Question 7:

Download data from https://finance.yahoo.com/quote/LPL/history?period1=1507536513&period2=1539072513&interval=1d&filter=history&frequency=1d

OR see Data at the end of this question.

LG company, daily historical data one year from now to today

Problems:

Value at Risk of the stock

Calculate daily VaR at 5% and 1% probability levels of a $100,000 position in the stock, using:

A) Historical method

B )Analytical method

Estimate annual values from calculated values in both cases.

C) Comment the results, compare, discuss why they could be different.

Assume you now buy $200,000 worth of corporate bonds that have an annual total return of 7.5% with standard deviation of 1% and the correlation between these bonds and your stock is 0.35.

Using the analytical method and your previous results, calculate:

D) 5% daily VaR of your portfolio

E) 1% daily VaR of your portfolio

Adjusted returns

Assuming the annual risk-free rate is 1%, and using your earlier results, calculate on an annual basis:

F) Sharpe ratio for your stock.

G) Using the sharpe ratio criteria, discuss whether adding the corporate bond was a good idea. DATA

Date	Open	High	Low	Close	Adj Close	Volume
09/10/2017	13.740000	13.780000	13.650000	13.680000	13.449546	368400
10/10/2017	13.320000	13.330000	13.100000	13.160000	12.938306	1010700
11/10/2017	13.250000	13.480000	13.230000	13.340000	13.115273	1241300
12/10/2017	12.840000	12.870000	12.540000	12.610000	12.397571	1639900
13/10/2017	12.850000	12.880000	12.720000	12.750000	12.535213	879200
16/10/2017	12.990000	12.990000	12.840000	12.940000	12.722012	686300
17/10/2017	12.860000	12.880000	12.710000	12.730000	12.515550	328900
18/10/2017	12.710000	12.730000	12.630000	12.700000	12.486054	669400
19/10/2017	12.690000	12.750000	12.510000	12.740000	12.525381	1108500
20/10/2017	13.340000	13.580000	13.310000	13.320000	13.095611	2184100
23/10/2017	13.180000	13.210000	12.850000	12.940000	12.722012	850800
24/10/2017	12.990000	13.080000	12.960000	12.970000	12.751507	603900
25/10/2017	13.070000	13.290000	12.970000	13.170000	12.948137	885400
26/10/2017	12.940000	13.000000	12.500000	12.560000	12.348413	1070700
27/10/2017	12.950000	13.160000	12.880000	13.120000	12.898979	1027800
30/10/2017	13.080000	13.110000	12.930000	12.990000	12.771170	781500
31/10/2017	13.000000	13.030000	12.860000	12.990000	12.771170	875900
01/11/2017	13.120000	13.170000	13.040000	13.130000	12.908812	816000
02/11/2017	13.170000	13.220000	13.080000	13.190000	12.967800	1028600
03/11/2017	13.200000	13.230000	13.090000	13.180000	12.957970	642300
06/11/2017	13.130000	13.220000	13.120000	13.210000	12.987464	705900
07/11/2017	13.180000	13.200000	13.070000	13.090000	12.869485	637800
08/11/2017	13.040000	13.120000	12.970000	13.070000	12.849822	403200
09/11/2017	13.250000	13.360000	13.150000	13.280000	13.056284	935300
10/11/2017	13.350000	13.510000	13.350000	13.500000	13.272578	663400
13/11/2017	13.320000	13.370000	13.250000	13.320000	13.095611	344100
14/11/2017	13.170000	13.180000	13.060000	13.100000	12.879317	547800
15/11/2017	13.180000	13.200000	13.100000	13.170000	12.948137	362300
16/11/2017	13.310000	13.570000	13.290000	13.560000	13.331568	942100
17/11/2017	13.690000	13.780000	13.600000	13.740000	13.508534	650100
20/11/2017	13.600000	13.700000	13.600000	13.660000	13.429883	406700
21/11/2017	14.510000	14.520000	14.300000	14.360000	14.118091	2205200
22/11/2017	14.440000	14.470000	14.370000	14.470000	14.226237	737800
24/11/2017	14.410000	14.420000	14.270000	14.290000	14.049270	469200
27/11/2017	14.030000	14.070000	13.920000	13.950000	13.714997	664200
28/11/2017	14.160000	14.230000	14.090000	14.200000	13.960786	863200
29/11/2017	14.200000	14.220000	13.860000	13.920000	13.685503	1027800
30/11/2017	14.050000	14.140000	14.010000	14.060000	13.823145	922600
01/12/2017	13.690000	13.700000	13.390000	13.580000	13.351231	960900
04/12/2017	14.000000	14.020000	13.720000	13.780000	13.547861	1254900
05/12/2017	13.960000	14.020000	13.850000	13.910000	13.675672	1234300
06/12/2017	13.690000	13.690000	13.450000	13.480000	13.252914	936000
07/12/2017	13.590000	13.630000	13.470000	13.590000	13.361062	1141000
08/12/2017	13.590000	13.660000	13.570000	13.610000	13.380725	1007800
11/12/2017	13.610000	13.620000	13.540000	13.590000	13.361062	499500
12/12/2017	13.680000	13.690000	13.620000	13.630000	13.400389	427000
13/12/2017	13.650000	13.650000	13.500000	13.580000	13.351231	934200
14/12/2017	13.660000	13.690000	13.600000	13.610000	13.380725	738800
15/12/2017	13.840000	13.870000	13.740000	13.840000	13.606851	1232500
18/12/2017	13.710000	13.760000	13.630000	13.680000	13.449546	670800
19/12/2017	13.610000	13.610000	13.370000	13.400000	13.174262	749200
20/12/2017	13.520000	13.580000	13.440000	13.560000	13.331568	721500
21/12/2017	13.500000	13.560000	13.450000	13.500000	13.272578	639800
22/12/2017	13.720000	13.810000	13.700000	13.760000	13.528198	566800
26/12/2017	13.650000	13.650000	13.540000	13.550000	13.321736	371000
27/12/2017	13.820000	13.990000	13.810000	13.890000	13.656009	353600
28/12/2017	13.890000	13.890000	13.740000	13.790000	13.790000	429700
29/12/2017	13.890000	13.900000	13.740000	13.760000	13.760000	572800
02/01/2018	13.920000	14.110000	13.860000	14.110000	14.110000	787400
03/01/2018	14.390000	14.530000	14.360000	14.480000	14.480000	727800
04/01/2018	14.260000	14.300000	14.160000	14.290000	14.290000	543700
05/01/2018	14.170000	14.290000	14.100000	14.250000	14.250000	815100
08/01/2018	14.210000	14.280000	14.120000	14.260000	14.260000	967500
09/01/2018	14.230000	14.260000	14.080000	14.120000	14.120000	750700
10/01/2018	13.980000	14.050000	13.870000	13.980000	13.980000	630700
11/01/2018	14.000000	14.110000	14.000000	14.080000	14.080000	433300
12/01/2018	13.720000	13.810000	13.620000	13.780000	13.780000	997800
16/01/2018	14.480000	14.670000	14.380000	14.400000	14.400000	927200
17/01/2018	14.620000	14.740000	14.600000	14.730000	14.730000	1226000
18/01/2018	14.420000	14.480000	14.360000	14.410000	14.410000	767800
19/01/2018	14.370000	14.410000	14.150000	14.180000	14.180000	975100
22/01/2018	14.210000	14.300000	14.150000	14.260000	14.260000	897800
23/01/2018	15.080000	15.660000	14.750000	15.590000	15.590000	3875500
24/01/2018	15.710000	15.880000	15.540000	15.650000	15.650000	1223500
25/01/2018	15.500000	15.740000	15.450000	15.590000	15.590000	899200
26/01/2018	15.420000	15.460000	15.350000	15.450000	15.450000	716000
29/01/2018	15.330000	15.530000	15.320000	15.400000	15.400000	494300
30/01/2018	15.140000	15.230000	15.000000	15.140000	15.140000	632000
31/01/2018	15.190000	15.200000	14.840000	14.910000	14.910000	723500
01/02/2018	14.660000	14.790000	14.540000	14.740000	14.740000	425200
02/02/2018	14.550000	14.550000	14.280000	14.300000	14.300000	553200
05/02/2018	14.220000	14.250000	13.730000	13.740000	13.740000	1200400
06/02/2018	13.780000	14.370000	13.750000	14.260000	14.260000	1069500
07/02/2018	13.820000	14.020000	13.720000	13.800000	13.800000	1036000
08/02/2018	13.830000	13.900000	13.440000	13.440000	13.440000	962000
09/02/2018	13.730000	13.940000	13.460000	13.820000	13.820000	1418400
12/02/2018	13.830000	13.830000	13.640000	13.750000	13.750000	867300
13/02/2018	13.990000	14.050000	13.930000	14.000000	14.000000	690700
14/02/2018	13.820000	14.250000	13.790000	14.250000	14.250000	636600
15/02/2018	14.430000	14.440000	14.220000	14.420000	14.420000	522400
16/02/2018	14.390000	14.640000	14.390000	14.490000	14.490000	610600
20/02/2018	14.220000	14.290000	14.100000	14.160000	14.160000	522500
21/02/2018	14.210000	14.380000	14.110000	14.110000	14.110000	376400
22/02/2018	14.030000	14.070000	13.850000	13.890000	13.890000	628400
23/02/2018	13.870000	13.910000	13.780000	13.880000	13.880000	414300
26/02/2018	13.930000	14.060000	13.900000	14.050000	14.050000	381400
27/02/2018	14.000000	14.030000	13.710000	13.720000	13.720000	401000
28/02/2018	13.740000	13.830000	13.590000	13.600000	13.600000	570300
01/03/2018	13.640000	13.730000	13.340000	13.450000	13.450000	835400
02/03/2018	13.360000	13.540000	13.270000	13.530000	13.530000	559100
05/03/2018	13.460000	13.460000	13.280000	13.370000	13.370000	945100
06/03/2018	13.460000	13.500000	13.370000	13.410000	13.410000	897500
07/03/2018	13.120000	13.120000	12.750000	12.930000	12.930000	1838900
08/03/2018	13.030000	13.060000	12.920000	13.000000	13.000000	837000
09/03/2018	13.040000	13.150000	13.020000	13.120000	13.120000	453300
12/03/2018	13.200000	13.350000	13.200000	13.300000	13.300000	493700
13/03/2018	13.330000	13.370000	13.140000	13.160000	13.160000	755200
14/03/2018	13.170000	13.200000	13.030000	13.060000	13.060000	566700
15/03/2018	13.100000	13.130000	13.010000	13.070000	13.070000	562200
16/03/2018	13.100000	13.140000	13.040000	13.070000	13.070000	764000
19/03/2018	12.950000	13.000000	12.770000	12.820000	12.820000	736500
20/03/2018	12.820000	12.890000	12.670000	12.880000	12.880000	1002200
21/03/2018	12.800000	12.870000	12.750000	12.780000	12.780000	687900
22/03/2018	12.500000	12.500000	12.310000	12.310000	12.310000	1110600
23/03/2018	12.500000	12.500000	11.860000	11.870000	11.870000	1370300
26/03/2018	12.080000	12.160000	11.890000	12.120000	12.120000	981900
27/03/2018	11.950000	11.950000	11.590000	11.680000	11.680000	1421700
28/03/2018	11.950000	12.070000	11.900000	12.020000	12.020000	1102000
29/03/2018	12.020000	12.140000	12.000000	12.100000	12.100000	878500
02/04/2018	12.050000	12.080000	11.740000	11.850000	11.850000	1071600
03/04/2018	11.900000	11.980000	11.770000	11.960000	11.960000	934700
04/04/2018	11.480000	11.700000	11.420000	11.680000	11.680000	926400
05/04/2018	11.710000	11.790000	11.590000	11.600000	11.600000	683500
06/04/2018	11.490000	11.510000	11.280000	11.330000	11.330000	997400
09/04/2018	11.790000	11.890000	11.730000	11.730000	11.730000	1132700
10/04/2018	11.780000	11.800000	11.590000	11.700000	11.700000	959400
11/04/2018	11.590000	11.610000	11.440000	11.530000	11.530000	452200
12/04/2018	11.640000	11.770000	11.620000	11.690000	11.690000	489800
13/04/2018	11.680000	11.680000	11.440000	11.470000	11.470000	560600
16/04/2018	11.580000	11.580000	11.470000	11.530000	11.530000	515500
17/04/2018	11.970000	12.040000	11.920000	11.930000	11.930000	1167400
18/04/2018	12.040000	12.070000	11.990000	12.030000	12.030000	1243200
19/04/2018	11.820000	11.850000	11.620000	11.710000	11.710000	744300
20/04/2018	11.630000	11.640000	11.420000	11.470000	11.470000	979300
23/04/2018	11.470000	11.550000	11.390000	11.390000	11.390000	830700
24/04/2018	11.410000	11.430000	11.170000	11.200000	11.200000	926200
25/04/2018	11.220000	11.370000	11.190000	11.280000	11.280000	831100
26/04/2018	11.040000	11.060000	10.650000	10.670000	10.670000	1798600
27/04/2018	10.960000	11.060000	10.920000	10.940000	10.940000	1420700
30/04/2018	10.890000	10.890000	10.770000	10.800000	10.800000	762900
01/05/2018	10.800000	10.850000	10.660000	10.840000	10.840000	783800
02/05/2018	10.890000	10.940000	10.770000	10.850000	10.850000	753400
03/05/2018	10.860000	10.860000	10.740000	10.840000	10.840000	617400
04/05/2018	10.610000	10.710000	10.480000	10.690000	10.690000	841600
07/05/2018	10.610000	10.710000	10.580000	10.620000	10.620000	479300
08/05/2018	10.510000	10.510000	10.380000	10.480000	10.480000	794000
09/05/2018	10.500000	10.600000	10.210000	10.530000	10.530000	2062600
10/05/2018	10.530000	10.620000	10.470000	10.580000	10.580000	808700
11/05/2018	10.910000	11.020000	10.890000	10.910000	10.910000	686900
14/05/2018	10.910000	10.950000	10.880000	10.920000	10.920000	364800
15/05/2018	10.740000	10.750000	10.570000	10.600000	10.600000	604500
16/05/2018	10.600000	10.650000	10.560000	10.600000	10.600000	432100
17/05/2018	10.580000	10.650000	10.520000	10.540000	10.540000	578000
18/05/2018	10.480000	10.500000	10.340000	10.400000	10.400000	932700
21/05/2018	10.350000	10.410000	10.290000	10.300000	10.300000	349900
22/05/2018	10.360000	10.430000	10.310000	10.310000	10.310000	559100
23/05/2018	10.300000	10.470000	10.300000	10.470000	10.470000	717700
24/05/2018	10.400000	10.400000	10.160000	10.300000	10.300000	538400
25/05/2018	10.230000	10.280000	10.160000	10.260000	10.260000	375800
29/05/2018	10.650000	10.730000	10.310000	10.380000	10.380000	1144900
30/05/2018	10.400000	10.410000	10.250000	10.390000	10.390000	688400
31/05/2018	10.350000	10.350000	10.190000	10.270000	10.270000	650400
01/06/2018	10.550000	10.740000	10.550000	10.650000	10.650000	968500
04/06/2018	10.800000	10.800000	10.600000	10.690000	10.690000	733800
05/06/2018	10.570000	10.600000	10.380000	10.450000	10.450000	549600
06/06/2018	10.490000	10.570000	10.490000	10.550000	10.550000	383300
07/06/2018	10.430000	10.540000	10.350000	10.470000	10.470000	896000
08/06/2018	10.360000	10.440000	10.320000	10.440000	10.440000	317100
11/06/2018	10.420000	10.440000	10.330000	10.420000	10.420000	673600
12/06/2018	10.490000	10.530000	10.380000	10.410000	10.410000	442300
13/06/2018	10.430000	10.440000	10.310000	10.340000	10.340000	396300
14/06/2018	10.250000	10.290000	10.200000	10.270000	10.270000	661700
15/06/2018	9.610000	9.680000	9.460000	9.520000	9.520000	1732300
18/06/2018	9.240000	9.250000	9.020000	9.090000	9.090000	1392500
19/06/2018	9.000000	9.000000	8.850000	8.920000	8.920000	867300
20/06/2018	8.940000	8.950000	8.870000	8.900000	8.900000	644700
21/06/2018	8.630000	8.630000	8.470000	8.480000	8.480000	1046500
22/06/2018	8.540000	8.590000	8.500000	8.580000	8.580000	779400
25/06/2018	8.490000	8.510000	8.320000	8.360000	8.360000	900900
26/06/2018	8.140000	8.200000	8.100000	8.150000	8.150000	1068800
27/06/2018	8.200000	8.300000	8.080000	8.090000	8.090000	741900
28/06/2018	7.850000	7.910000	7.770000	7.880000	7.880000	1039600
29/06/2018	8.170000	8.290000	8.170000	8.240000	8.240000	978400
02/07/2018	8.160000	8.170000	8.030000	8.050000	8.050000	931700
03/07/2018	7.990000	8.030000	7.880000	7.890000	7.890000	527400
05/07/2018	8.120000	8.270000	8.070000	8.250000	8.250000	1213600
06/07/2018	8.120000	8.220000	8.080000	8.170000	8.170000	638500
09/07/2018	8.380000	8.640000	8.380000	8.620000	8.620000	1207100
10/07/2018	8.830000	8.930000	8.800000	8.860000	8.860000	1749300
11/07/2018	8.760000	8.860000	8.620000	8.680000	8.680000	1190400
12/07/2018	8.770000	8.770000	8.620000	8.740000	8.740000	818100
13/07/2018	8.720000	8.750000	8.600000	8.610000	8.610000	364300
16/07/2018	8.820000	8.820000	8.650000	8.650000	8.650000	472700
17/07/2018	8.930000	9.030000	8.880000	8.980000	8.980000	1180000
18/07/2018	8.970000	9.020000	8.850000	8.990000	8.990000	733700
19/07/2018	9.310000	9.410000	9.260000	9.370000	9.370000	2023700
20/07/2018	9.600000	9.700000	9.500000	9.540000	9.540000	1127200
23/07/2018	9.190000	9.380000	9.050000	9.360000	9.360000	869000
24/07/2018	9.520000	9.840000	9.490000	9.730000	9.730000	1538300
25/07/2018	9.070000	9.300000	8.890000	9.170000	9.170000	2143800
26/07/2018	9.470000	9.610000	9.420000	9.540000	9.540000	976000
27/07/2018	9.580000	9.610000	9.400000	9.480000	9.480000	600300
30/07/2018	9.520000	9.520000	9.350000	9.360000	9.360000	558600
31/07/2018	9.360000	9.410000	9.350000	9.380000	9.380000	628300
01/08/2018	9.570000	9.670000	9.560000	9.660000	9.660000	716500
02/08/2018	9.550000	9.640000	9.510000	9.620000	9.620000	713900
03/08/2018	9.630000	9.760000	9.620000	9.760000	9.760000	714700
06/08/2018	9.820000	9.880000	9.770000	9.860000	9.860000	359500
07/08/2018	10.020000	10.110000	9.930000	10.040000	10.040000	619300
08/08/2018	9.680000	9.770000	9.570000	9.750000	9.750000	560800
09/08/2018	9.750000	9.810000	9.720000	9.740000	9.740000	382400
10/08/2018	9.780000	9.790000	9.690000	9.720000	9.720000	466400
13/08/2018	9.540000	9.540000	9.410000	9.440000	9.440000	735100
14/08/2018	9.620000	9.860000	9.610000	9.830000	9.830000	467100
15/08/2018	9.600000	9.650000	9.500000	9.500000	9.500000	523900
16/08/2018	9.910000	9.920000	9.750000	9.840000	9.840000	692300
17/08/2018	9.810000	9.970000	9.750000	9.940000	9.940000	577500
20/08/2018	10.110000	10.250000	10.050000	10.230000	10.230000	1085700
21/08/2018	10.330000	10.390000	10.250000	10.290000	10.290000	721500
22/08/2018	9.970000	9.970000	9.780000	9.870000	9.870000	843000
23/08/2018	9.800000	9.800000	9.600000	9.690000	9.690000	908600
24/08/2018	9.520000	9.570000	9.440000	9.550000	9.550000	515100
27/08/2018	9.480000	9.580000	9.400000	9.520000	9.520000	802800
28/08/2018	9.580000	9.640000	9.530000	9.560000	9.560000	368200
29/08/2018	9.560000	9.630000	9.480000	9.620000	9.620000	290800
30/08/2018	9.540000	9.540000	9.410000	9.420000	9.420000	855800
31/08/2018	9.420000	9.470000	9.350000	9.470000	9.470000	453100
04/09/2018	9.430000	9.450000	9.350000	9.440000	9.440000	411000
05/09/2018	9.740000	9.810000	9.690000	9.710000	9.710000	864000
06/09/2018	9.540000	9.540000	9.410000	9.460000	9.460000	324800
07/09/2018	9.300000	9.370000	9.200000	9.300000	9.300000	393000
10/09/2018	9.330000	9.380000	9.310000	9.360000	9.360000	264700
11/09/2018	8.910000	8.920000	8.760000	8.900000	8.900000	733800
12/09/2018	8.980000	9.090000	8.890000	9.040000	9.040000	518900
13/09/2018	9.130000	9.150000	9.030000	9.110000	9.110000	411400
14/09/2018	9.900000	9.900000	9.130000	9.260000	9.260000	1059100
17/09/2018	8.810000	8.840000	8.600000	8.620000	8.620000	1208000
18/09/2018	8.690000	8.820000	8.660000	8.810000	8.810000	753000
19/09/2018	8.460000	8.550000	8.410000	8.420000	8.420000	711300
20/09/2018	8.500000	8.550000	8.440000	8.530000	8.530000	451400
21/09/2018	8.530000	8.620000	8.510000	8.550000	8.550000	419900
24/09/2018	8.500000	8.610000	8.450000	8.580000	8.580000	380300
25/09/2018	8.600000	8.680000	8.560000	8.610000	8.610000	483500
26/09/2018	8.620000	8.700000	8.510000	8.510000	8.510000	404800
27/09/2018	8.740000	8.860000	8.740000	8.770000	8.770000	403300
28/09/2018	8.590000	8.670000	8.550000	8.670000	8.670000	427200
01/10/2018	8.670000	8.700000	8.600000	8.660000	8.660000	415700
02/10/2018	8.670000	8.730000	8.610000	8.620000	8.620000	512500
03/10/2018	8.600000	8.710000	8.600000	8.600000	8.600000	215900
04/10/2018	8.480000	8.490000	8.330000	8.360000	8.360000	470300
05/10/2018	8.340000	8.340000	8.060000	8.120000	8.120000	663600
08/10/2018	8.060000	8.160000	8.040000	8.110000	8.110000	365200