Computation of portfolio VAR? The provided yields data file (yields.xls) contains 5-year yields from 1953 to 1994. Using this information and the
Computation of portfolio VAR
The provided yields data file (yields.xls) contains 5-year yields from 1953 to 1994. Using this information and the duration approximation, compute the portfolio VAR as of December 1994. Risk should be measured over a month at the 95% level. Report the distribution and compute the VAR:
· using a normal distribution for yield changes (Delta-Normal method) and a 12-month moving average model for the volatility of yield changes
· using the actual distribution for yield changes (Historical-Simulation method using all the available past data)
· Compare and discuss the differences between the VAR obtained using the two methods
Hint: Consider yield changes as if they were log-returns
YIELDS
| Date | 5-Year Yield |
| 12/1952 | 2.35 |
| 12/1952 | 2.42 |
| 12/1952 | 2.45 |
| 12/1952 | 2.53 |
| 12/1952 | 2.77 |
| 12/1952 | 3.07 |
| 12/1952 | 2.79 |
| 12/1952 | 2.72 |
| 12/1952 | 2.79 |
| 12/1952 | 2.41 |
| 12/1952 | 2.37 |
| 12/1952 | 2.38 |
| 12/1952 | 2.18 |
| 12/1952 | 1.87 |
| 12/1952 | 1.57 |
| 12/1952 | 1.53 |
| 12/1952 | 1.42 |
| 12/1952 | 1.73 |
| 12/1952 | 1.31 |
| 12/1952 | 1.38 |
| 12/1952 | 1.38 |
| 12/1952 | 1.52 |
| 12/1952 | 1.61 |
| 12/1952 | 1.68 |
| 12/1952 | 1.72 |
| 12/1952 | 2.27 |
| 12/1952 | 2.4 |
| 12/1952 | 2.4 |
| 12/1952 | 2.42 |
| 12/1952 | 2.46 |
| 12/1952 | 2.57 |
| 01/1953 | 2.76 |
| 01/1953 | 2.8 |
| 01/1953 | 2.67 |
| 01/1953 | 2.57 |
| 01/1953 | 2.73 |
| 01/1953 | 2.8 |
| 01/1953 | 2.71 |
| 01/1953 | 2.75 |
| 01/1953 | 3 |
| 01/1953 | 3.05 |
| 01/1953 | 2.87 |
| 01/1953 | 2.92 |
| 01/1953 | 3.17 |
| 01/1953 | 3.46 |
| 01/1953 | 3.31 |
| 01/1953 | 3.42 |
| 01/1953 | 3.59 |
| 01/1953 | 3.63 |
| 01/1953 | 3.26 |
| 01/1953 | 3.33 |
| 01/1953 | 3.34 |
| 01/1953 | 3.57 |
| 01/1953 | 3.66 |
| 01/1953 | 3.9 |
| 01/1953 | 3.99 |
| 01/1953 | 3.85 |
| 01/1953 | 3.9 |
| 01/1953 | 3.88 |
| 01/1953 | 3.2 |
| 01/1953 | 2.84 |
| 01/1953 | 2.82 |
| 02/1953 | 2.59 |
| 02/1953 | 2.53 |
| 02/1953 | 2.46 |
| 02/1953 | 2.38 |
| 02/1953 | 2.5 |
| 02/1953 | 2.81 |
| 02/1953 | 3.65 |
| 02/1953 | 3.76 |
| 02/1953 | 3.82 |
| 02/1953 | 3.59 |
| 02/1953 | 3.81 |
| 02/1953 | 3.95 |
| 02/1953 | 3.78 |
| 02/1953 | 3.93 |
| 02/1953 | 4.13 |
| 02/1953 | 4.2 |
| 02/1953 | 4.47 |
| 02/1953 | 4.48 |
| 02/1953 | 4.77 |
| 02/1953 | 4.82 |
| 02/1953 | 4.48 |
| 02/1953 | 4.82 |
| 02/1953 | 4.98 |
| 02/1953 | 4.71 |
| 02/1953 | 4.64 |
| 02/1953 | 4.09 |
| 02/1953 | 4.31 |
| 02/1953 | 4.32 |
| 03/1953 | 3.9 |
| 03/1953 | 3.34 |
| 03/1953 | 3.43 |
| 03/1953 | 3.43 |
| 03/1953 | 3.46 |
| 03/1953 | 3.77 |
| 03/1953 | 3.31 |
| 03/1953 | 3.63 |
| 03/1953 | 3.5 |
| 03/1953 | 3.48 |
| 03/1953 | 3.42 |
| 03/1953 | 3.55 |
| 03/1953 | 3.68 |
| 03/1953 | 3.73 |
| 03/1953 | 3.76 |
| 03/1953 | 3.65 |
| 03/1953 | 3.69 |
| 03/1953 | 3.81 |
| 03/1953 | 3.84 |
| 03/1953 | 4.02 |
| 03/1953 | 3.77 |
| 03/1953 | 3.66 |
| 03/1953 | 3.67 |
| 03/1953 | 3.63 |
| 03/1953 | 3.75 |
| 03/1953 | 3.84 |
| 03/1953 | 3.65 |
| 03/1953 | 3.66 |
| 03/1953 | 3.62 |
| 03/1953 | 3.55 |
| 03/1953 | 3.5 |
| 04/1953 | 3.68 |
| 04/1953 | 3.7 |
| 04/1953 | 3.7 |
| 04/1953 | 3.71 |
| 04/1953 | 3.74 |
| 04/1953 | 3.78 |
| 04/1953 | 3.85 |
| 04/1953 | 3.88 |
| 04/1953 | 3.92 |
| 04/1953 | 3.98 |
| 04/1953 | 3.96 |
| 04/1953 | 4.04 |
| 04/1953 | 4.02 |
| 04/1953 | 4.07 |
| 04/1953 | 4.11 |
| 04/1953 | 4.11 |
| 04/1953 | 3.99 |
| 04/1953 | 3.99 |
| 04/1953 | 4.01 |
| 04/1953 | 4.02 |
| 04/1953 | 3.99 |
| 04/1953 | 3.99 |
| 04/1953 | 4.09 |
| 04/1953 | 4.03 |
| 04/1953 | 4.13 |
| 04/1953 | 4.16 |
| 04/1953 | 4.14 |
| 04/1953 | 4.16 |
| 04/1953 | 4.15 |
| 04/1953 | 4.13 |
| 05/1953 | 4.16 |
| 05/1953 | 4.2 |
| 05/1953 | 4.29 |
| 05/1953 | 4.37 |
| 05/1953 | 4.44 |
| 05/1953 | 4.9 |
| 05/1953 | 4.82 |
| 05/1953 | 5.07 |
| 05/1953 | 4.77 |
| 05/1953 | 4.89 |
| 05/1953 | 4.96 |
| 05/1953 | 5.1 |
| 05/1953 | 5.25 |
| 05/1953 | 5.65 |
| 05/1953 | 5.26 |
| 05/1953 | 5.19 |
| 05/1953 | 5.22 |
| 05/1953 | 4.79 |
| 05/1953 | 4.59 |
| 05/1953 | 4.7 |
| 05/1953 | 4.37 |
| 05/1953 | 4.66 |
| 05/1953 | 4.65 |
| 05/1953 | 5.3 |
| 05/1953 | 5.08 |
| 05/1953 | 5.28 |
| 05/1953 | 5.37 |
| 05/1953 | 5.62 |
| 05/1953 | 5.66 |
| 05/1953 | 5.77 |
| 05/1953 | 5.48 |
| 06/1953 | 5.49 |
| 06/1953 | 5.63 |
| 06/1953 | 5.77 |
| 06/1953 | 5.74 |
| 06/1953 | 5.47 |
| 06/1953 | 5.18 |
| 06/1953 | 5.23 |
| 06/1953 | 5.2 |
| 06/1953 | 5.28 |
| 06/1953 | 5.41 |
| 06/1953 | 5.96 |
| 06/1953 | 6.37 |
| 06/1953 | 6.51 |
| 06/1953 | 6.4 |
| 06/1953 | 6.36 |
| 06/1953 | 6.66 |
| 06/1953 | 6.99 |
| 06/1953 | 6.93 |
| 06/1953 | 7.11 |
| 06/1953 | 7.99 |
| 06/1953 | 7.35 |
| 06/1953 | 7.61 |
| 06/1953 | 8.29 |
| 06/1953 | 8.2 |
| 06/1953 | 7.3 |
| 06/1953 | 7.24 |
| 06/1953 | 7.9 |
| 06/1953 | 7.78 |
| 06/1953 | 7.8 |
| 06/1953 | 7.57 |
| 07/1953 | 7.43 |
| 07/1953 | 7.07 |
| 07/1953 | 6.97 |
| 07/1953 | 5.91 |
| 07/1953 | 5.9 |
| 07/1953 | 5.7 |
| 07/1953 | 5.26 |
| 07/1953 | 4.93 |
| 07/1953 | 5.85 |
| 07/1953 | 5.93 |
| 07/1953 | 6.56 |
| 07/1953 | 6.63 |
| 07/1953 | 5.85 |
| 07/1953 | 5.91 |
| 07/1953 | 5.45 |
| 07/1953 | 5.43 |
| 07/1953 | 5.25 |
| 07/1953 | 5.56 |
| 07/1953 | 5.63 |
| 07/1953 | 5.7 |
| 07/1953 | 5.77 |
| 07/1953 | 5.86 |
| 07/1953 | 5.87 |
| 07/1953 | 5.95 |
| 07/1953 | 6.04 |
| 07/1953 | 6.13 |
| 07/1953 | 6.23 |
| 07/1953 | 6.25 |
| 07/1953 | 5.85 |
| 07/1953 | 6.41 |
| 07/1953 | 6.71 |
| 08/1953 | 6.73 |
| 08/1953 | 6.71 |
| 08/1953 | 6.71 |
| 08/1953 | 6.86 |
| 08/1953 | 7.76 |
| 08/1953 | 7.25 |
| 08/1953 | 6.74 |
| 08/1953 | 6.77 |
| 08/1953 | 6.74 |
| 08/1953 | 6.79 |
| 08/1953 | 6.87 |
| 08/1953 | 6.91 |
| 08/1953 | 7.51 |
| 08/1953 | 8.01 |
| 08/1953 | 7.86 |
| 08/1953 | 8.22 |
| 08/1953 | 8.38 |
| 08/1953 | 8.57 |
| 08/1953 | 7.97 |
| 08/1953 | 7.87 |
| 08/1953 | 7.43 |
| 08/1953 | 7.12 |
| 08/1953 | 7.3 |
| 08/1953 | 7.09 |
| 08/1953 | 7.37 |
| 08/1953 | 7.98 |
| 08/1953 | 7.49 |
| 08/1953 | 7.58 |
| 08/1953 | 7.82 |
| 08/1953 | 8 |
| 08/1953 | 8.15 |
| 09/1953 | 7.36 |
| 09/1953 | 7.54 |
| 09/1953 | 7.19 |
| 09/1953 | 7.43 |
| 09/1953 | 7.36 |
| 09/1953 | 7.33 |
| 09/1953 | 7.19 |
| 09/1953 | 7.71 |
| 09/1953 | 7.47 |
| 09/1953 | 7.32 |
| 09/1953 | 6.97 |
| 09/1953 | 6.92 |
| 09/1953 | 6.67 |
| 09/1953 | 5.94 |
| 09/1953 | 6 |
| 09/1953 | 6.73 |
| 09/1953 | 6.73 |
| 09/1953 | 6.73 |
| 09/1953 | 6.74 |
| 09/1953 | 6.74 |
| 09/1953 | 6.62 |
| 09/1953 | 6.75 |
| 09/1953 | 6.89 |
| 09/1953 | 7 |
| 09/1953 | 7.33 |
| 09/1953 | 7.27 |
| 09/1953 | 7.51 |
| 09/1953 | 7.73 |
| 09/1953 | 7.84 |
| 09/1953 | 7.91 |
| 10/1953 | 8 |
| 10/1953 | 8.2 |
| 10/1953 | 8.43 |
| 10/1953 | 8.36 |
| 10/1953 | 8.33 |
| 10/1953 | 8.35 |
| 10/1953 | 8.87 |
| 10/1953 | 8.82 |
| 10/1953 | 8.83 |
| 10/1953 | 8.95 |
| 10/1953 | 9.28 |
| 10/1953 | 9.18 |
| 10/1953 | 9.29 |
| 10/1953 | 8.99 |
| 10/1953 | 8.64 |
| 10/1953 | 8.87 |
| 10/1953 | 9.33 |
| 10/1953 | 9.51 |
| 10/1953 | 11.12 |
| 10/1953 | 10.33 |
| 10/1953 | 10.33 |
| 10/1953 | 10.93 |
| 10/1953 | 12.94 |
| 10/1953 | 12.85 |
| 10/1953 | 10.09 |
| 10/1953 | 9.03 |
| 10/1953 | 9.44 |
| 10/1953 | 9.96 |
| 10/1953 | 11.33 |
| 10/1953 | 11.71 |
| 10/1953 | 12.44 |
| 11/1953 | 12.64 |
| 11/1953 | 12.45 |
| 11/1953 | 12.75 |
| 11/1953 | 13.71 |
| 11/1953 | 13.28 |
| 11/1953 | 14.27 |
| 11/1953 | 13.85 |
| 11/1953 | 14.04 |
| 11/1953 | 15.33 |
| 11/1953 | 16.36 |
| 11/1953 | 16.25 |
| 11/1953 | 14.72 |
| 11/1953 | 13.11 |
| 11/1953 | 13.96 |
| 11/1953 | 13.97 |
| 11/1953 | 13.85 |
| 11/1953 | 14.06 |
| 11/1953 | 13.55 |
| 11/1953 | 13.43 |
| 11/1953 | 14.17 |
| 11/1953 | 13.15 |
| 11/1953 | 12.09 |
| 11/1953 | 11.44 |
| 11/1953 | 10.18 |
| 11/1953 | 10.2 |
| 11/1953 | 9.9 |
| 11/1953 | 10.57 |
| 11/1953 | 10.1 |
| 11/1953 | 10.48 |
| 11/1953 | 9.97 |
| 12/1953 | 10.59 |
| 12/1953 | 10.8 |
| 12/1953 | 11.68 |
| 12/1953 | 11.75 |
| 12/1953 | 11.08 |
| 12/1953 | 11.31 |
| 12/1953 | 11.27 |
| 12/1953 | 11.41 |
| 12/1953 | 11.37 |
| 12/1953 | 11.81 |
| 12/1953 | 12.19 |
| 12/1953 | 12.51 |
| 12/1953 | 13.63 |
| 12/1953 | 13.65 |
| 12/1953 | 12.74 |
| 12/1953 | 12.76 |
| 12/1953 | 12.42 |
| 12/1953 | 11.54 |
| 12/1953 | 11.21 |
| 12/1953 | 11.04 |
| 12/1953 | 10.81 |
| 12/1953 | 11.52 |
| 12/1953 | 11.31 |
| 12/1953 | 10.84 |
| 12/1953 | 9.74 |
| 12/1953 | 9.63 |
| 12/1953 | 10.02 |
| 12/1953 | 9.82 |
| 12/1953 | 9.73 |
| 12/1953 | 9.49 |
| 12/1953 | 9.11 |
| 01/1954 | 8.55 |
| 01/1954 | 8.7 |
| 01/1954 | 8.15 |
| 01/1954 | 7.43 |
| 01/1954 | 7.37 |
| 01/1954 | 8.16 |
| 01/1954 | 7.56 |
| 01/1954 | 7.28 |
| 01/1954 | 6.68 |
| 01/1954 | 7.18 |
| 01/1954 | 6.87 |
| 01/1954 | 6.69 |
| 01/1954 | 6.85 |
| 01/1954 | 6.85 |
| 01/1954 | 6.83 |
| 01/1954 | 7.08 |
| 01/1954 | 7.93 |
| 01/1954 | 8.21 |
| 01/1954 | 8.06 |
| 01/1954 | 8.18 |
| 01/1954 | 8.49 |
| 01/1954 | 9.12 |
| 01/1954 | 8.44 |
| 01/1954 | 8.4 |
| 01/1954 | 8.32 |
| 01/1954 | 7.82 |
| 01/1954 | 7.68 |
| 01/1954 | 8.07 |
| 01/1954 | 8.36 |
| 01/1954 | 8.7 |
| 01/1954 | 8.39 |
| 02/1954 | 8.71 |
| 02/1954 | 8.95 |
| 02/1954 | 8.59 |
| 02/1954 | 8.37 |
| 02/1954 | 8.92 |
| 02/1954 | 9.17 |
| 02/1954 | 8.96 |
| 02/1954 | 9.27 |
| 02/1954 | 9.34 |
| 02/1954 | 8.95 |
| 02/1954 | 8.6 |
| 02/1954 | 7.91 |
| 02/1954 | 7.45 |
| 02/1954 | 8.34 |
| 02/1954 | 8.33 |
| 02/1954 | 7.86 |
| 02/1954 | 7.79 |
| 02/1954 | 7.94 |
| 02/1954 | 8.42 |
| 02/1954 | 8.55 |
| 02/1954 | 8.71 |
| 02/1954 | 9.07 |
| 02/1954 | 8.64 |
| 02/1954 | 8.43 |
| 02/1954 | 8.19 |
| 02/1954 | 8.59 |
| 02/1954 | 8.51 |
| 02/1954 | 8.26 |
| 03/1954 | 7.95 |
| 03/1954 | 7.7 |
| 03/1954 | 7.72 |
| 03/1954 | 7.74 |
| 03/1954 | 7.83 |
| 03/1954 | 7.72 |
| 03/1954 | 7.73 |
| 03/1954 | 7.93 |
| 03/1954 | 7.78 |
| 03/1954 | 7.32 |
| 03/1954 | 6.93 |
| 03/1954 | 6.73 |
| 03/1954 | 6.53 |
| 03/1954 | 5.97 |
| 03/1954 | 6.83 |
| 03/1954 | 6.9 |
| 03/1954 | 7.2 |
| 03/1954 | 7.11 |
| 03/1954 | 6.74 |
| 03/1954 | 6.47 |
| 03/1954 | 6.04 |
| 03/1954 | 5.81 |
| 03/1954 | 5.47 |
| 03/1954 | 6.01 |
| 03/1954 | 6.34 |
| 03/1954 | 6.11 |
| 03/1954 | 5.88 |
| 03/1954 | 5.47 |
| 03/1954 | 5.49 |
| 03/1954 | 5.4 |
| 03/1954 | 5.51 |
| 04/1954 | 5.17 |
| 04/1954 | 5.26 |
| 04/1954 | 4.86 |
| 04/1954 | 4.83 |
| 04/1954 | 4.88 |
| 04/1954 | 5.19 |
| 04/1954 | 5.22 |
| 04/1954 | 5.15 |
| 04/1954 | 5.75 |
| 04/1954 | 6.38 |
| 04/1954 | 6.7 |
| 04/1954 | 6.82 |
| 04/1954 | 6.99 |
| 04/1954 | 6.73 |
| 04/1954 | 6.81 |
| 04/1954 | 7.28 |
| 04/1954 | 7.48 |
| 04/1954 | 7.79 |
| 04/1954 | 7.83 |
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