historical data for precious metal prices, 10- year government bond yields (assumed to be the risk-free rate of interest), and the aggregate equity market index. All data are in monthly frequency. Your client is interested in investing in the precious metals as they have historically been considered as safe-haven/hedge against equity market volatility. However, he has been warned off by his financial planner. You are asked to compare the historical performance of the precious metals and equity asset class using suitable portfolio performance measures.

a) Evaluate the performance of the precious metals using appropriate portfolio performance measures and explain your results. b) Do you think the investments in precious metals can hedge against equity market volatility based on your results?

Data set

Code	Gold	Silver	Platinum	Palladium	Ruthenium	10-year government bond yield (monthly return)	Equity market index
1/30/1998	304.85	6.05	386.50	235.00	39.00	0.004483599	980.28
2/27/1998	297.40	6.37	383.50	233.00	39.00	0.004626285	1049.34
3/31/1998	301.00	6.35	407.00	266.00	39.50	0.004604897	1101.75
4/30/1998	310.70	6.22	403.00	365.00	47.00	0.004608858	1111.75
5/29/1998	293.60	4.96	361.00	285.00	68.00	0.004535151	1090.82
6/30/1998	296.30	5.36	357.25	297.00	55.00	0.004420906	1133.84
7/31/1998	288.85	5.53	377.50	307.50	53.50	0.004469319	1120.67
8/31/1998	288.85	5.53	350.00	272.50	48.50	0.00410201	957.28
9/30/1998	293.85	5.39	350.00	280.00	43.00	0.00360515	1017.01
10/30/1998	292.30	5.06	334.25	275.00	39.50	0.003763608	1098.67
11/30/1998	294.70	4.93	354.00	274.00	40.00	0.003857113	1163.63
12/31/1998	294.70	5.01	361.50	329.00	40.50	0.003792389	1229.23
1/29/1999	285.40	5.24	344.50	335.00	40.50	0.003801262	1279.64
2/26/1999	287.05	5.58	378.00	351.00	40.50	0.00429523	1238.33
3/31/1999	279.45	5.03	361.00	362.00	38.50	0.004263983	1286.37
4/30/1999	286.60	5.44	350.00	332.00	40.00	0.004356183	1335.18
5/31/1999	268.60	4.94	364.00	338.00	39.00	0.004642601	1301.84
6/30/1999	261.00	5.22	349.00	321.00	39.00	0.004715509	1372.71
7/30/1999	255.60	5.45	343.75	337.00	39.00	0.004792313	1328.72
8/31/1999	254.80	5.08	349.00	341.00	39.00	0.004895117	1320.41
9/30/1999	299.00	5.58	393.00	377.00	39.00	0.004778001	1282.71
10/29/1999	299.10	5.29	418.00	395.00	39.00	0.004874897	1362.93
11/30/1999	291.35	5.18	437.00	394.00	40.50	0.004998358	1388.91
12/31/1999	291.35	5.18	445.00	454.00	47.00	0.005209922	1469.25
1/31/2000	283.30	5.26	495.00	484.00	61.00	0.005392803	1394.46
2/29/2000	293.65	5.10	490.00	722.00	82.50	0.005295511	1366.42
3/31/2000	276.75	4.94	482.00	573.00	78.50	0.004883033	1498.58
4/28/2000	275.05	4.94	525.00	600.00	115.00	0.005040316	1452.43
5/31/2000	272.25	4.90	551.00	568.00	135.00	0.005096282	1420.6
6/30/2000	288.15	5.02	588.00	638.00	160.00	0.004885561	1454.6
7/31/2000	276.75	4.95	582.00	822.00	167.50	0.004897328	1430.83
8/31/2000	277.00	4.91	588.00	716.00	167.50	0.004774205	1517.68
9/29/2000	273.65	4.89	569.00	712.00	171.50	0.004707042	1436.51
10/31/2000	264.50	4.74	584.00	758.00	170.00	0.004673956	1429.4
11/30/2000	269.10	4.63	605.00	811.00	160.00	0.004428765	1314.95
12/29/2000	269.10	4.58	611.00	954.00	160.00	0.004157599	1320.28
1/31/2001	264.50	4.79	604.00	1050.00	153.50	0.004198751	1366.01
2/28/2001	266.70	4.43	610.00	839.00	158.00	0.00409731	1239.94
3/30/2001	257.70	4.33	563.00	738.00	152.00	0.004021913	1160.33
4/30/2001	263.15	4.37	594.00	682.00	140.00	0.004341167	1249.46
5/31/2001	267.50	4.43	614.00	653.00	135.00	0.00439661	1255.82
6/29/2001	270.60	4.34	558.00	602.00	135.00	0.004393593	1224.42
7/31/2001	265.90	4.22	476.00	457.00	130.00	0.004105516	1211.23
8/31/2001	273.00	4.20	446.00	453.00	130.00	0.004015215	1133.58
9/28/2001	293.10	4.59	429.00	360.00	118.00	0.003737538	1040.94
10/31/2001	278.75	4.28	423.00	320.00	90.00	0.003489734	1059.78
11/30/2001	275.50	4.14	443.00	347.00	75.00	0.003873327	1139.45
12/31/2001	275.50	4.52	477.00	440.00	73.00	0.004105994	1148.08
1/31/2002	282.30	4.28	455.00	370.00	73.00	0.004098505	1130.2
2/28/2002	296.85	4.44	493.00	377.00	72.50	0.004010989	1106.73
3/29/2002	301.40	4.68	516.00	386.00	74.50	0.004402407	1147.39
4/30/2002	308.20	4.60	536.00	360.00	72.50	0.004152583	1076.92
5/31/2002	326.60	5.05	548.00	348.00	67.00	0.004108861	1067.14
6/28/2002	318.50	4.87	545.00	321.00	67.00	0.003935041	989.81
7/31/2002	304.65	4.66	529.00	322.00	62.00	0.003646712	911.62
8/30/2002	312.80	4.57	564.00	330.00	62.50	0.003363813	916.07
9/30/2002	323.70	4.53	563.00	318.00	59.50	0.002954514	815.28
10/31/2002	316.90	4.48	579.00	311.00	59.50	0.003193877	885.76
11/29/2002	319.05	4.43	592.00	262.00	52.50	0.003446416	936.31
12/31/2002	319.05	4.67	598.00	233.00	46.00	0.003135685	879.82
1/31/2003	367.50	4.87	667.00	256.00	37.00	0.003255248	855.7
2/28/2003	347.45	4.60	681.00	244.00	35.00	0.003018948	841.15
3/31/2003	334.85	4.46	642.00	180.00	35.00	0.003132626	848.18
4/30/2003	336.75	4.61	603.00	154.00	35.00	0.003160399	916.92
5/30/2003	361.40	4.56	642.00	183.00	32.50	0.002739591	963.59
6/30/2003	346.00	4.51	667.00	179.00	32.50	0.002894151	974.5
7/31/2003	354.75	5.08	684.00	178.00	32.50	0.003655919	990.31
8/29/2003	375.60	5.11	707.00	201.50	32.50	0.00358288	1008.01
9/30/2003	388.00	5.12	710.00	209.00	32.50	0.003224125	995.97
10/31/2003	386.25	5.14	753.00	203.00	32.50	0.003513952	1050.71
11/28/2003	398.35	5.35	765.00	188.00	41.00	0.003513791	1058.2
12/31/2003	398.35	5.97	813.00	195.00	41.00	0.003485484	1111.92
1/30/2004	399.75	6.23	837.00	230.00	43.00	0.003383086	1131.13
2/27/2004	395.85	6.58	877.00	229.00	45.00	0.003246081	1144.94
3/31/2004	423.70	7.83	903.00	285.00	70.50	0.003144139	1126.21
4/30/2004	388.50	5.95	798.00	252.00	65.50	0.00367601	1107.3
5/31/2004	393.25	6.17	832.00	246.00	60.50	0.003784395	1120.68
6/30/2004	395.80	5.91	793.00	217.00	60.50	0.003766487	1140.84
7/30/2004	391.40	6.42	818.00	216.00	60.50	0.003654478	1101.72
8/31/2004	407.25	6.74	864.00	213.75	65.50	0.003373611	1104.24
9/30/2004	415.65	6.67	854.00	217.00	66.50	0.003368391	1114.58
10/29/2004	425.55	7.16	835.00	213.00	81.00	0.003296166	1130.2
11/30/2004	453.40	7.76	867.00	210.00	77.50	0.003565733	1173.82
12/31/2004	453.40	6.82	861.00	184.00	77.50	0.003449064	1211.92
1/31/2005	422.15	6.72	869.00	189.00	62.50	0.003382122	1181.27
2/28/2005	435.45	7.35	864.00	182.00	54.50	0.003571742	1203.6
3/31/2005	427.50	7.19	864.00	198.50	60.50	0.003672648	1180.59
4/29/2005	435.70	6.98	867.00	196.00	60.50	0.00343775	1156.85
5/31/2005	414.45	7.13	859.50	185.00	69.50	0.003297613	1191.5
6/30/2005	437.10	7.10	884.00	183.00	75.50	0.003227825	1191.33
7/29/2005	429.00	7.15	898.00	192.00	82.50	0.003500641	1234.18
8/31/2005	433.25	6.74	888.00	182.00	85.50	0.003307819	1220.33
9/30/2005	473.25	7.53	929.00	194.00	85.50	0.003535597	1228.81
10/31/2005	470.75	7.77	938.00	227.00	85.50	0.00372058	1207.01
11/30/2005	495.65	8.21	979.00	258.00	85.50	0.003674649	1249.48
12/30/2005	495.65	8.83	964.00	253.00	87.50	0.003592814	1248.29
1/31/2006	568.75	9.91	1072.00	290.00	89.50	0.003698818	1280.08
2/28/2006	556.00	9.70	1046.00	282.60	99.50	0.00371402	1280.66
3/31/2006	582.00	11.76	1076.00	332.00	164.50	0.003957704	1294.83
4/28/2006	644.00	12.56	1145.00	362.00	169.50	0.004130605	1310.61
5/31/2006	653.00	13.13	1280.00	355.00	180.00	0.004163411	1270.09
6/30/2006	613.50	10.70	1226.00	312.00	175.50	0.00418355	1270.2
7/31/2006	632.50	11.44	1228.00	309.50	170.00	0.004063764	1276.66
8/31/2006	623.50	12.60	1245.00	341.00	170.00	0.003857353	1303.82
9/29/2006	599.25	11.55	1140.00	315.00	185.00	0.003780078	1335.85
10/31/2006	603.75	12.08	1073.00	316.00	215.00	0.00375993	1377.94
11/30/2006	646.70	13.68	1171.00	327.00	340.00	0.00364447	1400.63
12/29/2006	646.70	12.90	1117.00	324.00	520.00	0.003842734	1418.3
1/31/2007	650.50	13.36	1160.00	331.00	790.00	0.003935041	1438.24
2/28/2007	664.20	14.31	1239.00	346.00	880.00	0.00371802	1406.82
3/30/2007	661.75	13.35	1244.00	351.75	775.00	0.003796386	1420.86
4/30/2007	677.00	13.50	1286.00	371.00	655.00	0.003780078	1482.37
5/31/2007	659.10	13.25	1280.00	367.00	615.00	0.003986185	1530.62
6/29/2007	650.50	12.54	1273.00	365.00	525.00	0.004100178	1503.35
7/31/2007	665.50	12.93	1292.00	365.00	385.00	0.003892972	1455.27
8/31/2007	672.00	11.95	1268.00	330.00	465.00	0.003707299	1473.99
9/28/2007	743.00	13.65	1377.00	343.75	495.00	0.003736178	1526.75
10/31/2007	789.50	14.32	1440.00	370.00	540.00	0.003648713	1549.38
11/30/2007	783.50	14.23	1440.00	349.00	450.00	0.003248494	1481.14
12/31/2007	783.50	14.76	1529.00	365.00	405.00	0.003301229	1468.35
1/31/2008	923.25	16.74	1731.00	388.00	390.00	0.002980648	1378.55
2/29/2008	971.50	19.62	2150.00	568.00	400.00	0.002895362	1330.63
3/31/2008	933.50	17.99	2040.00	445.00	400.00	0.002814843	1322.7
4/30/2008	871.00	16.47	1929.00	420.00	365.00	0.003081645	1385.59
5/30/2008	885.75	16.85	2008.00	430.00	325.00	0.003309828	1400.38
6/30/2008	930.25	17.65	2064.00	467.00	285.00	0.003254605	1280
7/31/2008	918.00	17.48	1758.00	382.00	290.00	0.003257258	1267.38
8/29/2008	833.00	13.76	1479.00	302.00	285.00	0.003122963	1282.83
9/30/2008	884.50	12.96	1004.00	199.00	275.00	0.003131901	1166.36
10/31/2008	730.75	9.28	814.00	198.00	215.00	0.003258947	968.75
11/28/2008	814.50	10.12	876.00	187.00	190.00	0.002437878	896.24
12/31/2008	814.50	10.79	898.00	183.50	90.00	0.001856917	903.25
1/30/2009	919.50	12.51	983.00	196.00	75.00	0.002339982	825.88
2/27/2009	952.00	13.21	1059.00	195.00	70.00	0.002501868	735.09
3/31/2009	916.50	13.11	1124.00	215.00	70.00	0.002212299	797.87
4/30/2009	883.25	12.63	1093.00	218.00	80.00	0.002567758	872.81
5/29/2009	975.50	15.52	1175.00	236.00	80.00	0.002842875	919.14
6/30/2009	934.50	13.94	1186.00	249.00	80.00	0.002886724	919.32
7/31/2009	939.00	13.63	1189.00	256.00	80.00	0.002870737	987.48
8/31/2009	955.50	14.54	1244.00	289.00	80.00	0.002790116	1020.62
9/30/2009	995.75	16.45	1287.00	294.00	80.00	0.002713064	1057.08
10/30/2009	1040.00	16.57	1320.00	324.00	80.00	0.002777185	1036.19
11/30/2009	1175.75	18.14	1442.00	360.50	150.00	0.002627689	1095.63
12/31/2009	1175.75	16.99	1461.00	393.00	150.00	0.00314124	1115.1
1/29/2010	1078.50	16.29	1512.00	419.00	165.00	0.002942331	1073.87
2/26/2010	1108.25	16.12	1533.00	430.00	180.00	0.002961693	1104.49
3/31/2010	1115.50	17.50	1645.00	479.00	180.00	0.00313649	1169.43
4/30/2010	1179.25	18.62	1738.00	552.00	230.00	0.002997824	1186.69
5/31/2010	1207.50	18.53	1555.00	471.00	235.00	0.0027036	1089.41
6/30/2010	1244.00	18.74	1532.00	446.00	225.00	0.002414834	1030.71
7/30/2010	1169.00	17.66	1555.00	487.00	190.00	0.002390648	1101.6
8/31/2010	1246.00	18.87	1515.00	487.50	185.00	0.002036778	1049.33
9/30/2010	1307.00	22.07	1662.00	568.00	170.00	0.002063665	1141.2
10/29/2010	1346.75	23.96	1700.00	640.00	165.00	0.00214371	1183.26
11/30/2010	1383.50	27.13	1658.00	697.00	165.00	0.002300664	1180.55
12/31/2010	1383.50	30.63	1755.00	797.00	170.00	0.002715734	1257.64
1/31/2011	1327.00	27.75	1781.00	806.00	170.00	0.00277476	1286.12
2/28/2011	1411.00	33.49	1804.00	790.00	170.00	0.002803046	1327.22
3/31/2011	1439.00	37.87	1773.00	766.00	170.00	0.00283294	1325.83
4/29/2011	1535.50	48.70	1835.00	777.00	170.00	0.002706027	1363.61
5/31/2011	1536.50	38.65	1828.00	777.00	170.00	0.002506003	1345.2
6/30/2011	1505.50	35.02	1722.00	761.00	170.00	0.002593517	1320.64
7/29/2011	1628.50	39.63	1779.00	824.00	170.00	0.002307164	1292.28
8/31/2011	1813.50	41.35	1845.00	783.00	165.00	0.001825722	1218.89
9/30/2011	1620.00	30.45	1511.00	614.00	150.00	0.001592642	1131.42
10/31/2011	1722.00	34.24	1606.00	653.00	140.00	0.001793862	1253.3
11/30/2011	1746.00	31.35	1558.00	620.00	140.00	0.001707212	1246.96
12/30/2011	1746.00	28.18	1354.00	630.00	120.00	0.001549231	1257.6
1/31/2012	1744.00	33.60	1624.00	692.00	100.00	0.001489405	1312.41
2/29/2012	1770.00	37.23	1726.00	722.00	120.00	0.001633576	1365.68
3/30/2012	1662.50	32.43	1640.00	651.00	110.00	0.001829806	1408.47
4/30/2012	1651.25	31.20	1570.00	679.00	105.00	0.001582815	1397.91
5/31/2012	1558.00	28.10	1405.00	611.00	105.00	0.001308048	1310.33
6/29/2012	1598.50	27.08	1428.00	578.00	105.00	0.001371277	1362.16
7/31/2012	1622.00	28.20	1427.00	591.00	105.00	0.001232445	1379.32
8/31/2012	1648.50	30.52	1517.00	623.00	100.00	0.001293261	1406.58
9/28/2012	1776.00	34.65	1668.00	642.00	100.00	0.001353216	1440.67
10/31/2012	1719.00	32.28	1570.00	606.00	100.00	0.001393438	1412.16
11/30/2012	1726.00	34.28	1612.00	685.00	80.00	0.001336794	1416.18
12/31/2012	1726.00	29.95	1527.00	704.00	80.00	0.001446765	1426.19
1/31/2013	1664.75	32.03	1672.00	739.00	75.00	0.001639551	1498.11
2/28/2013	1588.50	28.95	1598.00	744.00	75.00	0.001561519	1514.68
3/29/2013	1598.25	28.64	1576.00	770.00	75.00	0.001529485	1569.19
4/30/2013	1469.00	24.42	1507.00	699.00	80.00	0.001385559	1597.57
5/31/2013	1394.50	22.57	1459.00	744.00	80.00	0.001783403	1630.74
6/28/2013	1192.00	18.86	1317.00	643.00	80.00	0.002042889	1606.28
7/31/2013	1314.50	19.94	1433.00	733.00	77.00	0.002135163	1685.73
8/30/2013	1394.75	23.64	1514.00	727.00	70.50	0.00226141	1632.97
9/30/2013	1326.50	21.68	1411.00	726.00	57.50	0.002154372	1681.55
10/31/2013	1324.00	22.20	1450.00	742.00	54.50	0.002094454	1756.54
11/29/2013	1253.00	19.93	1376.00	724.00	54.50	0.002268563	1805.81
12/31/2013	1253.00	19.50	1357.00	716.00	54.50	0.002471947	1848.36
1/31/2014	1251.00	19.31	1382.00	707.00	57.50	0.002195217	1782.59
2/28/2014	1326.50	21.27	1455.00	746.00	62.50	0.002190987	1859.45
3/31/2014	1291.75	19.97	1418.00	778.00	66.50	0.002243118	1872.34
4/30/2014	1288.50	19.28	1424.00	803.00	69.50	0.002180574	1883.95
5/30/2014	1250.50	19.00	1464.00	836.00	69.50	0.002024065	1923.57
6/30/2014	1315.00	20.87	1480.00	844.00	67.50	0.002072056	1960.23
7/31/2014	1285.25	20.69	1472.00	880.00	65.50	0.002106261	1930.67
8/29/2014	1285.75	19.47	1424.00	898.00	63.50	0.001933881	2003.37
9/30/2014	1216.50	17.11	1300.00	775.00	60.50	0.002065376	1972.29
10/31/2014	1164.25	16.20	1227.00	784.00	55.50	0.001924988	2018.05
11/28/2014	1182.75	15.97	1205.00	809.00	55.50	0.00181208	2067.56
12/31/2014	1182.75	15.97	1206.00	811.00	55.50	0.001791329	2058.9
1/30/2015	1260.25	16.92	1221.00	775.00	53.50	0.001356008	1994.99
2/27/2015	1214.00	16.53	1177.00	808.00	53.50	0.0016524	2104.5
3/31/2015	1187.00	16.60	1129.00	729.00	52.00	0.001591986	2067.89
4/30/2015	1180.25	16.52	1136.00	779.00	48.00	0.001680791	2085.51
5/29/2015	1191.40	16.67	1115.00	783.00	48.00	0.00175161	2107.39
6/30/2015	1171.00	15.70	1078.00	677.00	48.00	0.001936328	2063.11
7/31/2015	1098.40	14.56	979.00	610.00	43.00	0.001804156	2103.84
8/31/2015	1135.00	14.44	1003.00	573.00	40.00	0.00182613	1972.18
9/30/2015	1114.00	14.65	908.00	661.00	40.00	0.001679564	1920.03
10/30/2015	1142.35	15.63	988.00	677.00	40.00	0.001770164	2079.36
11/30/2015	1061.90	14.08	831.00	538.00	40.00	0.001821556	2080.41
12/31/2015	1061.90	13.82	868.00	555.00	40.00	0.001871858	2043.94
1/29/2016	1111.80	14.08	866.00	501.00	40.00	0.001594034	1940.24
2/29/2016	1234.90	14.75	919.00	494.00	40.00	0.001438645	1932.23
3/31/2016	1237.00	15.38	976.00	569.00	40.00	0.001475057	2059.74
4/29/2016	1285.65	17.86	1065.00	628.00	40.00	0.001503505	2065.3
5/31/2016	1212.10	16.06	971.00	540.00	40.00	0.001514651	2096.96
6/30/2016	1320.75	18.36	999.00	589.00	40.00	0.001234254	2098.86
7/29/2016	1342.00	20.04	1143.00	707.00	40.00	0.001206791	2173.6
8/31/2016	1309.25	18.74	1050.00	674.00	40.00	0.001296794	2170.95
9/30/2016	1322.50	19.35	1034.00	722.00	40.00	0.001328418	2168.27
10/31/2016	1272.00	17.76	976.00	612.00	38.00	0.001515389	2126.15
11/30/2016	1178.10	16.67	920.00	770.00	38.00	0.001951745	2198.81
12/30/2016	1178.10	16.24	898.00	670.00	38.00	0.002016403	2238.83
1/31/2017	1212.80	17.29	991.00	756.00	38.00	0.002032622	2278.87
2/28/2017	1255.60	18.28	1029.00	781.00	38.00	0.00194473	2363.64
3/31/2017	1244.85	18.06	940.00	798.00	43.00	0.001974417	2362.72
4/28/2017	1266.45	17.41	946.00	824.00	63.00	0.00188247	2384.2
5/31/2017	1266.20	17.31	947.00	814.00	63.00	0.001812244	2411.8
6/30/2017	1242.25	16.47	922.00	841.00	63.00	0.00189757	2423.41
7/31/2017	1267.55	16.76	938.00	894.00	63.00	0.00188998	2470.3
8/31/2017	1311.75	17.34	986.00	935.00	63.00	0.00175071	2471.65
9/29/2017	1283.10	16.86	920.00	935.00	68.00	0.001917645	2519.36
10/31/2017	1270.15	16.82	915.00	977.00	93.00	0.001957944	2575.26
11/30/2017	1280.20	16.57	940.00	1010.00	163.00	0.001991214	2647.58
12/29/2017	1280.20	16.87	927.00	1056.00	188.00	0.001987627	2673.61
1/31/2018	1345.05	17.23	1003.00	1051.00	193.00	0.002233361	2823.81
2/28/2018	1317.85	16.44	979.00	1041.00	198.00	0.002359959	2713.83
3/30/2018	1323.85	16.28	936.00	970.00	213.00	0.002259459	2640.87
4/30/2018	1313.20	16.38	905.00	963.00	248.00	0.00241524	2648.05
5/31/2018	1305.35	16.55	907.00	986.00	248.00	0.00235192	2705.27
6/29/2018	1250.45	16.03	851.00	953.00	248.00	0.00235192	2718.37
7/31/2018	1220.95	15.43	831.00	928.00	248.00	0.002434471	2816.29
8/31/2018	1202.45	14.66	792.00	979.00	258.00	0.002353544	2901.52
9/28/2018	1187.25	14.31	815.00	1094.00	263.00	0.002518001	2913.98
10/31/2018	1214.95	14.34	834.00	1082.00	263.00	0.002594084	2711.74
11/30/2018	1217.55	14.24	805.00	1205.00	268.00	0.002479408	2760.17
12/31/2018	1279.00	15.47	794.00	1263.00	268.00	0.002212055	2506.85