| Kontak | \(\downarrow\) |
| naftaligunawan@gmail.com | |
| https://www.instagram.com/nbrigittag/ | |
| RPubs | https://rpubs.com/naftalibrigitta/ |
| Nama | Naftali Brigitta Gunawan |
| NIM | 20214920002 |
Lab Exercise 1
Question
Calculate Value at Risk using case example above! Write down your complete answer in your Rpubs and share the link at google clasroom.
Answer
- Identify Portfolio Assets
Let’s assume we have a portfolio consisting of three assets: stocks (ST), bonds (BD), and commodities (CM)
- Collect Historical Data
Gather historical data on the returns of each asset over the desired time horizon. For demonstration purposes, we’ll use simulated data.
library(quantmod)
# Define a list of ticker symbols for the datasets you want to fetch
symbols <- c("AAPL", # stock market
"GOOG", # stock market
"MSFT", # stock market
"^TNX", # bond
"GLD") # commodity
# Set the start and end dates for historical data retrieval
start_date <- "2023-01-01"
end_date <- Sys.Date() # Current date
# Fetch historical price data
getSymbols(symbols, src = "yahoo", from = start_date, to = end_date)## [1] "AAPL" "GOOG" "MSFT" "TNX" "GLD"# Extract adjusted closing prices for each asset
prices <- merge(Ad(AAPL), Ad(MSFT), Ad(GOOG), Ad(TNX),Ad(GLD))
# rename column names
colnames(prices) <- symbols
# Interpolate missing values
prices <- na.approx(prices)
# print the result
head(prices)## AAPL GOOG MSFT ^TNX GLD
## 2023-01-03 124.2163 237.0360 89.70 3.793 171.06
## 2023-01-04 125.4975 226.6673 88.71 3.709 172.67
## 2023-01-05 124.1666 219.9494 86.77 3.720 170.52
## 2023-01-06 128.7352 222.5415 88.16 3.569 173.71
## 2023-01-09 129.2616 224.7083 88.80 3.517 174.10
## 2023-01-10 129.8376 226.4199 89.24 3.621 174.74- Calculate Daily Return
# Calculate daily returns for each asset
asset_returns <- na.omit(ROC(prices, type = "discrete"))
# Display the first few rows of the returns data
asset_returns## AAPL GOOG MSFT ^TNX
## 2023-01-04 1.031418e-02 -4.374320e-02 -1.103677e-02 -0.0221460249
## 2023-01-05 -1.060464e-02 -2.963783e-02 -2.186904e-02 0.0029657368
## 2023-01-06 3.679413e-02 1.178527e-02 1.601944e-02 -0.0405914037
## 2023-01-09 4.088876e-03 9.736445e-03 7.259521e-03 -0.0145699203
## 2023-01-10 4.456228e-03 7.617094e-03 4.954896e-03 0.0295706832
## 2023-01-11 2.111249e-02 3.023812e-02 3.384138e-02 -0.0185032173
## 2023-01-12 -5.992850e-04 1.162157e-02 -3.793610e-03 -0.0295441818
## 2023-01-13 1.011910e-02 3.018750e-03 9.683379e-03 0.0179762361
## 2023-01-16 6.567262e-03 3.511318e-03 -5.172409e-03 0.0051267805
## 2023-01-17 2.174805e-03 1.166344e-03 -1.733101e-03 0.0017002102
## 2023-01-18 -5.370047e-03 -1.888912e-02 -4.123317e-03 -0.0452616922
## 2023-01-19 4.438314e-04 -1.645402e-02 2.320772e-02 0.0065185406
## 2023-01-20 1.922075e-02 3.574352e-02 5.718235e-02 0.0256108011
## 2023-01-23 2.350025e-02 9.824352e-03 1.943997e-02 0.0117681195
## 2023-01-24 1.006297e-02 -2.226028e-03 -1.976089e-02 -0.0158865228
## 2023-01-25 -4.700506e-03 -5.908156e-03 -2.499744e-02 -0.0020179325
## 2023-01-26 1.480330e-02 3.071358e-02 2.512147e-02 0.0089544016
## 2023-01-27 1.368428e-02 6.451976e-04 1.563126e-02 0.0071571305
## 2023-01-30 -2.007804e-02 -2.196160e-02 -2.740544e-02 0.0093803956
## 2023-01-31 9.020938e-03 2.101270e-02 1.960190e-02 -0.0061954586
## 2023-02-01 7.900640e-03 1.993462e-02 1.562028e-02 -0.0374043547
## 2023-02-02 3.706273e-02 4.688426e-02 7.266098e-02 -0.0002944262
## 2023-02-03 2.439981e-02 -2.362052e-02 -3.290443e-02 0.0400471614
## 2023-02-06 -1.792884e-02 -6.115892e-03 -1.663182e-02 0.0288788211
## 2023-02-07 1.924472e-02 4.202225e-02 4.416739e-02 0.0110071440
## 2023-02-08 -1.765276e-02 -3.102034e-03 -7.441689e-02 -0.0057158161
## 2023-02-09 -6.911624e-03 -1.165980e-02 -4.540001e-02 0.0082124200
## 2023-02-10 2.456332e-03 -1.972603e-03 -6.285339e-03 0.0165625492
## 2023-02-13 1.880680e-02 3.124278e-02 1.475853e-03 -0.0072115253
## 2023-02-14 -4.225070e-03 3.133055e-03 -5.263479e-04 0.0118374792
## 2023-02-15 1.390344e-02 -7.993186e-03 2.264351e-02 0.0127625893
## 2023-02-16 -1.042935e-02 -2.662250e-02 -1.359423e-02 0.0089262063
## 2023-02-17 -7.546665e-03 -1.560168e-02 -1.242433e-02 -0.0039031659
## 2023-02-20 -2.000981e-02 -1.566498e-02 -2.013950e-02 0.0248824163
## 2023-02-21 -6.806124e-03 -5.304760e-03 -6.851144e-03 0.0080927711
## 2023-02-22 2.895924e-03 -4.591035e-03 -2.715915e-03 -0.0080909803
## 2023-02-23 3.290563e-03 1.296176e-02 -7.952106e-03 -0.0112159438
## 2023-02-24 -1.800527e-02 -2.178436e-02 -1.888658e-02 0.0180458711
## 2023-02-27 8.247402e-03 3.771808e-03 8.393956e-03 -0.0068371616
## 2023-02-28 -3.447716e-03 -2.958116e-03 2.219807e-03 -0.0015298424
## 2023-03-01 -1.424599e-02 -1.262931e-02 2.325571e-03 0.0199183021
## 2023-03-02 4.129227e-03 1.965322e-02 1.988725e-02 0.0197796688
## 2023-03-03 3.508993e-02 1.664612e-02 1.852453e-02 -0.0267615931
## 2023-03-06 1.853962e-02 6.188922e-03 1.659227e-02 0.0047931517
## 2023-03-07 -1.449658e-02 -1.058891e-02 -1.475208e-02 -0.0020085703
## 2023-03-08 8.377225e-03 -1.770600e-03 5.097200e-03 0.0002516141
## 2023-03-09 -1.491466e-02 -5.439468e-03 -2.102481e-02 -0.0128269913
## 2023-03-10 -1.387874e-02 -1.478292e-02 -1.780705e-02 -0.0585987317
## 2023-03-13 1.326605e-02 2.144097e-02 7.142089e-03 -0.0487144334
## 2023-03-14 1.408902e-02 2.705569e-02 2.825656e-02 0.0349928600
## 2023-03-15 2.621583e-03 1.783046e-02 2.440322e-02 -0.0401319153
## 2023-03-16 1.869395e-02 4.053665e-02 4.681509e-02 0.0266322830
## 2023-03-17 -5.453978e-03 1.169431e-02 1.375284e-02 -0.0529986207
## 2023-03-20 1.548394e-02 -2.576674e-02 -5.172738e-03 0.0253313597
## 2023-03-21 1.194404e-02 5.693721e-03 3.835962e-02 0.0359092220
## 2023-03-22 -9.103401e-03 -5.442229e-03 -1.530608e-02 -0.0293954376
## 2023-03-23 6.969441e-03 1.972154e-02 1.957399e-02 -0.0268571717
## 2023-03-24 8.305522e-03 1.048048e-02 -1.882219e-03 -0.0076335247
## 2023-03-27 -1.229334e-02 -1.493386e-02 -2.828588e-02 0.0437869813
## 2023-03-28 -3.980243e-03 -4.160888e-03 -1.649522e-02 0.0102040175
## 2023-03-29 1.979080e-02 1.918388e-02 5.327554e-03 0.0005611935
## 2023-03-30 9.889809e-03 1.261982e-02 -5.691873e-03 -0.0042063563
## 2023-03-31 1.564419e-02 1.496201e-02 2.645085e-02 -0.0160518610
## 2023-04-03 7.701655e-03 -3.711269e-03 8.750035e-03 -0.0183170842
## 2023-04-04 -3.249542e-03 -1.741769e-04 2.001707e-03 -0.0271137527
## 2023-04-05 -1.129035e-02 -9.889209e-03 -1.617255e-03 -0.0149835043
## 2023-04-06 5.495919e-03 2.553280e-02 3.763701e-02 0.0003042793
## 2023-04-07 -3.993087e-03 -1.894699e-03 -4.476594e-03 0.0096563147
## 2023-04-10 -1.202729e-02 -5.694886e-03 -1.349017e-02 0.0286918862
## 2023-04-11 -7.591159e-03 -2.266845e-02 -7.760582e-03 0.0055637053
## 2023-04-12 -4.353173e-03 2.333576e-03 -8.480979e-03 -0.0037856760
## 2023-04-13 3.410361e-02 2.239928e-02 2.822658e-02 0.0090616483
## 2023-04-14 -2.114054e-03 -1.276560e-02 1.173858e-02 0.0202781500
## 2023-04-17 1.210802e-04 9.296221e-03 -2.777271e-02 0.0195911426
## 2023-04-18 7.504674e-03 -1.488969e-03 -1.221571e-02 -0.0052910200
## 2023-04-19 6.968302e-03 2.775174e-04 -9.513518e-04 0.0083986481
## 2023-04-20 -5.846274e-03 -8.112438e-03 8.379403e-03 -0.0158245202
## 2023-04-21 -9.780931e-03 -1.223151e-03 9.444888e-05 0.0070521457
## 2023-04-24 1.878533e-03 -1.396298e-02 8.214475e-03 -0.0154061147
## 2023-04-25 -9.435734e-03 -2.253601e-02 -2.032214e-02 -0.0338549624
## 2023-04-26 -6.107244e-05 7.243483e-02 -1.529525e-03 0.0106007109
## 2023-04-27 2.839527e-02 3.202764e-02 3.752998e-02 0.0279720853
## 2023-04-28 7.541045e-03 7.971753e-03 -1.384161e-03 -0.0215420100
## 2023-05-01 -5.303267e-04 -5.532860e-03 -4.712642e-03 0.0353418257
## 2023-05-02 -6.191453e-03 -4.908830e-04 -1.606161e-02 -0.0377728022
## 2023-05-03 -6.467310e-03 -3.307003e-03 1.320998e-03 -0.0104680942
## 2023-05-04 -9.913393e-03 3.317976e-03 -8.575232e-03 -0.0152806477
## 2023-05-05 4.692693e-02 1.715721e-02 9.552298e-03 0.0283497543
## 2023-05-08 -4.033694e-04 -6.438262e-03 1.906512e-02 0.0217643085
## 2023-05-09 -9.971153e-03 -5.345756e-03 -2.771576e-03 0.0000000000
## 2023-05-10 1.042095e-02 1.729635e-02 4.020749e-02 -0.0232888439
## 2023-05-11 1.094569e-03 -7.044209e-03 4.114716e-02 -0.0122127997
## 2023-05-12 -5.417510e-03 -3.676073e-03 8.725378e-03 0.0194289029
## 2023-05-15 -2.897277e-03 1.585953e-03 -8.141105e-03 0.0129944664
## 2023-05-16 0.000000e+00 7.367587e-03 2.676126e-02 0.0116876080
## 2023-05-17 3.603141e-03 9.451596e-03 1.157471e-02 0.0090166426
## 2023-05-18 1.366614e-02 1.439492e-02 1.679283e-02 0.0187098326
## 2023-05-19 6.283390e-04 -5.652086e-04 -2.185854e-03 0.0120613789
## 2023-05-22 -5.480696e-03 8.921440e-03 2.125763e-02 0.0073131607
## 2023-05-23 -1.515495e-02 -1.843203e-02 -2.049735e-02 -0.0056467186
## 2023-05-24 1.632002e-03 -4.472601e-03 -1.338309e-02 0.0056787851
## 2023-05-25 6.692277e-03 3.845799e-02 2.227885e-02 0.0255444441
## 2023-05-26 1.410488e-02 2.138552e-02 8.685178e-03 -0.0010487542
## 2023-05-29 7.994625e-03 -3.785071e-03 -4.723756e-03 -0.0216535230
## 2023-05-30 2.643739e-03 -1.266484e-03 -1.582059e-03 -0.0073775918
## 2023-05-31 -2.820156e-04 -8.514153e-03 -1.018932e-02 -0.0170270170
## 2023-06-01 1.602256e-02 1.275904e-02 8.105698e-03 -0.0079736165
## 2023-06-02 4.775453e-03 8.479358e-03 6.914856e-03 0.0230044190
## 2023-06-05 -7.571139e-03 1.610014e-03 1.117938e-02 0.0005418839
## 2023-06-06 -2.060283e-03 -6.727354e-03 1.010824e-02 0.0016246421
## 2023-06-07 -7.756372e-03 -3.086792e-02 -3.885545e-02 0.0229791946
## 2023-06-08 1.546507e-02 5.813505e-03 -2.196228e-03 -0.0184989257
## 2023-06-09 2.159869e-03 4.703965e-03 1.630428e-03 0.0083467687
## 2023-06-12 1.563879e-02 1.548396e-02 1.204522e-02 0.0053405127
## 2023-06-13 -2.611714e-03 7.352681e-03 6.433601e-04 0.0196546825
## 2023-06-14 3.491349e-03 9.123767e-03 -4.018569e-04 -0.0112008291
## 2023-06-15 1.119869e-02 3.189661e-02 1.133626e-02 -0.0179136138
## 2023-06-16 -5.859879e-03 -1.657577e-02 -1.375311e-02 0.0109978886
## 2023-06-19 3.650203e-04 -9.376888e-03 -1.269541e-03 -0.0079596633
## 2023-06-20 1.216290e-04 -3.155215e-03 -4.237184e-04 -0.0026745093
## 2023-06-21 -5.675359e-03 -1.328200e-02 -2.091236e-02 -0.0016090217
## 2023-06-22 1.652535e-02 1.843749e-02 2.152400e-02 0.0204136380
## 2023-06-23 -1.711310e-03 -1.380588e-02 -6.862082e-03 -0.0157936147
## 2023-06-26 -7.552927e-03 -1.916302e-02 -3.194603e-02 -0.0053490186
## 2023-06-27 1.505900e-02 1.816802e-02 -6.717122e-04 0.0131755270
## 2023-06-28 6.327762e-03 3.825756e-03 1.739349e-02 -0.0153927418
## 2023-06-29 1.796598e-03 -2.382030e-03 -8.837130e-03 0.0388140302
## 2023-06-30 2.310252e-02 1.638562e-02 7.999326e-03 -0.0090814958
## 2023-07-03 -7.784622e-03 -7.488164e-03 -3.389300e-03 0.0102121064
## 2023-07-04 -2.935699e-03 2.366676e-04 8.584936e-03 0.0112752582
## 2023-07-05 -2.944343e-03 2.366116e-04 8.511862e-03 0.0111495442
## 2023-07-06 2.508711e-03 9.226713e-03 -1.386281e-02 0.0243345901
## 2023-07-07 -5.891296e-03 -1.186745e-02 -6.532712e-03 0.0022272461
## 2023-07-10 -1.085581e-02 -1.598366e-02 -2.721822e-02 -0.0108642338
## 2023-07-11 -2.809994e-03 1.928858e-03 7.187442e-03 -0.0064902702
## 2023-07-12 8.985523e-03 1.422685e-02 1.622635e-02 -0.0298994868
## 2023-07-13 4.057444e-03 1.619210e-02 4.355458e-02 -0.0259000625
## 2023-07-14 7.873383e-04 7.529281e-03 6.969439e-03 0.0154214541
## 2023-07-17 1.730557e-02 1.419442e-03 -5.091483e-03 -0.0057606898
## 2023-07-18 -1.340328e-03 3.979976e-02 -7.836205e-03 -0.0021068994
## 2023-07-19 7.071686e-03 -1.226739e-02 -1.047714e-02 -0.0124043101
## 2023-07-20 -1.009730e-02 -2.312150e-02 -2.647011e-02 0.0299305146
## 2023-07-21 -6.161647e-03 -8.937142e-03 6.525548e-03 -0.0044110529
## 2023-07-24 4.219961e-03 3.897876e-03 1.304962e-02 0.0052124628
## 2023-07-25 4.513695e-03 1.700912e-02 7.466391e-03 0.0142597425
## 2023-07-26 4.544919e-03 -3.763746e-02 5.594920e-02 -0.0155930141
## 2023-07-27 -6.580968e-03 -2.087203e-02 1.619555e-03 0.0418073255
## 2023-07-28 1.350799e-02 2.313124e-02 2.417802e-02 -0.0107178420
## 2023-07-31 3.165973e-03 -7.240582e-03 7.518691e-04 -0.0025195239
## 2023-08-01 -4.275921e-03 1.250264e-03 -9.165361e-03 0.0232381927
## 2023-08-02 -1.549001e-02 -2.628291e-02 -2.464175e-02 0.0066650085
## 2023-08-03 -7.321610e-03 -2.564817e-03 1.010610e-03 0.0272192396
## 2023-08-04 -4.802001e-02 3.428455e-03 -1.786216e-03 -0.0307949828
## 2023-08-07 -1.725373e-02 7.108571e-03 2.645098e-02 0.0044335286
## 2023-08-08 5.311602e-03 -1.229897e-02 -7.579665e-04 -0.0127513597
## 2023-08-09 -8.954230e-03 -1.171598e-02 -1.281859e-02 -0.0034773817
## 2023-08-10 -1.234791e-03 2.172398e-03 4.611050e-04 0.0169491123
## 2023-08-11 3.375923e-04 -5.945578e-03 -3.072617e-04 0.0215687008
## 2023-08-14 9.393292e-03 9.438951e-03 1.275258e-02 0.0038387220
## 2023-08-15 -1.120040e-02 -6.727600e-03 -1.183340e-02 0.0088432551
## 2023-08-16 -4.959109e-03 -2.428527e-03 -8.904611e-03 0.0087656244
## 2023-08-17 -1.455509e-02 -1.098615e-02 1.045625e-02 0.0117426472
## 2023-08-18 2.816134e-03 -1.262355e-03 -1.801323e-02 -0.0132312347
## 2023-08-21 7.736693e-03 1.706261e-02 6.400687e-03 0.0214067470
## 2023-08-22 7.904979e-03 1.801920e-03 5.894748e-03 -0.0032243065
## 2023-08-23 2.194887e-02 1.407933e-02 2.714168e-02 -0.0300369945
## 2023-08-24 -2.617045e-02 -2.149846e-02 -2.094444e-02 0.0088137636
## 2023-08-25 1.264316e-02 9.407112e-03 2.070267e-03 0.0009444415
## 2023-08-28 8.846101e-03 2.229268e-03 8.416794e-03 -0.0063694153
## 2023-08-29 2.181016e-02 1.455048e-02 2.807506e-02 -0.0213674449
## 2023-08-30 1.917234e-02 1.157027e-03 1.062800e-02 -0.0009704480
## 2023-08-31 1.172347e-03 -3.132559e-03 3.067359e-03 -0.0060709313
## 2023-09-01 8.463339e-03 2.745805e-03 -4.004390e-03 0.0195455473
## 2023-09-04 9.500730e-04 1.115889e-02 -4.934010e-04 0.0170740960
## 2023-09-05 3.163904e-04 3.678582e-03 -1.645482e-04 0.0055958217
## 2023-09-06 -3.579339e-02 -2.008543e-03 -9.801855e-03 0.0051546006
## 2023-09-07 -2.924936e-02 -8.922174e-03 6.131357e-03 -0.0069929448
## 2023-09-08 3.491765e-03 1.321564e-02 7.342144e-03 -0.0004695614
## 2023-09-11 6.622576e-03 1.097920e-02 3.935922e-03 0.0070456107
## 2023-09-12 -1.706057e-02 -1.825771e-02 -1.212428e-02 -0.0055970539
## 2023-09-13 -1.185482e-02 1.293074e-02 1.050924e-02 -0.0035177924
## 2023-09-14 8.782456e-03 7.855745e-03 1.083640e-02 0.0091786382
## 2023-09-15 -4.153912e-03 -2.503691e-02 -4.964403e-03 0.0079290856
## 2023-09-18 1.691337e-02 -3.512822e-03 4.772261e-03 -0.0006941831
## 2023-09-19 6.180817e-03 -1.245981e-03 -9.355561e-04 0.0106506150
## 2023-09-20 -1.999222e-02 -2.397695e-02 -3.054099e-02 -0.0036654742
## 2023-09-21 -8.889437e-03 -3.865682e-03 -2.399878e-02 0.0301218769
## 2023-09-22 4.944600e-03 -7.886489e-03 -8.373981e-04 -0.0093749591
## 2023-09-25 7.380319e-03 1.671884e-03 7.009510e-03 0.0234338914
## 2023-09-26 -2.339850e-02 -1.700575e-02 -2.057957e-02 0.0035227370
## 2023-09-27 -8.897459e-03 2.082318e-03 1.552731e-02 0.0149187886
## 2023-09-28 1.525620e-03 2.717569e-03 1.270347e-02 -0.0062688729
## 2023-09-29 3.046502e-03 6.727353e-03 -9.614653e-03 -0.0052208325
## 2023-10-02 1.483544e-02 1.916076e-02 2.518007e-02 0.0240542608
## 2023-10-03 -7.769821e-03 -2.613415e-02 -1.383439e-02 0.0254110518
## 2023-10-04 7.308708e-03 1.777330e-02 2.228058e-02 -0.0139525014
## 2023-10-05 7.197977e-03 1.254027e-03 -2.054735e-03 -0.0038015048
## 2023-10-06 1.475042e-02 2.473707e-02 2.014847e-02 0.0142039246
## 2023-10-09 8.451219e-03 7.822466e-03 5.550381e-03 0.0027173937
## 2023-10-10 -3.352158e-03 -4.335605e-03 -2.150560e-03 -0.0296017769
## 2023-10-11 7.903981e-03 1.227196e-02 1.795977e-02 -0.0128894558
## 2023-10-12 5.061231e-03 -3.790478e-03 -9.950626e-03 0.0254624828
## 2023-10-13 -1.029270e-02 -1.035748e-02 -1.218898e-02 -0.0176145391
## 2023-10-16 -7.269835e-04 1.498179e-02 1.378268e-02 0.0179303744
## 2023-10-17 -8.784675e-03 -1.743541e-03 3.558972e-03 0.0286503039
## 2023-10-18 -7.394869e-03 -5.872482e-03 -1.212857e-02 0.0117597858
## 2023-10-19 -2.160950e-03 3.665451e-03 -2.153956e-03 0.0171288976
## 2023-10-20 -1.470427e-02 -1.403469e-02 -1.611736e-02 -0.0128308201
## 2023-10-23 6.941263e-04 8.112035e-03 8.483168e-03 -0.0174654690
## 2023-10-24 2.543335e-03 3.674244e-03 1.609863e-02 0.0004134626
## 2023-10-25 -1.349167e-02 3.067806e-02 -9.598913e-02 0.0233470894
## 2023-10-26 -2.460555e-02 -3.751428e-02 -2.549930e-02 -0.0218050226
## 2023-10-27 7.969297e-03 5.855601e-03 -3.240515e-04 0.0000000000
## 2023-10-30 1.230528e-02 2.274032e-02 1.904375e-02 0.0061919940
## 2023-10-31 2.818824e-03 2.371704e-03 -3.578505e-03 0.0000000000
## 2023-11-01 1.873862e-02 2.354268e-02 1.811649e-02 -0.0176410186
## 2023-11-02 2.069323e-02 6.501588e-03 7.917239e-03 -0.0250573992
## 2023-11-03 -5.181137e-03 1.286166e-02 1.392124e-02 -0.0237738397
## 2023-11-06 1.460522e-02 1.057266e-02 8.284129e-03 0.0228170447
## 2023-11-07 1.445072e-02 1.121925e-02 7.227059e-03 -0.0195195360
## 2023-11-08 5.884941e-03 7.405748e-03 6.495473e-03 -0.0105010577
## 2023-11-09 -2.624541e-03 -6.910828e-03 -1.178142e-02 0.0236569437
## 2023-11-10 2.322007e-02 2.489676e-02 1.799677e-02 -0.0004320371
## 2023-11-13 -8.583612e-03 -8.088346e-03 -3.132912e-03 0.0008643447
## 2023-11-14 1.428567e-02 9.790458e-03 1.339414e-02 -0.0412348847
## 2023-11-15 3.040899e-03 4.060870e-04 7.014784e-03 0.0211663731
## 2023-11-16 9.042218e-03 1.758326e-02 1.701123e-02 -0.0198455742
## 2023-11-17 -1.055006e-04 -1.680095e-02 -1.268922e-02 -0.0008999295
## 2023-11-20 9.278267e-03 2.052183e-02 7.156388e-03 -0.0042783277
## 2023-11-21 -4.230829e-03 -1.157801e-02 5.075384e-03 -0.0009045025
## 2023-11-22 3.514465e-03 1.281261e-02 1.009962e-02 -0.0004527686
## 2023-11-23 -3.502156e-03 -5.558102e-04 -6.427664e-03 0.0063406062
## 2023-11-24 -3.514465e-03 -5.561193e-04 -6.469246e-03 0.0063006562
## 2023-11-27 -9.475625e-04 3.126418e-03 -1.229910e-03 -0.0185599689
## 2023-11-28 3.214078e-03 1.080278e-02 4.128881e-03 -0.0120756377
## 2023-11-29 -5.409660e-03 -1.006018e-02 -1.601501e-02 -0.0149907882
## 2023-11-30 3.062752e-03 1.584183e-04 -1.818179e-02 0.0189651908
## 2023-12-01 6.791366e-03 -1.161225e-02 -4.480218e-03 -0.0289522972
## 2023-12-04 -9.464627e-03 -1.433871e-02 -2.017703e-02 0.0146711493
## 2023-12-05 2.106324e-02 9.156301e-03 1.347313e-02 -0.0272854711
## 2023-12-06 -5.687048e-03 -9.986045e-03 -7.251354e-03 -0.0119875787
## 2023-12-07 1.013932e-02 5.829788e-03 5.341250e-02 0.0019413672
## 2023-12-08 7.412319e-03 8.842191e-03 -1.307329e-02 0.0280938952
## 2023-12-11 -1.292731e-02 -7.829489e-03 -1.419791e-02 -0.0014134375
## 2023-12-12 7.920130e-03 8.295250e-03 -7.869321e-03 -0.0077848534
## 2023-12-13 1.669145e-02 -2.678636e-05 2.469334e-03 -0.0411316845
## 2023-12-14 7.577387e-04 -2.254451e-02 -5.747587e-03 -0.0255392824
## 2023-12-15 -2.725732e-03 1.311734e-02 4.804800e-03 -0.0005089296
## 2023-12-18 -8.503379e-03 5.178853e-03 2.502993e-02 0.0066191505
## 2023-12-19 5.360221e-03 1.637041e-03 6.633163e-03 -0.0080930867
## 2023-12-20 -1.071394e-02 -7.072912e-03 1.129614e-02 -0.0114736968
## 2023-12-21 -7.699904e-04 7.878777e-03 1.532292e-02 0.0043848232
## 2023-12-22 -5.547434e-03 2.784106e-03 6.487998e-03 0.0017976295
## 2023-12-25 -2.130690e-03 1.602038e-04 5.255366e-04 -0.0028838961
## 2023-12-26 -7.117464e-04 5.339272e-05 1.750868e-04 -0.0009640790
## 2023-12-27 5.179017e-04 -1.574726e-03 -9.662546e-03 -0.0249613705
## 2023-12-28 2.226283e-03 3.234599e-03 -1.131248e-03 0.0160992003
## 2023-12-29 -5.424106e-03 2.025178e-03 -2.477393e-03 0.0041558527
## 2024-01-01 -2.684000e-02 -1.031141e-02 -7.290828e-03 0.0155199489
## 2024-01-02 -9.193417e-03 -3.472948e-03 -2.448125e-03 0.0050942538
## 2024-01-03 -7.487533e-03 -7.280155e-04 5.732323e-03 -0.0098834347
## 2024-01-04 -1.270015e-02 -7.177551e-03 -1.652898e-02 0.0214998390
## 2024-01-05 -4.013031e-03 -5.163530e-04 -4.708736e-03 0.0127787223
## 2024-01-08 2.417487e-02 1.887150e-02 2.285464e-02 -0.0098960821
## 2024-01-09 -2.263415e-03 2.935820e-03 1.444531e-02 0.0042479258
## 2024-01-10 5.671375e-03 1.857408e-02 8.698131e-03 0.0027370381
## 2024-01-11 -3.222475e-03 4.859397e-03 -9.040673e-04 -0.0131514166
## 2024-01-12 1.778087e-03 9.983632e-03 3.967476e-03 -0.0067890245
## 2024-01-15 -9.237833e-03 3.475141e-03 -8.319658e-04 0.0220253042
## 2024-01-16 -3.107989e-03 1.154369e-03 -2.775528e-04 0.0071835482
## 2024-01-17 -5.173459e-03 -2.049862e-03 -8.259317e-03 0.0098376690
## 2024-01-18 3.257068e-02 1.129740e-02 1.469666e-02 0.0092547753
## 2024-01-19 1.553299e-02 1.218683e-02 2.055311e-02 0.0004825905
## 2024-01-22 1.216327e-02 -5.418073e-03 -1.757076e-03 -0.0125422207
## 2024-01-23 6.653281e-03 6.027594e-03 6.566826e-03 0.0117245572
## 2024-01-24 -3.483988e-03 9.175193e-03 1.123227e-02 0.0086913987
## 2024-01-25 -1.696633e-03 5.738324e-03 2.188223e-02 -0.0110100536
## 2024-01-26 -9.012733e-03 -2.321728e-03 9.762685e-04 0.0067763500
## 2024-01-29 -3.585889e-03 1.433413e-02 6.827512e-03 -0.0165864831
## 2024-01-30 -1.924584e-02 -2.757944e-03 -1.156028e-02 -0.0078220641
## 2024-01-31 -1.935758e-02 -2.694635e-02 -7.350539e-02 -0.0226656830
## 2024-02-01 1.334064e-02 1.559438e-02 6.417515e-03 -0.0262163074
## 2024-02-02 -5.405115e-03 1.842588e-02 5.815896e-03 0.0440072690
## 2024-02-05 9.846565e-03 -1.354507e-02 9.683708e-03 0.0324820338
## 2024-02-06 8.631794e-03 -3.944888e-04 3.312020e-03 -0.0177713451
## 2024-02-07 5.811065e-04 2.111024e-02 8.733849e-03 0.0048899707
## 2024-02-08 -5.754695e-03 1.449506e-04 3.681542e-03 0.0145985257
## 2024-02-09 4.093944e-03 1.555139e-02 2.037767e-02 0.0040766718
## 2024-02-12 -9.001918e-03 -1.257871e-02 -9.918822e-03 -0.0035824856
## 2024-02-13 -1.127438e-02 -2.152867e-02 -1.586768e-02 0.0345158331
## 2024-02-14 -4.809768e-03 9.665367e-03 5.260670e-03 -0.0113530553
## 2024-02-15 -1.574767e-03 -7.155224e-03 -2.174797e-02 -0.0063277305
## 2024-02-16 -8.430344e-03 -6.149154e-03 -1.514525e-02 0.0129717708
## 2024-02-19 -3.085404e-03 -2.357303e-03 2.327891e-03 -0.0034924297
## 2024-02-20 -1.031651e-03 -7.876243e-04 7.741615e-04 -0.0011682232
## 2024-02-21 4.185998e-03 -1.514476e-03 1.153305e-02 0.0116958392
## 2024-02-22 1.124390e-02 2.354667e-02 1.028929e-02 0.0004625045
## 2024-02-23 -1.003412e-02 -3.182309e-03 -2.065375e-04 -0.0154841484
## 2024-02-26 -7.451241e-03 -6.823580e-03 -4.501338e-02 0.0091548252
## 2024-02-27 8.114381e-03 -1.472188e-04 9.729774e-03 0.0037218590
## 2024-02-28 -6.625454e-03 5.889620e-04 -1.905791e-02 -0.0095017124
## 2024-02-29 -3.693078e-03 1.451980e-02 1.709966e-02 -0.0051474759
## 2024-03-01 -6.030409e-03 4.496628e-03 -1.216195e-02 -0.0169332148
## 2024-03-04 -2.538126e-02 -1.395876e-03 -2.809969e-02 0.0093301521
## 2024-03-05 -2.844095e-02 -2.957201e-02 -3.129644e-03 -0.0194358335
## 2024-03-06 -5.878204e-03 -1.390780e-03 -9.119459e-03 -0.0079767928
## 2024-03-07 -7.095265e-04 1.753343e-02 2.021732e-02 -0.0029239970
## 2024-03-08 1.023666e-02 -7.136954e-03 7.763885e-03 -0.0007330847
## 2024-03-11 1.183157e-02 -4.184954e-03 1.944390e-02 0.0036683457
## 2024-03-12 2.778557e-03 2.659945e-02 4.894146e-03 0.0124269291
## 2024-03-13 -1.212256e-02 -4.334249e-04 8.236708e-03 0.0089048618
## 2024-03-14 1.092734e-02 2.437966e-02 2.536046e-02 0.0252862473
## 2024-03-15 -2.196560e-03 -2.069514e-02 -1.503394e-02 0.0013960079
## 2024-03-18 6.372414e-03 2.161265e-03 4.438347e-02 0.0083643710
## 2024-03-19 1.358508e-02 9.800624e-03 -3.771535e-03 -0.0099078847
## 2024-03-20 1.470920e-02 9.064824e-03 1.189829e-02 -0.0055853312
## 2024-03-21 -4.085746e-02 9.735870e-03 -6.279979e-03 -0.0004680213
## 2024-03-22 5.310169e-03 -1.467277e-03 2.037111e-02 -0.0124092658
## 2024-03-25 -8.300399e-03 -1.371462e-02 -4.085197e-03 0.0082977354
## 2024-03-26 -6.672516e-03 -2.861447e-03 3.638790e-03 -0.0044673354
## 2024-03-27 2.121260e-02 -5.217627e-04 1.582106e-03 -0.0089749894
## 2024-03-28 -1.055912e-02 -1.684720e-03 2.106042e-03 0.0023831630
## 2024-03-29 -2.113945e-03 2.287748e-03 6.961785e-03 0.0073109932
## 2024-04-01 -6.355269e-03 6.847580e-03 2.074096e-02 0.0217737915
## 2024-04-02 -6.998779e-03 -7.372176e-03 -4.025590e-03 0.0083159563
## 2024-04-03 4.797427e-03 -2.349066e-03 3.207801e-03 -0.0022908941
## 2024-04-04 -4.892347e-03 -6.112516e-03 -2.833020e-02 -0.0105625726
## 2024-04-05 4.501804e-03 1.828272e-02 1.316309e-02 0.0160129420
## 2024-04-08 -6.663550e-03 -2.185544e-03 1.429126e-02 0.0105070823
## 2024-04-09 7.242513e-03 3.980316e-03 1.280902e-02 -0.0131102201
## 2024-04-10 -1.113927e-02 -7.084520e-03 -3.035258e-03 0.0444342097
## 2024-04-11 4.327092e-02 1.103337e-02 1.985278e-02 0.0035088314
## 2024-04-12 8.626656e-03 -1.409109e-02 -9.950811e-03 -0.0168269531
## 2024-04-15 -2.186350e-02 -1.957805e-02 -1.796596e-02 0.0286729736
## 2024-04-16 -1.916728e-02 2.272440e-03 -2.110931e-03 0.0066983878
## 2024-04-17 -8.147390e-03 -6.609075e-03 5.641057e-03 -0.0158832116
## 2024-04-18 -5.714326e-03 -1.838094e-02 3.697105e-03 0.0135223113
## 2024-04-19 -1.221260e-02 -1.273900e-02 -1.105046e-02 -0.0068861773
## 2024-04-22 5.090887e-03 4.610133e-03 1.432055e-02 0.0017335589
## 2024-04-23 6.391688e-03 1.648547e-02 1.247231e-02 -0.0054077643
## 2024-04-24 1.270228e-02 3.655790e-03 7.378739e-03 0.0117442149
## 2024-04-25 5.147291e-03 -2.449516e-02 -1.955313e-02 0.0116078894
## GLD
## 2023-01-04 9.411906e-03
## 2023-01-05 -1.245146e-02
## 2023-01-06 1.870750e-02
## 2023-01-09 2.245118e-03
## 2023-01-10 3.676045e-03
## 2023-01-11 -6.867939e-04
## 2023-01-12 1.156800e-02
## 2023-01-13 1.200178e-02
## 2023-01-16 -4.908809e-03
## 2023-01-17 -1.644341e-03
## 2023-01-18 -2.871752e-03
## 2023-01-19 1.586852e-02
## 2023-01-20 -3.335406e-03
## 2023-01-23 1.896434e-03
## 2023-01-24 3.618515e-03
## 2023-01-25 4.603960e-03
## 2023-01-26 -9.055267e-03
## 2023-01-27 -1.392990e-03
## 2023-01-30 -2.566715e-03
## 2023-01-31 3.636212e-03
## 2023-02-01 1.259681e-02
## 2023-02-02 -2.075194e-02
## 2023-02-03 -2.495777e-02
## 2023-02-06 2.075410e-03
## 2023-02-07 9.204257e-04
## 2023-02-08 2.471594e-03
## 2023-02-09 -7.912418e-03
## 2023-02-10 1.907194e-03
## 2023-02-13 -5.076170e-03
## 2023-02-14 7.537389e-04
## 2023-02-15 -9.964667e-03
## 2023-02-16 -8.192369e-04
## 2023-02-17 2.986791e-03
## 2023-02-20 -2.802753e-03
## 2023-02-21 -9.368770e-04
## 2023-02-22 -5.626489e-03
## 2023-02-23 -5.304511e-04
## 2023-02-24 -7.194676e-03
## 2023-02-27 3.920335e-03
## 2023-02-28 4.555969e-03
## 2023-03-01 5.772151e-03
## 2023-03-02 -5.855636e-04
## 2023-03-03 1.072309e-02
## 2023-03-06 -5.043831e-03
## 2023-03-07 -1.748048e-02
## 2023-03-08 -4.744504e-04
## 2023-03-09 9.849316e-03
## 2023-03-10 2.156286e-02
## 2023-03-13 2.294821e-02
## 2023-03-14 -5.791065e-03
## 2023-03-15 7.804133e-03
## 2023-03-16 2.020092e-03
## 2023-03-17 2.912021e-02
## 2023-03-20 3.808677e-04
## 2023-03-21 -1.887512e-02
## 2023-03-22 1.702061e-02
## 2023-03-23 1.253818e-02
## 2023-03-24 -1.125235e-02
## 2023-03-27 -9.256722e-03
## 2023-03-28 8.189093e-03
## 2023-03-29 -4.960770e-03
## 2023-03-30 9.039577e-03
## 2023-03-31 -5.212246e-03
## 2023-04-03 7.204410e-03
## 2023-04-04 1.864096e-02
## 2023-04-05 -7.979248e-04
## 2023-04-06 -7.134091e-03
## 2023-04-07 -1.849972e-03
## 2023-04-10 -5.560201e-03
## 2023-04-11 6.320556e-03
## 2023-04-12 4.885139e-03
## 2023-04-13 1.351567e-02
## 2023-04-14 -1.771031e-02
## 2023-04-17 -4.453755e-03
## 2023-04-18 3.880781e-03
## 2023-04-19 -4.778520e-03
## 2023-04-20 3.938259e-03
## 2023-04-21 -9.887669e-03
## 2023-04-24 3.039335e-03
## 2023-04-25 5.086318e-03
## 2023-04-26 -5.437386e-03
## 2023-04-27 5.410039e-05
## 2023-04-28 2.706525e-04
## 2023-05-01 -4.491352e-03
## 2023-05-02 1.929664e-02
## 2023-05-03 8.479076e-03
## 2023-05-04 7.032953e-03
## 2023-05-05 -1.564795e-02
## 2023-05-08 1.226906e-03
## 2023-05-09 7.086162e-03
## 2023-05-10 -1.428443e-03
## 2023-05-11 -8.582756e-03
## 2023-05-12 -1.710080e-03
## 2023-05-15 2.141262e-03
## 2023-05-16 -1.249939e-02
## 2023-05-17 -3.461889e-03
## 2023-05-18 -1.297291e-02
## 2023-05-19 9.898829e-03
## 2023-05-22 -2.341498e-03
## 2023-05-23 1.200731e-03
## 2023-05-24 -8.068450e-03
## 2023-05-25 -9.618027e-03
## 2023-05-26 3.995567e-03
## 2023-05-29 4.642916e-03
## 2023-05-30 1.540486e-03
## 2023-05-31 1.538201e-03
## 2023-06-01 7.898130e-03
## 2023-06-02 -1.474745e-02
## 2023-06-05 6.020416e-03
## 2023-06-06 1.098040e-03
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## 2024-04-25 5.963468e-03- Determine Asset Weights
We’ll assign weights to each asset in the portfolio composition. For example: - Stocks: 50% - Bonds: 30% - Commodities: 20%
library(fPortfolio) # Load Necessary Libraries
portfolio_weights <- c(0.2, 0.2, 0.2,0.2,0.2) # Example weights (sums to 1)- Calculate Portfolio Return
Calculate the historical returns of the entire portfolio by aggregating the returns of individual assets based on their respective weights.
# Remove column indexes
colnames(asset_returns) <- NULL
# Calculate portfolio returns
portfolio_returns <- colSums(asset_returns* portfolio_weights) / sum(portfolio_weights)- Estimate Portfolio Volatility
Calculate the volatility of the portfolio return, which represents the standard deviation of the portfolio’s historical returns.
library(PerformanceAnalytics)
# Calculate portfolio volatility
portfolio_volatility <- StdDev(portfolio_returns)
portfolio_volatility## [,1]
## StdDev 0.03459949- Calculate the value at risk (VaR) of Apple (AAPL)
AAPL.returns <- dailyReturn(AAPL)
AAPL.returns <- na.omit(AAPL.returns)
sorted_return.AAPL <- sort(AAPL.returns)
persentil_5.AAPL <- quantile(sorted_return.AAPL, 0.05);persentil_5.AAPL## 5%
## -0.01921048Apple’s 5% percentile return VaR is -1.92%.
market_value <- 5000000
VAR.AAPL <- persentil_5.AAPL * market_value
VAR.AAPL## 5%
## -96052.4Value at Risk in Apple stock is at -Rp96,052.4
- Calculate the value at risk (VaR) of Google (GOOG)
GOOG.returns <- dailyReturn(GOOG)
GOOG.returns <- na.omit(GOOG.returns)
sorted_return.GOOG <- sort(GOOG.returns)
persentil_5.GOOG <- quantile(sorted_return.GOOG, 0.05);persentil_5.GOOG## 5%
## -0.02603324Google’s 5% percentile return VaR is -2.6%.
market_value <- 5000000
VAR.GOOG <- persentil_5.GOOG * market_value
VAR.GOOG## 5%
## -130166.2Value at Risk in Google stock is at -Rp130,166.2
- Calculate the value at risk (VaR) of Microsoft (MSFT)
MSFT.returns <- dailyReturn(MSFT)
MSFT.returns <- na.omit(MSFT.returns)
sorted_return.MSFT <- sort(MSFT.returns)
persentil_5.MSFT <- quantile(sorted_return.MSFT, 0.05);persentil_5.MSFT## 5%
## -0.0226127Microsoft’s 5% percentile return VaR is -2.26%.
market_value <- 5000000
VAR.MSFT <- persentil_5.MSFT * market_value
VAR.MSFT## 5%
## -113063.5Value at Risk in Microsoft stock is at -Rp113,063.5
- Calculate the value at risk (VaR) of TNX
TNX.returns <- dailyReturn(TNX)
TNX.returns <- na.omit(TNX.returns)
sorted_return.TNX <- sort(TNX.returns)
persentil_5.TNX <- quantile(sorted_return.TNX, 0.05);persentil_5.TNX## 5%
## -0.02919602TNX’s 5% percentile return VaR is -2.91%.
market_value <- 5000000
VAR.GOOG <- persentil_5.TNX * market_value
VAR.GOOG## 5%
## -145980.1Value at Risk in TNX bond is at -Rp145,980.1
- Calculate the value at risk (VaR) of Gold (GLD)
GLD.returns <- dailyReturn(GLD)
GLD.returns <- na.omit(GLD.returns)
sorted_return.GLD <- sort(GLD.returns)
persentil_5.GLD <- quantile(sorted_return.GLD, 0.05);persentil_5.GLD## 5%
## -0.0122064Gold’s 5% percentile return VaR is -1.22%.
market_value <- 5000000
VAR.GLD <- persentil_5.GLD * market_value
VAR.GLD## 5%
## -61032Value at Risk in Gold commodity is at -Rp61,032
Lab Exercise 2
Question
Let’s assume we have a portfolio consisting of three assets (Stocks from Indonesia): stocks (ST), bonds (BD), and commodities (CM). Calculate Value at Risk using using Copulae method!. Write down your complete answer in your Rpubs and share the link at google clasroom.
Answer
- Identify Portfolio Assets
Let’s assume we have a portfolio consisting of three assets: TLKM.JK as stocks (ST), IRX as bonds (BD), and USO as commodities (CM)
# Load necessary libraries
library(quantmod)
library(copula)
# Set the time period for historical data
start_date <- as.Date("2020-01-01") # adjust start date as needed
end_date <- as.Date("2022-01-01") # adjust end date as needed
# Download historical data
getSymbols("TLKM.JK", src = "yahoo", from = start_date, to = end_date)## [1] "TLKM.JK"getSymbols("^IRX", src = "yahoo", from = start_date, to = end_date)## [1] "IRX"getSymbols("USO", src = "yahoo", from = start_date, to = end_date)## [1] "USO"# Calculate daily returns
returns_TLKM <- dailyReturn(Cl(TLKM.JK))
returns_IRX <- dailyReturn(Cl(IRX))
returns_USO <- dailyReturn(Cl(USO))
# Merge the returns into one data frame by dates
combined_returns <- na.omit(merge(returns_TLKM, returns_IRX, returns_USO))
# Estimate correlation matrix
rho <- cor(combined_returns, use = "complete.obs")
# Assuming the number of dimensions (assets) is 3
dim <- ncol(combined_returns)
normalCop <- normalCopula(dim = dim, dispstr = "ex")
# Set the parameters for the copula using the lower triangular part of the correlation matrix
normalCop@parameters <- t(rho)[lower.tri(rho)]
# Simulate data from the copula
set.seed(123)
n <- 1000
U <- rCopula(n, normalCop)
X <- qnorm(U)
# Transform to asset returns using the standard deviations of the assets
asset_returns <- sapply(1:ncol(X), function(i) X[, i] * sd(combined_returns[, i]))
# Calculate portfolio returns assuming equal weights
portfolio_returns <- rowSums(asset_returns) / ncol(asset_returns)
# Calculate initial portfolio value and final portfolio value
initial_portfolio <- 1000000
portfolio_value <- initial_portfolio * (1 + portfolio_returns)
# Sort simulated portfolio values
sorted_portfolio_values <- sort(portfolio_value)
# Calculate VaR
confidence_level <- 0.95
var_percentile <- 1 - confidence_level
var_index <- round(var_percentile * n)
VaR <- sorted_portfolio_values[var_index]
VaR## [1] 697770.2Value at Risk of TLKM.JK stock, IRX bond, USO commodity is Rp697,770.2