.35
2017/2/6 94.67 45.26 10.23
2017/2/7 95.28 45.88 10.64
2017/2/8 95.42 46.27 10.67
2017/2/9 96.17 46.18 10.69
2017/2/10 96.84 46.11 10.66
2017/2/13 97.12 45.64 10.57
2017/2/14 97.46 45.16 10.78
2017/2/15 98.53 45.45 11.09
2017/2/16 98.68 45.41 10.98
2017/2/17 99.09 45.27 11.23
2017/2/20 99.09 45.27 11.23
2017/2/21 99.19 45.18 10.99
2017/2/22 98.52 45.3 10.78
2017/2/23 98.26 45.51 10.78
2017/2/24 96.61 45.23 10.72
2017/2/27 96.72 45.22 10.85
2017/2/28 96.48 45.55 10.57
2017/3/1 97.53 45.51 10.41
2017/3/2 97.94 45.59 10.38
2017/3/3 98.29 45.42 10.48
2017/3/6 99.13 45.2 10.07
2017/3/7 98.74 45.72 10.1
2017/3/8 98.35 45.52 10.8
2017/3/9 98.31 45.62 10.59
2017/3/10 97.66 45.49 10.21
2017/3/13 97.44 45.55 10.5
2017/3/14 97.27 45.25 10.21
2017/3/15 96.66 45.77 10.37
2017/3/16 97.31 45.73 10.33
2017/3/17 96.76 46.14 10.45
2017/3/20 96.29 45.88 10.27
2017/3/21 95.43 46.14 10.29
2017/3/22 95.21 46.69 10.51
2017/3/23 96.64 46.98 10.45
2017/3/24 96.55 47.37 10.44
2017/3/27 96.79 47.28 10.49
2017/3/28 97.82 47.08 10.25
2017/3/29 98.19 47.05 10.38
2017/3/30 97.87 46.98 10.49
2017/3/31 96.89 46.98 10.48
2017/4/3 96.79 46.98 10.37
2017/4/4 96.88 46.97 10.24
2017/4/5 97.04 47.17 10.2
2017/4/6 97.81 47.1 10.2
2017/4/7 97.32 47.14 10.26
2017/4/10 97.18 47.21 10.23
2017/4/11 96.84 47.49 10.38
2017/4/12 96.06 47.69 10.3
2017/4/13 94.63 47.35 10.21
2017/4/14 94.63 47.35 10.21
2017/4/17 95.92 47.44 10.29
2017/4/18 95.43 47.43 10.35
2017/4/19 95.18 47.14 10.35
2017/4/20 95.78 47.36 10.45
2017/4/21 94.55 47.49 10.44
2017/4/24 96.07 47.73 10.37
2017/4/25 97.03 47.57 10.45
2017/4/26 95.47 47.69 10.39
2017/4/27 93.66 47.26 10.58
2017/4/28 93.47 47.25 10.58
2017/5/1 93.28 47.33 10.52
2017/5/2 92.66 47.29 10.52
2017/5/3 92.8 47.14 10.5
2017/5/4 92.75 47.06 10.38
2017/5/5 93.74 47.39 10.49
2017/5/8 94.18 47.57 10.39
2017/5/9 92.94 47.21 10.37
2017/5/10 93.33 47.14 10.37
2017/5/11 92.75 47.02 10.57
2017/5/12 92.48 47.01 11.16
2017/5/15 93.62 47.02 11.34
2017/5/16 93.03 46.9 11.75
2017/5/17 91.45 46.67 11.6
2017/5/18 92.42 46.7 11.28
2017/5/19 93.02 47.06 11.74
2017/5/22 93.02 47.06 11.74
2017/5/23 93.53 47.51 11.63
2017/5/24 93 47.64 11.68
2017/5/25 93.74 47.77 11.56
2017/5/26 93.92 47.81 11.65
2017/5/29 94.47 47.6 11.69
2017/5/30 93.54 47.85 11.67
2017/5/31 93.37 48.18 11.45
2017/6/1 93.8 48.59 11.61
2017/6/2 93.76 48.78 11.63
2017/6/5 93.57 48.86 11.5
2017/6/6 92.81 48.9 11.62
2017/6/7 93.1 48.89 11.63
2017/6/8 93.97 48.89 11.65
2017/6/9 95.28 48.63 11.7
2017/6/12 94.26 48.18 11.74
2017/6/13 93.89 48.19 11.74
2017/6/14 93.36 48.33 11.54
2017/6/15 93.63 48.61 11.47
2017/6/16 93.55 48.64 11.3
2017/6/19 94.3 48.45 11.22
2017/6/20 93.76 48.48 11.15
2017/6/21 93.28 48.67 11.26
2017/6/22 94.02 48.64 11.24
2017/6/23 94.12 48.86 11.14
2017/6/26 93.99 48.86 11.42
2017/6/27 94.1 48.8 11.52
2017/6/28 95.06 48.89 11.52
2017/6/29 94.7 48.61 11.46
2017/6/30 94.16 48.21 11.42
2017/7/3 94.16 48.21 11.42
2017/7/4 94.18 47.85 11.36
2017/7/5 94.96 48.02 11.34
2017/7/6 95.13 47.44 11.27
2017/7/7 95.09 47.34 11.2
2017/7/10 94.9 47.22 11.25
2017/7/11 95.02 47.13 11.43
2017/7/12 94.9 47.16 11.58
2017/7/13 95.1 46.91 11.9
2017/7/14 95.25 46.73 11.87
2017/7/17 95.16 46.96 11.37
2017/7/18 94.68 46.92 11.2
2017/7/19 94.91 47.01 11.06
2017/7/20 95.21 47.27 11.2
2017/7/21 94.75 47.21 11.14
2017/7/24 93.67 47.14 11.14
2017/7/25 93.89 46.7 11.2
2017/7/26 93.25 46.64 11.6
2017/7/27 93.22 46.68 11.42
2017/7/28 92.77 46 11.3
2017/7/31 93.01 46.4 11.14
2017/8/1 93.4 46.89 11.24
2017/8/2 94.12 47 11.03
2017/8/3 93.96 46.8 10.77
2017/8/4 94.52 46.92 10.55
2017/8/7 94.52 46.92 10.55
2017/8/8 94.71 46.74 10.27
2017/8/9 94.32 46.87 10.11
2017/8/10 92.88 46.7 10.07
2017/8/11 92.51 46.95 10.33
2017/8/14 93.54 46.93 10.6
2017/8/15 93.33 47.29 10.62
2017/8/16 92.96 47.37 10.83
2017/8/17 92.5 47.32 10.83
2017/8/18 92.25 47.24 10.61
2017/8/21 92.07 47.2 10.31
2017/8/22 92.01 47.32 10.24
2017/8/23 93.01 47.82 10.43
2017/8/24 92.92 47.87 10.32
2017/8/25 93.25 47.87 10.48
2017/8/28 93.04 47.95 10.34
2017/8/29 92.84 47.93 10.49
2017/8/30 92.35 48.01 10.87
2017/8/31 92.68 47.96 11.07
2017/9/1 92.11 47.8 10.89
2017/9/4 92.11 47.8 10.89
2017/9/5 90.77 47.99 10.69
2017/9/6 90.89 47.73 10.56
2017/9/7 90.46 47.82 10.64
2017/9/8 90.53 47.67 10.37
2017/9/11 91.06 47.39 10.5
2017/9/12 91.82 47.04 10.55
2017/9/13 92.15 46.38 10.41
2017/9/14 92.1 46.59 10.35
2017/9/15 91.97 45.99 10.32
2017/9/18 92.17 46.28 10.19
2017/9/19 92.98 46.22 10.08
2017/9/20 93.69 46.29 9.72
2017/9/21 94.23 46.49 9.69
2017/9/22 94.4 46.4 9.65
2017/9/25 94.45 46.89 9.29
2017/9/26 94.49 46.7 9
2017/9/27 95.44 46.69 9.16
2017/9/28 95.93 46.98 9.18
2017/9/29 96.54 47.26 8.99
2017/10/2 97.07 47.43 9.13
2017/10/3 97.83 47.36 9.34
2017/10/4 97.74 47.5 9.21
2017/10/5 98.19 47.93 9.09
2017/10/6 98.11 48.01 9.07
2017/10/9 98.11 48.01 9.07
2017/10/10 98.33 48.08 9.18
2017/10/11 98.83 48.17 9.1
2017/10/12 98.56 48.36 8.88
2017/10/13 99.08 48.17 9.06
2017/10/16 99.28 48.33 8.89
2017/10/17 99.78 48.58 8.94
2017/10/18 100.07 48.45 9.02
2017/10/19 100.82 48.47 9
2017/10/20 101.23 48.47 8.87
2017/10/23 101.42 48.62 8.8
2017/10/24 102.1 48.61 8.97
2017/10/25 100.26 48.76 8.68
2017/10/26 101.02 48.9 8.94
2017/10/27 101.17 48.92 8.82
2017/10/30 100.94 49.35 8.92
2017/10/31 100.87 48.6 8.93
2017/11/1 100.76 48.14 8.79
2017/11/2 101.32 48.05 8.91
2017/11/3 101.42 48.26 8.9
2017/11/6 101.39 48.58 8.88
2017/11/7 101.35 48.71 8.84
2017/11/8 101.06 48.53 9.31
2017/11/9 100.69 48.47 7.76
2017/11/10 99.84 48.46 7.16
2017/11/13 100.04 47.5 7.26
2017/11/14 99.94 47.3 7.01
2017/11/15 99.92 47.4 7.1
2017/11/16 100.54 47.7 7.1
2017/11/17 100.89 47.63 7.21
2017/11/20 101.01 47.69 7.16
2017/11/21 100.92 47.87 7.08
2017/11/22 101.33 48.42 7.2
2017/11/23 101.02 48.42 7.34
2017/11/24 101.06 48.63 7.56
2017/11/27 101 48.91 7.31
2017/11/28 100.45 48.93 7.34
2017/11/29 101.38 48.38 7.25
2017/11/30 100.85 48.56 7.38
2017/12/1 101.16 48.8 7.37
2017/12/4 101.31 48.66 7.15
2017/12/5 100.94 48.46 7.26
2017/12/6 101.3 49.3 7.27
2017/12/7 101.99 47.83 7.37
2017/12/8 102.47 48.13 7.44
2017/12/11 101.83 48.2 7.79
2017/12/12 102.05 47.93 7.72
2017/12/13 102.11 47.78 7.69
2017/12/14 101.46 47.64 7.65
2017/12/15 101.92 47.98 7.54
2017/12/18 102.32 47.75 7.55
2017/12/19 102.66 47.35 7.64
2017/12/20 102.39 47.3 7.54
2017/12/21 102.85 47.12 7.42
2017/12/22 102.45 46.82 7.45
2017/12/25 102.45 46.82 7.45
2017/12/26 102.45 46.82 7.45
2017/12/27 102.22 46.69 7.29
2017/12/28 102.6 47.22 7.26
2017/12/29 102.65 46.98 7.33

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