PerformanceAnalytics R 包的历史 VaR 与我的计算不符
PerformanceAnalytics R package's historic VaR doesn't match my calcs
我计算了一个简单股票投资组合的 历史 VaR （为简单起见，假设只有两只股票有一年的每日历史记录）。然后我使用 PerformanceAnalytics R 包再次完成了它。我的两个结果不匹配。
我是否遗漏了有关如何进行基本 VaR 的内容，或者 PerformanceAnalytics 是否在做一些奇怪的事情？
我的示例代码如下：
library(xts)
# (I'll define "sr" at the end of the question. It's a big xts structure)
weights = c(0.7929511, 0.2070489)
p = 0.95
# How I do it:
m = data.matrix(as.data.frame(sr))
daily_whatif_scenario = tcrossprod(weights, m)[1,]
my_historic_VaR = as.numeric(-quantile(daily_whatif_scenario, 1 - p)[1])
# How PerformanceAnalytics does it:
their_historic_VaR = PerformanceAnalytics::VaR(R = sr, p = p,
method = "historical", portfolio_method = "component", weights = weights)
我的计算结果是 1.325%，但包裹给了我 1.395%。为什么会有这么大的差异？当我在示例中添加更多股票和历史记录时，这些差异只会变得更大。我做错了什么吗？
这是 dput(sr) 的结果：
sr = structure(c(-0.0162, 0.0049, 0.0029, -1e-04, -0.0079, -0.0101,
0.0053, 0.007, -0.0107, 0.001, -0.003, -0.0033, 0.0013, 0.0163,
0.0102, 2e-04, -0.0027, 0.0303, -0.0149, 0.0034, 0.0073, 0.0111,
-0.0057, 0.0022, 0.0266, 0.0038, 0.0062, -0.0063, 0.0078, 0.0022,
0.0091, -0.0074, 0.008, 0.0068, 0.0048, 0.0031, 0.0142, -0.0034,
-0.0089, 0.001, 0.001, -0.0141, 0.0042, 0.0026, -0.017, 0.001,
-0.006, 0.0048, 0.0064, -0.0063, -0.0122, 0.0122, -0.0126, 0.0239,
-0.0236, -9e-04, 0.004, -0.0049, 0.0028, -0.0109, 0.0106, 0.0066,
0.0096, 0.0075, 0.0082, -0.008, 0.047, -6e-04, 5e-04, -0.005,
-0.0084, -0.0074, 0.0078, -0.0029, 0.0071, 5e-04, 0.0118, 0.0068,
-0.0032, 0.0068, -0.0011, -0.0095, 0.0029, -0.0019, -0.0084,
0.0065, -0.014, 0.0049, -0.0042, 0.0071, -0.0097, -0.0038, -0.0049,
0.0045, 0.001, -7e-04, -0.0056, 0.0098, -0.0112, 0.0093, 5e-04,
-6e-04, 0, -0.0013, 0.0026, 0.0199, -8e-04, 0.0023, -0.0038,
-0.0035, -0.0045, -0.0323, -0.0021, -0.0054, -0.0102, 0.0222,
-0.0139, -0.0027, 6e-04, -5e-04, -0.0069, -8e-04, 0.0074, -0.0071,
0.0017, -0.0142, 0.0111, 0.0022, -0.0085, 0.0183, -0.0061, -0.0031,
0.0083, 0.0111, -0.0028, -0.0051, -0.0149, 0.0026, -0.0046, -0.0105,
-0.003, 0.0019, 0.0055, 0.0471, 0.0042, 9e-04, -0.0226, -0.0175,
0.0169, 3e-04, 8e-04, -0.0258, -0.0047, -0.0044, 0.0071, 0.0129,
0.0063, 0.0248, 0.0107, 0.0133, -0.0214, 0.0045, 0.0175, -0.0034,
0.0048, -1e-04, -0.0118, 0.0082, -0.0024, 0.0019, -0.0139, 0.0037,
-0.0018, -0.0166, -0.002, -0.0058, 0.0053, -0.0086, 0.0159, 0.0027,
-0.0097, 0.0186, -0.0099, 0.0362, 0.0034, -0.0044, 0.005, -0.0074,
0.0031, 0.0151, 0, -0.0036, -0.0054, -0.004, -0.0088, 0, 0.015,
-0.0019, 3e-04, 0.0087, -0.0017, 0.0015, 0.0046, -0.0177, 0.0018,
0.0021, -0.0142, 4e-04, -0.005, -0.001, -0.0108, -5e-04, 0.0167,
0, -7e-04, -0.0079, 0.0397, -6e-04, -0.0132, -0.0013, -0.0022,
0.001, -0.0021, 0.0119, -0.0031, 0.0065, 0.001, -0.0014, -0.0054,
8e-04, -0.0021, 0.0103, -0.0016, -0.0014, 0.0169, -4e-04, -0.0067,
0.0249, 0.0018, 0.0047, -0.0117, -0.0015, 0.0133, 0.0144, -3e-04,
-0.0084, -0.0067, 0.0048, -0.0226, 0.001, -0.0079, -1e-04, 0.0062,
0.0037, 0, 7e-04, -0.0046, -0.0045, -7e-04, 0.0097, -0.0066,
-0.0054, -0.0029, -0.0041, -0.0113, 0.0059, -0.0134, -0.0177,
0.0057, -0.0043, -0.0106, -0.0115, -0.0198, 0.0131, 0.0086, -0.008,
0.0286, -0.0042, 6e-04, 0.0151, 0.0071, 0.0058, 0.0056, 0.0165,
0.0143, 0.0092, 0.0023, 0.0168, 0.0068, -0.0033, -0.0296, -5e-04,
0.0191, -0.0106, 0.0062, -0.002, -0.001, 0.0038, 0.0039, 0.001,
-0.01, 0.0059, 0.0036, -0.0063, -0.0082, -0.0034, 0.0039, 0.0184,
0.0055, -0.0084, 0.0093, -0.0104, 0.0289, -0.01, -0.0098, 0.0108,
-0.0068, -0.0056, 0.002, 0.0206, -0.008, 0.0212, 0.0496, 0.0038,
-0.008, 0.0122, 0.0029, -0.0014, -9e-04, -0.0077, -0.016, 0.0064,
0.0012, 0.0056, 0.0039, 0.0176, -0.0125, -0.0088, 0.0075, 0.0049,
-0.0131, -0.004, 0.0052, -0.004, 0.0021, -0.0162, -0.0126, 0.0042,
0.0032, -0.0059, 0.0014, -0.0034, 7e-04, 0.0043, -6e-04, -0.0067,
0.0067, 0.0045, 0.0096, -3e-04, -0.0082, 0.0038, 0.0053, -0.013,
0.0197, -0.0057, 0.0041, -0.0142, 0.0114, -0.0045, -0.0123, -0.0433,
-0.0066, -0.0212, 0.0257, -0.0068, 8e-04, -0.0031, -0.0029, -0.0097,
-0.0074, 0.0065, -0.013, -0.0036, -0.013, -0.002, 0.0032, -0.0087,
0.0054, -0.001, -0.0118, 0.0034, 0.0051, -0.0065, 2e-04, 0.0015,
-3e-04, 0.0043, -0.0168, 8e-04, -0.0033, -0.0094, -0.0017, -4e-04,
0.0024, -3e-04, -0.0087, 0.0073, 0.0176, 0.0014, -0.0121, -0.005,
-0.006, -0.0059, 0.0159, 0.0273, -0.0071, -0.0163, 0.0041, 0.004,
-6e-04, 0.0095, 0.0012, 0.0156, 0.003, 0.0153, -0.0203, -0.0024,
0.0101, -0.0108, 0.0118, -0.0172, -0.0077, -2e-04, 0, 2e-04,
0.0287, -0.0023, 0.0096, 0.0043, -0.0016, -0.0169, 0.0221, 0.0208,
-0.0036, -0.0236, 0.014, 0.0047, 0.0023, 0, -0.0013, -0.0033,
0.0024, -0.0134, 0, 0.0081, -0.0085, -0.006, -0.0014, -0.0184,
-0.0066, 0.0103, -0.0123, -0.0022, 0.0021, 0.0059, -0.0014, -0.0046,
0.0124, -0.009, 0.0079, 0.0096, -0.0019, -0.0025, -0.0024, -0.0063,
-0.0139, -0.0094, 0.0152, -0.0145, 0.0061, 0.0055, 0.016, -0.0105,
0.0061, 0.0053, -0.0058, -0.0272, -0.0345, -0.0021, 0.0322, -0.0092,
-0.0022, 0.0154, -0.0243, 0.0072, 0.0078, 0.0152, -7e-04, -0.0081,
-0.0042, 0.0038, 0.0157, -0.0064, -0.0063, -3e-04, 0.0094, -0.0162,
-0.0045, -0.0122, -0.0062, -0.0081, 0.0112, -1e-04, -0.0059,
9e-04, 0.0043, -0.0081), .indexCLASS = "Date", tclass = c("POSIXct",
"POSIXt"), .indexTZ = "", tzone = "", class = c("xts", "zoo"), index = structure(c(1459728000,
1459814400, 1459900800, 1459987200, 1460073600, 1460332800, 1460419200,
1460505600, 1460592000, 1460678400, 1460937600, 1461024000, 1461110400,
1461196800, 1461283200, 1461542400, 1461628800, 1461715200, 1461801600,
1461888000, 1462147200, 1462233600, 1462320000, 1462406400, 1462492800,
1462752000, 1462838400, 1462924800, 1463011200, 1463097600, 1463356800,
1463443200, 1463529600, 1463616000, 1463702400, 1463961600, 1464048000,
1464134400, 1464220800, 1464307200, 1464566400, 1464652800, 1464739200,
1464825600, 1464912000, 1465171200, 1465257600, 1465344000, 1465430400,
1465516800, 1465776000, 1465862400, 1465948800, 1466035200, 1466121600,
1466380800, 1466467200, 1466553600, 1466640000, 1466726400, 1466985600,
1467072000, 1467158400, 1467244800, 1467331200, 1467590400, 1467676800,
1467763200, 1467849600, 1467936000, 1468195200, 1468281600, 1468368000,
1468454400, 1468540800, 1468800000, 1468886400, 1468972800, 1469059200,
1469145600, 1469404800, 1469491200, 1469577600, 1469664000, 1469750400,
1470009600, 1470096000, 1470182400, 1470268800, 1470355200, 1470614400,
1470700800, 1470787200, 1470873600, 1470960000, 1471219200, 1471305600,
1471392000, 1471478400, 1471564800, 1471824000, 1471910400, 1471996800,
1472083200, 1472169600, 1472428800, 1472515200, 1472601600, 1472688000,
1472774400, 1473033600, 1473120000, 1473206400, 1473292800, 1473379200,
1473638400, 1473724800, 1473811200, 1473897600, 1473984000, 1474243200,
1474329600, 1474416000, 1474502400, 1474588800, 1474848000, 1474934400,
1475020800, 1475107200, 1475193600, 1475452800, 1475539200, 1475625600,
1475712000, 1475798400, 1476057600, 1476144000, 1476230400, 1476316800,
1476403200, 1476662400, 1476748800, 1476835200, 1476921600, 1477008000,
1477267200, 1477353600, 1477440000, 1477526400, 1477612800, 1477872000,
1477958400, 1478044800, 1478131200, 1478217600, 1478476800, 1478563200,
1478649600, 1478736000, 1478822400, 1479081600, 1479168000, 1479254400,
1479340800, 1479427200, 1479686400, 1479772800, 1479859200, 1479945600,
1480032000, 1480291200, 1480377600, 1480464000, 1480550400, 1480636800,
1480896000, 1480982400, 1481068800, 1481155200, 1481241600, 1481500800,
1481587200, 1481673600, 1481760000, 1481846400, 1482105600, 1482192000,
1482278400, 1482364800, 1482451200, 1482710400, 1482796800, 1482883200,
1482969600, 1483056000, 1483315200, 1483401600, 1483488000, 1483574400,
1483660800, 1483920000, 1484006400, 1484092800, 1484179200, 1484265600,
1484524800, 1484611200, 1484697600, 1484784000, 1484870400, 1485129600,
1485216000, 1485302400, 1485388800, 1485475200, 1485734400, 1485820800,
1485907200, 1485993600, 1486080000, 1486339200, 1486425600, 1486512000,
1486598400, 1486684800, 1486944000, 1487030400, 1487116800, 1487203200,
1487289600, 1487548800, 1487635200, 1487721600, 1487808000, 1487894400,
1488153600, 1488240000, 1488326400, 1488412800, 1488499200, 1488758400,
1488844800, 1488931200, 1489017600, 1489104000, 1489363200, 1489449600,
1489536000, 1489622400, 1489708800, 1489968000, 1490054400, 1490140800,
1490227200, 1490313600, 1490572800, 1490659200, 1490745600, 1490832000
), tclass = "Date"), .Dim = c(259L, 2L), .Dimnames = list(NULL,
c("DHR.US", "GIS.US")))
所以我挖出了当使用您指定的参数调用 VaR 时 运行 的代码。请看下面。
当您阅读我的回答时，请注意，这个领域不在我的技能范围内，数学也有点超出我的理解范围，但是看起来您的代码和他们的代码之间的主要区别在于它们对数据进行排序， select alpha 标识的转置叉积。你在哪里使用分位数。出于某种原因，这意味着您 select 相邻数字 - 它看起来基本上是一个舍入误差。请查看以下 excel 您 daily_whatif_scenario 的屏幕截图来说明这一点：
VaR 代码：
VaR.historical.portfolio = function(R,p,w)
{
alpha = .setalphaprob(p)
portret = c();
T = dim(R)[1]
N = dim(R)[2]
for( t in c(1:T) ){
portret = c(portret,sum(w*as.numeric(R[t,])))
}
hVaR = -1* sort(portret)[floor(alpha*T)]
return(hVaR)
}
其中：
.setalphaprob = function (p)
{
if ( p >= 0.51 ) {
# looks like p was a percent like .99
alpha <- 1-p
} else {
alpha = p
}
return (alpha)
}
我计算了一个简单股票投资组合的 历史 VaR （为简单起见，假设只有两只股票有一年的每日历史记录）。然后我使用 PerformanceAnalytics R 包再次完成了它。我的两个结果不匹配。
我是否遗漏了有关如何进行基本 VaR 的内容，或者 PerformanceAnalytics 是否在做一些奇怪的事情？
我的示例代码如下：
library(xts)
# (I'll define "sr" at the end of the question. It's a big xts structure)
weights = c(0.7929511, 0.2070489)
p = 0.95
# How I do it:
m = data.matrix(as.data.frame(sr))
daily_whatif_scenario = tcrossprod(weights, m)[1,]
my_historic_VaR = as.numeric(-quantile(daily_whatif_scenario, 1 - p)[1])
# How PerformanceAnalytics does it:
their_historic_VaR = PerformanceAnalytics::VaR(R = sr, p = p,
method = "historical", portfolio_method = "component", weights = weights)
我的计算结果是 1.325%，但包裹给了我 1.395%。为什么会有这么大的差异？当我在示例中添加更多股票和历史记录时，这些差异只会变得更大。我做错了什么吗？
这是 dput(sr) 的结果：
sr = structure(c(-0.0162, 0.0049, 0.0029, -1e-04, -0.0079, -0.0101,
0.0053, 0.007, -0.0107, 0.001, -0.003, -0.0033, 0.0013, 0.0163,
0.0102, 2e-04, -0.0027, 0.0303, -0.0149, 0.0034, 0.0073, 0.0111,
-0.0057, 0.0022, 0.0266, 0.0038, 0.0062, -0.0063, 0.0078, 0.0022,
0.0091, -0.0074, 0.008, 0.0068, 0.0048, 0.0031, 0.0142, -0.0034,
-0.0089, 0.001, 0.001, -0.0141, 0.0042, 0.0026, -0.017, 0.001,
-0.006, 0.0048, 0.0064, -0.0063, -0.0122, 0.0122, -0.0126, 0.0239,
-0.0236, -9e-04, 0.004, -0.0049, 0.0028, -0.0109, 0.0106, 0.0066,
0.0096, 0.0075, 0.0082, -0.008, 0.047, -6e-04, 5e-04, -0.005,
-0.0084, -0.0074, 0.0078, -0.0029, 0.0071, 5e-04, 0.0118, 0.0068,
-0.0032, 0.0068, -0.0011, -0.0095, 0.0029, -0.0019, -0.0084,
0.0065, -0.014, 0.0049, -0.0042, 0.0071, -0.0097, -0.0038, -0.0049,
0.0045, 0.001, -7e-04, -0.0056, 0.0098, -0.0112, 0.0093, 5e-04,
-6e-04, 0, -0.0013, 0.0026, 0.0199, -8e-04, 0.0023, -0.0038,
-0.0035, -0.0045, -0.0323, -0.0021, -0.0054, -0.0102, 0.0222,
-0.0139, -0.0027, 6e-04, -5e-04, -0.0069, -8e-04, 0.0074, -0.0071,
0.0017, -0.0142, 0.0111, 0.0022, -0.0085, 0.0183, -0.0061, -0.0031,
0.0083, 0.0111, -0.0028, -0.0051, -0.0149, 0.0026, -0.0046, -0.0105,
-0.003, 0.0019, 0.0055, 0.0471, 0.0042, 9e-04, -0.0226, -0.0175,
0.0169, 3e-04, 8e-04, -0.0258, -0.0047, -0.0044, 0.0071, 0.0129,
0.0063, 0.0248, 0.0107, 0.0133, -0.0214, 0.0045, 0.0175, -0.0034,
0.0048, -1e-04, -0.0118, 0.0082, -0.0024, 0.0019, -0.0139, 0.0037,
-0.0018, -0.0166, -0.002, -0.0058, 0.0053, -0.0086, 0.0159, 0.0027,
-0.0097, 0.0186, -0.0099, 0.0362, 0.0034, -0.0044, 0.005, -0.0074,
0.0031, 0.0151, 0, -0.0036, -0.0054, -0.004, -0.0088, 0, 0.015,
-0.0019, 3e-04, 0.0087, -0.0017, 0.0015, 0.0046, -0.0177, 0.0018,
0.0021, -0.0142, 4e-04, -0.005, -0.001, -0.0108, -5e-04, 0.0167,
0, -7e-04, -0.0079, 0.0397, -6e-04, -0.0132, -0.0013, -0.0022,
0.001, -0.0021, 0.0119, -0.0031, 0.0065, 0.001, -0.0014, -0.0054,
8e-04, -0.0021, 0.0103, -0.0016, -0.0014, 0.0169, -4e-04, -0.0067,
0.0249, 0.0018, 0.0047, -0.0117, -0.0015, 0.0133, 0.0144, -3e-04,
-0.0084, -0.0067, 0.0048, -0.0226, 0.001, -0.0079, -1e-04, 0.0062,
0.0037, 0, 7e-04, -0.0046, -0.0045, -7e-04, 0.0097, -0.0066,
-0.0054, -0.0029, -0.0041, -0.0113, 0.0059, -0.0134, -0.0177,
0.0057, -0.0043, -0.0106, -0.0115, -0.0198, 0.0131, 0.0086, -0.008,
0.0286, -0.0042, 6e-04, 0.0151, 0.0071, 0.0058, 0.0056, 0.0165,
0.0143, 0.0092, 0.0023, 0.0168, 0.0068, -0.0033, -0.0296, -5e-04,
0.0191, -0.0106, 0.0062, -0.002, -0.001, 0.0038, 0.0039, 0.001,
-0.01, 0.0059, 0.0036, -0.0063, -0.0082, -0.0034, 0.0039, 0.0184,
0.0055, -0.0084, 0.0093, -0.0104, 0.0289, -0.01, -0.0098, 0.0108,
-0.0068, -0.0056, 0.002, 0.0206, -0.008, 0.0212, 0.0496, 0.0038,
-0.008, 0.0122, 0.0029, -0.0014, -9e-04, -0.0077, -0.016, 0.0064,
0.0012, 0.0056, 0.0039, 0.0176, -0.0125, -0.0088, 0.0075, 0.0049,
-0.0131, -0.004, 0.0052, -0.004, 0.0021, -0.0162, -0.0126, 0.0042,
0.0032, -0.0059, 0.0014, -0.0034, 7e-04, 0.0043, -6e-04, -0.0067,
0.0067, 0.0045, 0.0096, -3e-04, -0.0082, 0.0038, 0.0053, -0.013,
0.0197, -0.0057, 0.0041, -0.0142, 0.0114, -0.0045, -0.0123, -0.0433,
-0.0066, -0.0212, 0.0257, -0.0068, 8e-04, -0.0031, -0.0029, -0.0097,
-0.0074, 0.0065, -0.013, -0.0036, -0.013, -0.002, 0.0032, -0.0087,
0.0054, -0.001, -0.0118, 0.0034, 0.0051, -0.0065, 2e-04, 0.0015,
-3e-04, 0.0043, -0.0168, 8e-04, -0.0033, -0.0094, -0.0017, -4e-04,
0.0024, -3e-04, -0.0087, 0.0073, 0.0176, 0.0014, -0.0121, -0.005,
-0.006, -0.0059, 0.0159, 0.0273, -0.0071, -0.0163, 0.0041, 0.004,
-6e-04, 0.0095, 0.0012, 0.0156, 0.003, 0.0153, -0.0203, -0.0024,
0.0101, -0.0108, 0.0118, -0.0172, -0.0077, -2e-04, 0, 2e-04,
0.0287, -0.0023, 0.0096, 0.0043, -0.0016, -0.0169, 0.0221, 0.0208,
-0.0036, -0.0236, 0.014, 0.0047, 0.0023, 0, -0.0013, -0.0033,
0.0024, -0.0134, 0, 0.0081, -0.0085, -0.006, -0.0014, -0.0184,
-0.0066, 0.0103, -0.0123, -0.0022, 0.0021, 0.0059, -0.0014, -0.0046,
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所以我挖出了当使用您指定的参数调用 VaR 时 运行 的代码。请看下面。
当您阅读我的回答时，请注意，这个领域不在我的技能范围内，数学也有点超出我的理解范围，但是看起来您的代码和他们的代码之间的主要区别在于它们对数据进行排序， select alpha 标识的转置叉积。你在哪里使用分位数。出于某种原因，这意味着您 select 相邻数字 - 它看起来基本上是一个舍入误差。请查看以下 excel 您 daily_whatif_scenario 的屏幕截图来说明这一点：
VaR 代码：
VaR.historical.portfolio = function(R,p,w)
{
alpha = .setalphaprob(p)
portret = c();
T = dim(R)[1]
N = dim(R)[2]
for( t in c(1:T) ){
portret = c(portret,sum(w*as.numeric(R[t,])))
}
hVaR = -1* sort(portret)[floor(alpha*T)]
return(hVaR)
}
其中：
.setalphaprob = function (p)
{
if ( p >= 0.51 ) {
# looks like p was a percent like .99
alpha <- 1-p
} else {
alpha = p
}
return (alpha)
}