#Q1. Find the median of the first column of the table
data(cars)
median(cars$speed)## [1] 15#Q2.
#install.packages(jsonlite)
library(jsonlite)
DATA <- fromJSON("https://min-api.cryptocompare.com/data/v2/histoday?fsym=BTC&tsym=USD&limit=100&toTs=1772405597")
#Load daily data
DATA <- DATA$Data$Data
#Find the max of the daily close price of BTC from past 100 days
max_close <- max(DATA$close, na.rm = TRUE)
max_close## [1] 96945.09library(quantmod)
# Find historical price chart data from the bast 5 years for BTC
btc_x <- getSymbols("BTC-USD",src = "yahoo",from = Sys.Date() - 5*365, auto.assign = FALSE)
#needs to be a dataframe and the open and close columns need to be set to numeric, and the date needs to be set as a date
btc <- data.frame(date = as.Date(index(btc_x)),btc_open = as.numeric(Op(btc_x)),btc_close = as.numeric(Ad(btc_x)))
head(btc)## date btc_open btc_close
## 1 2021-03-03 48415.82 50538.24
## 2 2021-03-04 50522.30 48561.17
## 3 2021-03-05 48527.03 48927.30
## 4 2021-03-06 48899.23 48912.38
## 5 2021-03-07 48918.68 51206.69
## 6 2021-03-08 51174.12 52246.52library(quantmod)
getSymbols("^GSPC", src = "yahoo", from = Sys.Date() - 5*365)## [1] "GSPC"#needs to be a dataframe and the open and close columns need to be set to numeric, and the date needs to be set as a date
sp500 <- data.frame(date = as.Date(index(GSPC)),sp_open = as.numeric(Op(GSPC)), sp_close = as.numeric(Ad(GSPC)))
head(sp500)## date sp_open sp_close
## 1 2021-03-03 3863.99 3819.72
## 2 2021-03-04 3818.53 3768.47
## 3 2021-03-05 3793.58 3841.94
## 4 2021-03-08 3844.39 3821.35
## 5 2021-03-09 3851.93 3875.44
## 6 2021-03-10 3891.99 3898.81library(dplyr)
combined <- inner_join(btc, sp500, by = "date") %>% arrange(date)
head(combined)## date btc_open btc_close sp_open sp_close
## 1 2021-03-03 48415.82 50538.24 3863.99 3819.72
## 2 2021-03-04 50522.30 48561.17 3818.53 3768.47
## 3 2021-03-05 48527.03 48927.30 3793.58 3841.94
## 4 2021-03-08 51174.12 52246.52 3844.39 3821.35
## 5 2021-03-09 52272.97 54824.12 3851.93 3875.44
## 6 2021-03-10 54824.01 56008.55 3891.99 3898.81btc_returns <- (btc$btc_close - btc$btc_open) / btc$btc_open
head(btc_returns)## [1] 0.0438374469 -0.0388172458 0.0082484633 0.0002689683 0.0467717390
## [6] 0.0209560283btc_returns * 100## [1] 4.383745e+00 -3.881725e+00 8.248463e-01 2.689683e-02 4.677174e+00
## [6] 2.095603e+00 4.880435e+00 2.160621e+00 3.291345e+00 -8.459332e-01
## [11] 6.800638e+00 -3.134239e+00 -5.669607e+00 1.726547e+00 3.598833e+00
## [16] -1.755989e+00 8.577479e-01 -3.191576e-02 -1.348814e+00 -5.196203e+00
## [21] 4.169478e-01 -3.539034e+00 -1.939406e+00 6.683629e+00 1.516108e+00
## [26] -4.322526e-02 3.221391e+00 2.021742e+00 -1.942179e-02 2.872153e-01
## [31] 4.829763e-01 -3.019525e+00 2.002809e+00 5.054450e-01 -1.655471e+00
## [36] -3.673653e+00 3.964425e+00 -1.398310e-01 2.642673e+00 5.994269e-01
## [41] -4.694437e-01 6.033455e+00 -6.518169e-01 3.786217e-01 -2.664804e+00
## [46] -1.375106e+00 -7.389726e+00 -8.316553e-01 1.421000e+00 -4.542213e+00
## [51] -3.889611e+00 -1.248857e+00 -2.135883e+00 -2.094943e+00 1.007372e+01
## [56] 1.856019e+00 -3.850773e-01 -2.375184e+00 7.805891e+00 1.964608e-01
## [61] -2.066178e+00 1.024403e+00 -6.782655e+00 7.834130e+00 -1.818888e+00
## [66] 1.670596e+00 2.529977e+00 -1.095623e+00 -4.104787e+00 1.535138e+00
## [71] -1.333696e+01 -3.868909e-02 3.976305e-01 -6.208560e+00 -5.577844e-01
## [76] -6.201295e+00 -1.330610e+00 -1.383756e+01 1.096236e+01 -8.109619e+00
## [81] 4.431282e-01 -7.356143e+00 1.154344e+01 -1.014437e+00 2.348301e+00
## [86] -2.238025e+00 -7.296000e+00 -2.993177e+00 3.093912e+00 4.695254e+00
## [91] -1.632623e+00 2.384904e+00 4.280268e+00 -5.983510e+00 -3.601393e+00
## [96] 9.110360e-01 -6.347263e+00 -3.479857e-01 1.175494e+01 -1.837194e+00
## [101] 1.736836e+00 -4.787418e+00 9.962007e+00 3.079449e+00 -5.169404e-02
## [106] -4.534947e+00 -7.509319e-01 -6.068930e+00 -6.656238e-01 3.800459e-01
## [111] -1.112324e+01 2.793222e+00 3.713012e+00 2.908418e+00 -8.717265e+00
## [116] 1.872510e+00 7.315894e+00 -7.058574e-01 4.038278e+00 -2.416012e+00
## [121] -4.178182e+00 1.035617e+00 2.404782e+00 1.794907e+00 -4.359837e+00
## [126] 1.517302e+00 -1.082087e+00 -2.986858e+00 2.849337e+00 -8.598402e-01
## [131] 2.181825e+00 -3.205954e+00 -1.278301e+00 3.010097e-01 -3.189803e+00
## [136] -1.319068e+00 4.323930e-01 8.337881e-01 -3.088614e+00 -3.343044e+00
## [141] 7.767439e+00 5.421236e-01 3.948472e+00 2.079897e+00 3.090946e+00
## [146] 5.520863e+00 5.716558e+00 1.247289e+00 3.242556e-02 5.516366e+00
## [151] -1.351088e+00 -3.583982e+00 -1.767389e+00 -2.617314e+00 4.014756e+00
## [156] 2.830678e+00 4.773257e+00 4.022628e+00 -1.741627e+00 5.876601e+00
## [161] -1.503465e+00 -1.330361e-02 -2.520115e+00 7.546472e+00 -1.492851e+00
## [166] -1.054513e-01 -2.159671e+00 -2.701771e+00 2.560882e-01 4.415763e+00
## [171] 5.599058e+00 -8.546666e-01 9.260388e-01 5.162589e-01 -3.745243e+00
## [176] 2.584542e+00 -4.204716e+00 4.614850e+00 -3.467997e-01 -1.664606e-01
## [181] -3.644666e+00 3.027106e-01 3.709686e+00 1.065146e+00 1.495539e+00
## [186] -1.293743e-01 3.635620e+00 1.669979e+00 -1.110767e+01 -1.572510e+00
## [191] 1.347205e+00 -3.260480e+00 7.390648e-01 1.894945e+00 -2.375612e+00
## [196] 4.742969e+00 2.289583e+00 -7.798077e-01 -1.053954e+00 2.125579e+00
## [201] -2.089622e+00 -9.347173e+00 -5.390463e+00 7.120699e+00 3.064260e+00
## [206] -4.576418e+00 -2.901361e-01 1.139728e+00 -2.309407e+00 -2.763817e+00
## [211] 1.216070e+00 5.390028e+00 9.814055e+00 -8.849249e-01 1.090448e+00
## [216] 1.875164e+00 4.758217e+00 7.525803e+00 -2.769568e+00 3.079861e-01
## [221] 1.925544e+00 -3.298142e-01 5.025501e+00 -2.582749e+00 2.431981e+00
## [226] -8.943012e-02 7.407760e+00 -1.164345e+00 1.093760e+00 7.754390e-01
## [231] 3.576265e+00 2.657324e+00 -5.745355e+00 -2.483415e+00 1.151648e+00
## [236] -7.129210e-01 3.523994e+00 -4.234256e+00 -3.097848e+00 3.679458e+00
## [241] 2.644284e+00 -5.631986e-01 -8.593808e-01 -5.153957e-01 3.712316e+00
## [246] -4.494381e-01 -2.366590e+00 -5.440968e-01 7.509643e-01 2.878838e+00
## [251] 6.666389e+00 -8.555271e-01 -2.924582e+00 -4.452167e-02 -1.091575e+00
## [256] 4.853731e-01 1.569254e+00 -2.996611e+00 -5.586758e+00 3.797673e-01
## [261] -5.662678e+00 2.150321e+00 2.722380e+00 -1.674239e+00 -4.118018e+00
## [266] 2.245857e+00 -2.232966e+00 1.911325e-01 -9.142628e+00 2.007295e+00
## [271] 4.443166e+00 8.983122e-01 -1.426052e+00 5.655856e-01 -1.292535e+00
## [276] -5.151232e+00 -8.426120e+00 3.400873e-01 2.366044e+00 2.337951e-01
## [281] -3.214113e-01 -5.506356e+00 -8.371576e-01 4.438573e+00 1.506398e+00
## [286] -6.739058e+00 -2.080749e-01 1.068564e+00 -2.525618e+00 -3.046112e+00
## [291] 1.362037e+00 -3.134246e-01 3.708536e-01 4.373441e+00 -6.305767e-01
## [296] 4.438325e+00 3.177679e-02 -8.358259e-01 7.551737e-01 -3.192580e-01
## [301] -6.099078e+00 -2.475986e+00 1.478835e+00 -1.829420e+00 2.969153e+00
## [306] -7.040699e-01 -1.870214e+00 -1.208117e+00 -5.077098e+00 -9.286750e-01
## [311] -3.697650e+00 4.149915e-01 4.238077e-01 -2.122841e-01 2.191197e+00
## [316] 2.823726e+00 -3.083669e+00 1.175684e+00 1.751663e-01 -1.347172e-01
## [321] -2.012078e+00 2.971796e-01 -1.486077e+00 -2.547932e+00 -1.042342e+01
## [326] -3.951952e+00 3.507954e+00 1.043656e+00 8.162619e-01 -2.662873e-01
## [331] 8.043984e-01 1.766534e+00 9.461569e-01 -6.141668e-01 1.484282e+00
## [336] 6.795629e-01 -4.621990e+00 5.678657e-01 1.171385e+01 -1.453356e-01
## [341] 2.343837e+00 3.380365e+00 6.015165e-01 5.490065e-01 -1.764885e+00
## [346] -2.669638e+00 -3.957155e-01 -9.245728e-02 1.018847e+00 4.669883e+00
## [351] -1.382777e+00 -7.736198e+00 -1.285151e+00 2.401758e-01 -4.204393e+00
## [356] -3.508113e+00 3.283783e+00 -2.582483e+00 2.827477e+00 2.296860e+00
## [361] -2.752489e-01 -3.552328e+00 1.455268e+01 2.685834e+00 -9.772842e-01
## [366] -3.354353e+00 -7.820727e+00 6.440529e-01 -2.497741e+00 -9.556916e-01
## [371] 1.779740e+00 8.363123e+00 -6.043277e+00 -1.635387e+00 2.823776e-01
## [376] -2.661874e+00 4.810078e+00 -8.205496e-01 4.597262e+00 -4.605274e-01
## [381] 2.091390e+00 9.474991e-01 -2.236432e+00 -4.076424e-01 3.127769e+00
## [386] 1.247695e+00 2.504931e+00 8.738486e-01 3.404041e-01 5.201928e+00
## [391] 6.538664e-01 7.755617e-01 -8.307209e-01 -3.237151e+00 1.596957e+00
## [396] -8.999596e-01 1.296225e+00 3.819600e-01 -2.291747e+00 -5.132617e+00
## [401] 6.858709e-01 -2.798457e+00 1.182673e+00 -1.340354e+00 -6.348509e+00
## [406] 1.501171e+00 2.599869e+00 -2.975453e+00 1.537485e+00 -3.152274e-01
## [411] -1.733950e+00 2.781919e+00 1.652227e+00 -3.068960e-01 -2.040419e+00
## [416] -1.938374e+00 -6.341225e-01 -2.300508e-02 2.497183e+00 -5.762798e+00
## [421] 2.940219e+00 1.356725e+00 -2.913838e+00 -2.307899e+00 2.004144e+00
## [426] 1.485245e-01 -2.018413e+00 5.166787e+00 -7.861310e+00 -1.455333e+00
## [431] -1.499759e+00 -4.066355e+00 -1.104833e+01 2.474931e+00 -6.705622e+00
## [436] 3.836562e-01 8.687063e-01 2.785061e+00 4.008585e+00 -4.604650e+00
## [441] 1.886818e+00 -5.601434e+00 5.549981e+00 -3.663273e+00 7.957819e-01
## [446] 3.028118e+00 -3.993766e+00 1.905290e+00 -3.061175e-01 -1.006443e+00
## [451] -2.131768e+00 6.717602e-01 1.468269e+00 7.753955e+00 2.157534e-01
## [456] -6.270256e+00 2.257426e+00 -2.505648e+00 4.267650e-01 2.398010e-01
## [461] 4.882564e+00 -6.893582e-01 -3.008284e+00 -3.418180e-01 -3.409213e+00
## [466] -2.488787e+00 -5.677355e+00 -1.589594e+01 -1.250416e+00 1.694436e+00
## [471] -9.721052e+00 4.207047e-01 -7.110599e+00 8.113077e+00 2.246153e-01
## [476] 5.647328e-01 -3.534775e+00 5.500031e+00 6.972268e-01 1.265581e+00
## [481] -2.182678e+00 -1.392222e+00 -2.174995e+00 -8.734530e-01 -1.609215e+00
## [486] -2.780476e+00 -1.690291e-01 2.857301e-01 4.839778e+00 -1.742283e-01
## [491] 1.751095e+00 5.303598e+00 4.342664e-01 -5.738457e-01 -3.383948e+00
## [496] -4.247132e+00 -3.237582e+00 4.585030e+00 1.773514e+00 1.279200e+00
## [501] 1.709759e+00 -1.961295e+00 8.198367e+00 4.101790e+00 -6.901965e-01
## [506] -2.951477e-01 -1.937395e+00 -1.063575e+00 6.394437e-01 -5.509119e+00
## [511] -5.681686e-01 7.938079e+00 3.969043e+00 -1.701812e-01 -5.908829e-01
## [516] -1.332542e+00 -9.649828e-02 -1.417154e+00 -5.865417e-01 -9.508743e-01
## [521] 2.927853e+00 -1.417451e+00 9.248795e-01 2.717739e+00 -2.717873e+00
## [526] 3.387936e+00 3.834751e-02 1.860047e+00 8.966761e-02 -4.491482e-01
## [531] -7.457085e-01 -1.006567e+00 -2.283452e+00 -5.496790e-01 -1.006216e+01
## [536] 1.404786e+00 1.766170e+00 -6.156325e-01 5.936297e-01 -6.105768e-01
## [541] 9.602286e-01 -6.186614e+00 -1.089413e+00 -2.116760e+00 3.481185e+00
## [546] -2.472104e+00 1.263570e+00 3.822478e-01 -7.766085e-01 -6.891978e-01
## [551] 7.777255e-01 -8.825846e-01 -4.945354e+00 2.402847e+00 2.068051e-01
## [556] 1.062188e+01 1.420350e+00 4.184455e-01 2.757449e+00 -9.274189e+00
## [561] 2.800912e-01 -2.673009e+00 3.480415e-01 1.772475e+00 -3.516273e+00
## [566] 6.465802e-01 -3.350130e+00 -1.820325e+00 4.741931e+00 -5.911774e-01
## [571] -1.865465e+00 -7.087595e-01 2.227046e+00 -5.789923e-01 1.685977e+00
## [576] 7.477514e-01 -7.236471e-01 -6.124704e-01 -1.386414e+00 3.043004e+00
## [581] 3.634707e+00 -8.614499e-01 -1.019767e+00 -2.057912e+00 -6.638575e-01
## [586] 1.490784e-01 -1.568061e+00 -4.576103e-01 5.500487e-01 1.179401e+00
## [591] -1.015744e+00 -6.140216e-01 1.044526e+00 1.464537e+00 -1.105093e+00
## [596] -1.011078e+00 -4.407217e-01 6.259610e-01 1.867718e-01 1.870462e+00
## [601] -1.135527e+00 3.881592e+00 3.375458e+00 -2.344252e+00 1.515158e+00
## [606] 1.084593e+00 -8.760643e-01 -6.684303e-01 -4.696291e-02 -1.579142e+00
## [611] 2.345859e-01 4.643830e+00 6.519767e-01 -1.684611e+00 -1.537924e+00
## [616] -9.996763e+00 -1.436052e+01 1.072591e+01 -3.122056e+00 -1.395147e+00
## [621] -2.656933e+00 1.627755e+00 1.607517e+00 -1.272791e+00 1.025277e-01
## [626] 5.911605e-02 9.179426e-02 -2.519535e+00 -3.093319e+00 2.581808e+00
## [631] 2.563156e+00 -4.317380e-02 -4.844382e-01 -3.467885e-01 -1.169582e-01
## [636] -1.355823e+00 1.401824e+00 4.396892e+00 -1.170020e+00 7.070470e-01
## [641] -1.064133e+00 1.314846e+00 -8.994647e-01 6.731312e-01 -1.412439e+00
## [646] 2.291904e+00 -5.744849e-01 -3.207671e-02 -1.489668e-01 6.077328e-01
## [651] 3.341057e+00 1.888644e-01 -2.519301e+00 -4.129463e+00 8.897070e-01
## [656] -2.240634e-01 -1.905606e+00 2.825226e+00 -5.146088e-01 7.111825e-02
## [661] -1.942489e-01 3.023121e-01 -3.276171e-02 4.604770e-01 -1.194596e+00
## [666] -9.800443e-01 5.438483e-01 -2.328188e-01 -3.383452e-01 4.663187e-01
## [671] 3.787008e-01 -5.386971e-02 1.097308e+00 -1.585458e-01 6.859875e-01
## [676] 1.746648e-02 8.080504e-01 5.999915e-01 1.473533e+00 2.800224e+00
## [681] 4.150629e+00 5.515253e+00 5.352752e+00 -4.609015e-01 1.376329e+00
## [686] -6.759806e-02 -2.231787e+00 1.933832e+00 7.546367e+00 4.418370e-01
## [691] -2.527454e-01 9.389680e-01 -1.278513e+00 2.113990e+00 -3.296459e-01
## [696] 2.084682e-01 -2.117638e-01 3.226532e+00 -3.930699e+00 1.306812e+00
## [701] 2.532361e+00 -1.049513e+00 -8.560011e-02 -4.882329e-01 -1.613998e+00
## [706] -8.447849e-01 2.227963e+00 -1.392820e+00 -4.913708e+00 -7.691563e-01
## [711] 1.011615e+00 -3.781244e-01 9.685392e-02 1.921777e+00 9.393343e+00
## [716] -2.813449e+00 3.997744e+00 3.093000e-01 -1.267794e+00 2.023803e+00
## [721] -1.597449e+00 -1.017187e+00 -1.005454e+00 -3.123196e+00 -1.066805e-01
## [726] 1.670234e+00 -1.637424e-01 -1.592071e+00 2.140826e+00 -7.254730e-01
## [731] -4.744944e+00 -4.281291e-02 3.640002e-01 -3.145987e-02 -9.298633e-01
## [736] -2.243210e+00 -6.247945e+00 -8.825934e-01 2.201981e+00 7.445791e+00
## [741] 9.212356e+00 2.249045e+00 -1.594469e+00 2.787180e+00 9.454380e+00
## [746] -1.756908e+00 3.964374e+00 -9.784221e-01 1.467222e+00 -3.023160e+00
## [751] 3.780006e+00 -2.933282e+00 2.680922e-02 1.814138e+00 -3.051288e+00
## [756] 4.984437e-01 3.965999e+00 -1.116672e+00 1.591818e+00 -2.187903e-01
## [761] -9.258987e-01 -1.393955e+00 1.341294e+00 2.931449e-02 -4.652525e-01
## [766] -4.033937e-01 9.771042e-02 1.361901e+00 4.647628e+00 1.960562e+00
## [771] -3.060683e-01 1.693810e+00 2.503710e-01 -5.649382e-01 -2.048734e-03
## [776] -2.876595e+00 3.220680e+00 -5.170422e+00 -2.004238e+00 -3.441936e+00
## [781] 2.023060e+00 -8.080191e-01 -2.406178e-01 2.881077e+00 4.333651e-01
## [786] 3.677027e+00 -4.774325e-01 -3.002332e-01 7.963961e-02 -3.885213e+00
## [791] 2.112570e+00 1.136014e+00 -6.323992e-01 2.366964e+00 -2.147125e+00
## [796] -1.545396e+00 -2.657896e+00 -1.310449e-01 -1.188982e-01 -2.245737e+00
## [801] -6.768718e-01 -8.837515e-02 5.288148e-01 9.702754e-01 -4.963407e-01
## [806] 1.343909e+00 -2.078128e+00 2.362380e-01 8.953310e-01 -1.344465e+00
## [811] 3.790100e-01 1.376847e+00 -3.268313e+00 5.573456e-01 9.258431e-01
## [816] 5.545317e-01 4.519672e+00 -1.174355e+00 -1.541656e-01 -1.735964e+00
## [821] -1.463860e+00 1.584493e+00 -6.502026e-01 1.623016e-01 -5.025278e+00
## [826] 5.855229e+00 -3.266499e+00 6.093996e-01 -9.638913e-02 -2.380965e+00
## [831] 3.331655e-01 -1.225604e-01 6.094717e-02 -3.069345e+00 1.810073e+00
## [836] 2.941041e+00 6.912466e-01 -6.572657e-01 1.957772e+00 5.535515e+00
## [841] 6.061134e+00 -2.788854e-01 2.672852e+00 -5.211643e-01 -2.124353e-01
## [846] -6.869717e-01 1.366979e+00 -1.988218e+00 1.193784e+00 1.179265e-01
## [851] 3.879990e-01 1.095227e-01 1.736922e+00 -1.217334e+00 -8.595502e-01
## [856] -1.959582e+00 1.452012e+00 -1.791973e-01 -3.973937e-01 8.022122e-01
## [861] 6.684227e-01 -7.530460e-01 3.582266e+00 -3.624027e+00 -1.186101e-01
## [866] -1.595507e-01 -3.429407e-01 -9.636353e-01 1.737220e-01 -4.119450e-01
## [871] 3.477015e-01 -4.577081e-01 9.883405e-01 -3.007633e+00 1.659412e-01
## [876] 4.421199e-01 -4.875327e-01 3.665666e-01 1.278082e-01 -2.785874e-01
## [881] -1.646376e-01 1.521882e+00 -1.858958e+00 5.783998e-02 -3.437640e-01
## [886] -1.143982e-01 -6.354917e-03 4.892277e-01 2.006416e+00 -6.893650e-01
## [891] -4.545426e-01 -9.239623e-02 5.502671e-02 -4.544363e-01 4.274786e-01
## [896] -8.082861e-01 -1.602022e+00 -7.091519e+00 -2.201981e+00 1.857085e-01
## [901] 3.553019e-01 -2.464834e-01 -3.792153e-01 1.502146e+00 -1.018279e+00
## [906] -4.434075e-01 -1.488507e-01 3.131745e-01 6.337831e-02 6.225101e+00
## [911] -1.546624e+00 -5.019634e+00 -5.139846e-01 2.631251e-01 3.869184e-01
## [916] -5.997878e-01 -1.354820e-01 -1.190482e-01 1.910350e+00 -1.293778e+00
## [921] -3.762936e-02 -2.432279e-01 -2.590074e+00 2.673561e+00 1.512409e+00
## [926] 1.187255e+00 2.821871e-01 -1.425155e-01 -1.269961e-01 8.340073e-01
## [931] 1.682553e+00 -2.874680e-01 -2.072283e+00 5.839364e-02 3.137809e-03
## [936] -1.213523e+00 1.702806e-01 -2.947653e-01 5.464384e-01 2.525949e+00
## [941] -4.185819e-01 2.089299e-01 3.768823e+00 -1.594227e+00 -2.845453e-01
## [946] 1.350101e+00 -1.376809e+00 1.949775e+00 7.893071e-02 -1.308033e-01
## [951] -1.255778e+00 -7.183305e-01 -1.893817e+00 -4.334941e-01 4.092871e-01
## [956] -1.673513e-02 1.123094e+00 4.995238e+00 -3.728674e-01 -2.998200e-01
## [961] 1.367305e+00 3.306800e+00 7.917941e-01 2.514892e-01 9.772667e+00
## [966] 2.491807e+00 1.730088e+00 -1.007529e+00 -7.222614e-01 5.363131e-01
## [971] 1.317447e+00 -8.507797e-02 4.860949e-01 2.250553e+00 -1.420185e+00
## [976] -6.014126e-01 9.957044e-01 -1.158627e-01 -2.116711e-02 1.129228e+00
## [981] 6.657376e-01 2.973293e+00 1.666706e+00 -4.610539e-01 -2.140159e-01
## [986] -1.532087e+00 -2.614694e+00 6.561442e+00 -4.554413e+00 1.194142e+00
## [991] -1.083073e-01 2.188778e+00 2.752786e-01 -4.417894e+00 4.686652e+00
## [996] -3.495751e-01 1.136747e+00 1.998305e-01 -8.405653e-01 -5.340482e-01
## [1001] 1.565437e+00 8.562002e-02 -3.918825e-01 2.573684e+00 2.034297e+00
## [1006] 1.282380e+00 5.006347e+00 4.988257e+00 -7.567558e-01 -1.088595e+00
## [1011] 2.017560e+00 -1.027693e+00 1.173526e-01 -5.818840e+00 5.128389e-01
## [1016] 3.429781e+00 3.257860e-01 -2.552956e+00 7.210092e-01 -2.063271e+00
## [1021] 3.084381e+00 -8.700076e-01 3.291307e+00 5.063845e-01 2.938615e-01
## [1026] -6.195015e-01 -1.628805e+00 1.400973e+00 -2.475801e+00 2.174083e+00
## [1031] -1.933238e+00 -1.209073e+00 1.547772e-01 2.682900e-01 4.463309e+00
## [1036] 1.744463e+00 -4.700513e+00 3.089675e+00 -6.853818e-02 -4.295208e-01
## [1041] -1.258389e-01 6.875736e+00 -1.804539e+00 1.097618e+00 -6.161862e-01
## [1046] -7.553965e+00 1.003226e-01 -2.441496e+00 1.910347e+00 1.542634e+00
## [1051] -9.029220e-01 -3.463205e+00 8.235416e-01 9.849008e-02 -3.016526e-01
## [1056] -4.924441e+00 8.270409e-01 5.002320e-01 -3.536874e-01 4.707573e+00
## [1061] 7.280285e-01 -2.149052e-01 2.991446e+00 -8.028069e-01 -8.467434e-01
## [1066] 1.188665e+00 2.512179e-01 -4.462545e-01 -9.567623e-01 1.903509e-01
## [1071] 1.001658e+00 2.850319e+00 2.186770e+00 4.083716e+00 1.310082e+00
## [1076] 1.098934e+00 3.440912e+00 -3.983031e-01 4.208938e+00 1.963269e-01
## [1081] 4.283525e-01 -9.560270e-01 8.915226e-01 -6.822082e-01 9.794722e-01
## [1086] -8.309281e-01 -1.060024e+00 -1.076277e+00 1.645231e+00 3.258465e-01
## [1091] 5.396934e+00 4.706599e+00 9.520916e+00 -2.081308e+00 2.080449e+00
## [1096] -6.435913e-01 1.830992e+00 8.225620e+00 -6.642940e+00 3.654591e+00
## [1101] 1.249237e+00 2.034716e+00 2.922799e-01 7.584369e-01 4.496283e+00
## [1106] -8.926653e-01 2.240257e+00 -2.302676e+00 -2.779326e+00 -5.875805e+00
## [1111] 4.706756e+00 -1.203299e+00 -8.353586e+00 9.661716e+00 -3.563744e+00
## [1116] -2.612872e+00 4.066918e-01 4.937382e+00 4.052585e+00 8.080472e-02
## [1121] -7.665954e-01 1.860516e+00 -1.204285e+00 -3.550270e-01 2.420561e+00
## [1126] -2.286915e+00 -6.108671e+00 8.161464e-01 3.839518e+00 -9.897244e-01
## [1131] 1.555911e+00 6.755658e-01 3.270936e+00 -3.480940e+00 2.093774e+00
## [1136] -7.298897e-01 -4.090007e+00 -5.011138e+00 2.980276e+00 -3.519090e+00
## [1141] 6.190015e-01 -4.002949e+00 3.651450e+00 5.240378e-01 1.790634e+00
## [1146] -1.018141e-01 2.929127e+00 -6.472440e-01 -3.210151e+00 3.215674e-01
## [1151] -1.132118e+00 -5.205373e-01 -4.892273e-01 1.164317e+00 -5.016591e+00
## [1156] -3.886329e+00 1.493005e+00 6.372443e+00 1.590754e+00 2.170517e-01
## [1161] -1.368498e+00 -1.310812e+00 -1.836436e+00 3.037629e+00 -3.587990e+00
## [1166] 5.847165e-04 1.077238e+00 2.359970e+00 -2.143033e+00 7.657512e+00
## [1171] -1.546314e+00 2.790958e+00 -1.869887e-01 -9.853345e-01 7.799564e+00
## [1176] -1.828773e+00 -1.444328e+00 -1.724132e+00 8.802962e-01 1.078442e+00
## [1181] -1.077316e+00 1.287910e+00 -1.579395e+00 -1.051678e+00 1.167434e+00
## [1186] -1.274239e+00 3.220172e-01 6.103671e-02 1.551029e+00 2.562614e+00
## [1191] 7.290361e-01 -4.581692e-01 -2.002004e+00 -2.655098e-02 5.057903e-01
## [1196] -1.895794e-01 -3.130639e+00 1.366301e+00 -2.178540e+00 -1.103376e+00
## [1201] 2.791500e-01 6.793955e-01 -2.194274e-01 -2.030697e+00 -2.860673e-01
## [1206] -2.026478e-01 -1.144066e+00 2.163570e-01 -1.662545e+00 -4.584112e+00
## [1211] 2.552604e+00 -1.583434e+00 1.304980e+00 -2.098051e+00 9.408241e-01
## [1216] 2.939552e+00 2.846094e-01 -1.297481e+00 -2.999001e+00 -5.269467e+00
## [1221] -6.320867e-01 2.902386e+00 -4.104299e+00 1.531835e+00 2.300746e+00
## [1226] -5.020976e-01 -6.668583e-01 9.735924e-01 2.285000e+00 2.638305e+00
## [1231] 6.667212e+00 4.827248e-01 -1.494871e+00 -2.038412e-01 4.279713e+00
## [1236] 6.801485e-01 1.473402e+00 -8.330180e-01 -2.451931e+00 -8.429313e-01
## [1241] 6.139139e-01 3.254054e+00 -1.450065e-01 6.595189e-01 -2.108351e+00
## [1246] -9.249443e-01 -2.389718e+00 1.132148e+00 -6.026355e+00 -1.196315e+00
## [1251] -4.217670e+00 -7.087969e+00 3.783882e+00 -1.807924e+00 1.213903e+01
## [1256] -1.373916e+00 1.060787e-01 -3.651506e+00 1.081621e+00 2.111589e+00
## [1261] -3.091485e+00 -1.997444e+00 2.317279e+00 9.940674e-01 -1.654950e+00
## [1266] 1.731754e+00 -8.079211e-01 3.660431e+00 -1.285637e+00 6.149956e+00
## [1271] 1.171865e-01 2.449122e-01 -2.271551e+00 -5.368305e+00 -8.071207e-01
## [1276] 6.110900e-01 -4.531593e-01 -2.496420e-01 -2.788398e+00 3.114610e+00
## [1281] -2.834167e+00 9.423439e-01 -3.124308e+00 -3.937731e+00 3.532990e-01
## [1286] 1.280996e+00 3.951821e+00 1.102442e+00 -5.327245e-01 1.366928e+00
## [1291] 4.199145e+00 -9.311612e-01 -1.363135e+00 -1.677308e+00 3.636261e+00
## [1296] 2.223018e+00 2.091284e+00 3.996585e-01 3.331522e-01 3.973485e-01
## [1301] -4.922777e-01 1.539835e+00 -1.803108e+00 3.234906e+00 9.358604e-01
## [1306] 1.451065e-01 -3.848808e-01 -3.512102e+00 -3.945013e+00 -3.345683e-01
## [1311] 2.093234e-01 2.160908e+00 3.599276e-02 1.182194e+00 -9.271848e-01
## [1316] -1.441231e-01 -2.494096e+00 -5.074610e-01 3.599523e+00 1.198512e+00
## [1321] -5.405197e-01 5.088000e+00 1.499980e+00 8.505920e-01 -3.212830e-01
## [1326] 1.482784e+00 -8.220261e-02 9.325402e-01 -2.368262e+00 1.043821e-03
## [1331] -1.380859e+00 2.261467e+00 -2.234103e+00 5.792710e-01 1.351497e+00
## [1336] 2.922568e+00 4.020088e+00 -5.168483e-01 -2.930612e+00 -1.045944e+00
## [1341] -2.831505e-01 -8.012909e-01 -1.353791e+00 2.283386e+00 9.055239e+00
## [1346] 3.540240e-01 8.466622e-01 2.908709e-01 4.817472e+00 1.022732e+01
## [1351] -8.452119e-01 3.018533e+00 -3.670392e+00 4.332776e+00 -5.555308e-01
## [1356] -7.869054e-01 7.779307e-01 1.995847e+00 2.163267e+00 4.420525e+00
## [1361] 5.088858e-01 -1.241795e+00 2.410832e-01 -5.030067e+00 -1.183793e+00
## [1366] 4.331889e+00 -3.152277e-01 1.889697e+00 -1.046240e+00 8.484779e-01
## [1371] -1.450207e+00 1.539523e-01 2.896179e+00 -2.175345e+00 2.932276e+00
## [1376] 6.630523e-03 1.315128e+00 -3.757857e+00 -7.859144e-01 4.673239e+00
## [1381] -1.111821e+00 1.411951e+00 -7.734612e-02 2.885530e+00 1.664667e+00
## [1386] 1.036625e-01 -5.752156e+00 -2.577912e+00 2.782328e-01 -5.436676e-01
## [1391] -2.173852e+00 -4.344386e-01 4.215850e+00 6.316448e-01 -3.526950e+00
## [1396] -1.609234e+00 1.065994e+00 -1.727181e+00 -9.451629e-01 8.483652e-01
## [1401] 1.064656e+00 2.616695e+00 1.265154e+00 1.317280e-01 8.251193e-02
## [1406] 3.827630e+00 -5.209006e+00 -1.940322e+00 -2.692920e+00 2.386046e+00
## [1411] -1.417540e-01 -8.173052e-02 2.924451e-02 2.131888e+00 4.113000e+00
## [1416] -7.446280e-01 4.435131e+00 2.719014e-01 -3.181342e+00 9.229120e-01
## [1421] 4.011351e+00 -2.339737e+00 2.918260e-01 8.212446e-01 -1.043490e-01
## [1426] -1.939307e+00 -5.771479e-01 -7.472789e-01 2.354664e+00 9.892733e-01
## [1431] -2.227032e+00 -1.705901e+00 -2.953027e+00 3.812734e+00 -3.478248e+00
## [1436] -1.289935e+00 -1.795222e-02 -5.408331e-02 -5.262921e-02 1.946620e-02
## [1441] 9.721233e-01 -1.735156e+00 2.235259e+00 -1.292164e+00 9.165501e-01
## [1446] 7.380776e-02 -1.440309e+00 -4.217396e-01 -2.446030e-01 1.154662e+00
## [1451] 1.760541e+00 -2.252501e+00 4.613911e-01 -3.146508e-01 -5.047665e+00
## [1456] -2.953883e+00 -4.841969e+00 7.461829e-01 -3.926743e-01 1.965119e+00
## [1461] 9.544922e+00 -8.682108e+00 1.345654e+00 3.898755e+00 -7.289954e-01
## [1466] -3.579915e+00 -6.779392e-01 -6.445720e+00 -2.562310e+00 5.524862e+00
## [1471] 1.043944e+00 -3.174943e+00 3.579890e+00 4.462430e-01 -2.079407e+00
## [1476] 1.815716e+00 -1.614281e+00 4.999373e+00 -3.114615e+00 -1.441187e-01
## [1481] -2.543521e-01 2.651111e+00 1.659079e+00 -4.698419e-02 -6.395496e-01
## [1486] 3.231943e-01 -3.248355e+00 -2.079954e+00 -3.177609e-01 2.585156e-01
## [1491] 3.170429e+00 -3.163746e+00 7.459939e-01 8.947683e-01 -4.053998e-01
## [1496] -6.335015e+00 1.296322e+00 -3.719490e+00 8.260255e+00 -3.560590e+00
## [1501] 4.746985e+00 2.257184e+00 -1.869726e+00 1.013050e+00 -1.029934e+00
## [1506] 4.294729e-01 1.029479e+00 -5.293072e-01 7.253293e-01 1.272357e-01
## [1511] 2.756046e+00 6.764041e+00 2.906245e-01 2.683232e-01 8.155565e-01
## [1516] -7.149765e-02 -9.571665e-01 1.304934e+00 -7.338984e-01 -8.395293e-02
## [1521] 2.419496e+00 4.301795e-01 -1.045188e+00 -1.628345e+00 4.542983e-01
## [1526] 2.167946e+00 2.397981e-01 6.396928e+00 -2.598564e-01 1.672871e+00
## [1531] -5.680085e-01 -1.242960e+00 1.320190e+00 -6.027937e-01 1.987781e-01
## [1536] -2.374952e-01 -2.881488e-01 3.158398e+00 -7.745443e-01 1.122745e+00
## [1541] 2.703184e+00 1.823402e+00 -3.932296e+00 4.778669e-01 1.143869e+00
## [1546] 3.821056e-01 -4.073136e-01 -1.091678e+00 -1.998053e+00 -1.559583e+00
## [1551] 6.186612e-01 9.698308e-01 2.193272e-01 -4.306491e-01 -6.661801e-01
## [1556] -3.030840e+00 2.772330e+00 1.173454e+00 1.667722e-01 4.254608e+00
## [1561] -3.486367e-02 -1.428574e+00 -2.536538e+00 1.570693e-01 -5.990869e-01
## [1566] 8.266232e-02 1.175839e+00 -2.053484e+00 2.688836e-01 -1.930504e-01
## [1571] -1.310103e+00 -1.023734e+00 -1.198382e+00 4.545412e+00 4.490957e-01
## [1576] 1.238929e+00 -3.865612e-01 1.248262e-01 2.214540e-01 9.855320e-01
## [1581] -1.151561e+00 -1.349676e+00 2.985928e+00 7.377103e-01 -1.460584e+00
## [1586] 1.993631e-01 9.247638e-01 -8.563865e-01 6.020845e-01 2.181070e+00
## [1591] 4.183995e+00 1.319775e+00 -8.124206e-02 1.433946e+00 6.161350e-01
## [1596] -1.732664e+00 8.162195e-01 4.643278e-01 -1.073808e+00 -4.927912e-02
## [1601] -5.454451e-01 1.134382e-01 2.187678e+00 -1.035426e+00 -3.392953e-01
## [1606] -6.185094e-01 2.571498e-01 1.274975e+00 -1.283341e+00 -1.393734e-02
## [1611] -7.700403e-02 -1.761322e+00 -2.089934e+00 -7.002063e-01 1.503537e+00
## [1616] 7.423672e-01 -8.088333e-01 7.771849e-01 2.144521e+00 -6.950938e-01
## [1621] -1.524826e-01 2.411240e+00 -4.822585e-01 1.225801e+00 2.642184e+00
## [1626] -4.037494e+00 -8.173221e-01 7.915753e-02 -3.381192e-02 -1.023034e+00
## [1631] -2.934123e+00 1.282234e+00 -1.624717e+00 3.949305e+00 -1.276705e+00
## [1636] -1.671726e+00 -2.937280e+00 1.524239e+00 -5.131220e-01 1.192017e+00
## [1641] -3.678070e+00 3.677394e-01 -5.346060e-01 9.441519e-01 1.791890e+00
## [1646] 4.789210e-01 -8.902286e-01 -6.505535e-02 -3.848828e-01 8.585353e-01
## [1651] 8.171909e-01 -4.880827e-01 2.173480e+00 1.356695e+00 5.140684e-01
## [1656] -1.232236e-01 -4.679875e-01 3.920479e-02 1.229755e+00 -3.183827e-01
## [1661] 5.803968e-01 -1.236846e+00 2.665368e-02 -3.664840e-01 -2.220734e+00
## [1666] -6.589156e-01 1.179356e+00 -3.777348e+00 6.158504e-01 -2.296597e-02
## [1671] 2.225248e+00 2.035811e+00 -2.975943e-01 4.025454e+00 1.709932e+00
## [1676] 1.333986e+00 1.291929e-01 8.934877e-01 1.005646e+00 -2.645853e+00
## [1681] 1.569816e+00 -1.322785e+00 -6.976207e+00 -2.144669e+00 3.933030e+00
## [1686] 9.499552e-02 -1.861988e+00 -2.060581e+00 -2.343457e+00 -1.581954e+00
## [1691] 6.710238e-01 1.364123e+00 1.768224e+00 -1.908660e+00 -7.400995e-01
## [1696] 2.219819e+00 8.763296e-01 5.485860e-01 2.537992e+00 -3.149230e-01
## [1701] -1.027715e+00 -2.538071e+00 -1.593368e+00 1.155770e+00 4.612970e-01
## [1706] 5.225987e-01 -3.704923e+00 -4.646924e+00 2.276648e+00 -2.495220e+00
## [1711] 2.059672e+00 -1.054047e+00 2.386273e+00 1.215407e+00 -2.829698e+00
## [1716] -1.308835e+00 -1.944109e+00 -5.313135e+00 1.195376e+00 -1.443945e+00
## [1721] -2.215949e+00 9.276813e-01 -1.592505e+00 -5.278250e+00 -1.661974e+00
## [1726] -5.290373e-01 2.547471e+00 1.695633e+00 -1.051400e+00 3.632446e+00
## [1731] 8.480207e-01 -4.010688e-01 -7.367499e-02 -4.886693e-01 -4.500032e+00
## [1736] 5.824277e+00 2.389522e+00 -1.404573e+00 -2.980334e+00 -1.308706e-01
## [1741] 1.263279e+00 2.384497e-01 2.263917e+00 -7.274258e-01 5.434455e-01
## [1746] -2.424777e+00 4.533023e-02 -2.349215e+00 -1.986249e+00 1.642566e+00
## [1751] -1.939562e+00 -7.915310e-01 3.073665e+00 2.750551e-01 3.135976e-01
## [1756] -1.482518e-01 -1.215991e+00 2.375633e-01 -4.264185e-01 7.556771e-02
## [1761] 5.735606e-01 4.156317e-02 -7.942644e-01 1.487107e+00 -1.041233e+00
## [1766] 1.398657e+00 1.365481e+00 7.317054e-01 8.945534e-01 2.699710e+00
## [1771] -1.575616e-01 -2.581329e+00 -3.094039e-01 -5.637624e-01 -1.363971e-01
## [1776] 4.891296e-01 4.042162e-01 4.536305e+00 1.685242e+00 -1.423794e+00
## [1781] -3.033295e-02 -4.451543e-01 -1.542305e+00 -1.176734e+00 -4.584041e+00
## [1786] 1.189284e+00 9.390364e-02 4.675516e-02 -4.417731e-01 -2.842213e+00
## [1791] 1.964521e+00 9.575322e-01 9.037012e-02 -5.167964e+00 -5.133116e-01
## [1796] -6.544172e+00 -2.100675e+00 2.234527e+00 -3.888454e+00 -3.464288e+00
## [1801] -1.412598e+01 1.252054e+01 -1.802636e+00 1.415917e+00 -1.744605e-01
## [1806] -1.915426e+00 -2.616430e+00 -1.149912e+00 3.993859e+00 1.322510e+00
## [1811] -1.400081e+00 8.833337e-02 -1.959347e+00 -1.574654e+00 8.007428e-01
## [1816] 1.563420e+00 5.170018e-03 -4.991814e-01 -4.509771e+00 -8.294734e-01
## [1821] 6.058818e+00 -7.373920e-01 -2.334421e+00 1.695428e+00 -1.892045e+00
## [1826] NAsp_returns <- (sp500$sp_close - sp500$sp_open) / sp500$sp_open
head(sp_returns)## [1] -0.011457074 -0.013109772 0.012747817 -0.005993095 0.006103437
## [6] 0.001752335sp_returns * 100## [1] -1.1457074072 -1.3109772140 1.2747816650 -0.5993095281 0.6103436507
## [6] 0.1752334507 0.6078356648 0.4795508308 0.6588953661 -0.2738110050
## [11] 0.6215878793 -0.9621863934 -0.0010169563 0.6156065534 -0.6877305326
## [16] -0.7854742202 0.7779656064 1.4658708479 0.0448448035 -0.1208586434
## [21] 0.1421612598 0.6784768430 1.0774722473 -0.0399975200 0.1389177514
## [26] 0.1765295612 0.7980728666 0.0795273721 0.2781953421 -0.4085378420
## [31] 0.7406264611 0.2714350202 -0.3957136666 -0.5828127984 1.0900053980
## [36] -0.8507450210 1.0000565110 0.0618951875 -0.0365256409 -0.0468314291
## [41] 0.1267213633 -0.4032818510 0.0162256448 -0.3440953587 -0.2267196236
## [46] 0.7790570574 0.5287044451 -0.9426946334 0.0424122836 -1.6344014433
## [51] 0.9204932983 1.0720223048 -0.1589930487 -0.9147962721 0.4204023386
## [56] 0.9012656668 -0.3058573582 0.6448109288 -0.4234501406 0.1049814221
## [61] -0.0252278378 -0.1581695561 -0.3434106894 0.0309091671 0.0338767871
## [66] 0.5668105025 -0.0666729164 -0.1547139073 -0.3175161988 0.2511520953
## [71] 0.1070032093 0.1610015196 -0.2042155121 -0.5923909458 0.0352989442
## [76] -0.9115718730 1.2313734107 0.5167359551 -0.1748576990 0.2236336890
## [81] 0.1462176354 0.1332577439 -0.0328461981 0.1596517500 0.4466674501
## [86] 0.5949185391 -0.2965692785 0.1636428685 -0.0057856043 0.9278447021
## [91] 0.2794734740 -0.2707070135 -0.1326464124 -0.2057723319 -0.9220529673
## [96] -0.8823589245 1.3587034606 0.6363249161 0.1423888205 0.6982069384
## [101] 0.2884566407 -0.3378314880 -0.0524661532 0.3533494069 0.0031773520
## [106] -0.4470236777 0.6922710278 -0.3009553658 0.4590809189 0.1682112861
## [111] -0.1221316529 0.0216412619 0.0051771981 0.3317529091 0.0707787146
## [116] 0.4047843060 -0.3146495095 -0.9157953589 0.5330332781 0.7053494991
## [121] 0.6570301225 0.0408098779 0.1278211726 -0.5285118220 0.7883153877
## [126] 0.3329878908 -0.1560753732 -0.1040002018 0.0544762543 0.0664160417
## [131] -0.3384523028 -0.0889760866 -0.4374063108 -1.0725693952 -0.1358734347
## [136] -0.8099486487 0.7467123970 -0.0745985421 -0.8221954313 -1.0270435240
## [141] -0.4631497217 0.6459167016 0.9583021607 0.3929649407 0.0222809395
## [146] -1.5139619883 -0.0676276463 -1.4443983174 0.9237526839 -1.1124779148
## [151] 0.8318138756 1.0181564892 0.3656654317 -0.3442616193 -0.5529661864
## [156] -0.4042789091 0.1328597083 1.1742124722 0.5324151659 0.5094348436
## [161] 0.4956271893 0.2601442778 0.3869951696 -0.0268407964 0.2808719791
## [166] -0.0851750696 -0.6231149972 0.7359468944 0.7109269407 0.0661473860
## [171] 0.3752175036 0.6461279195 0.3673630564 -0.0368138931 0.0046839473
## [176] -0.4673641723 -0.5042504244 -0.2171983219 0.5930921261 -0.1386134449
## [181] 0.4590308377 -0.2728932920 0.0812604036 -0.2225786163 -0.6167245033
## [186] 0.2612005372 0.5492169640 -1.5008643212 0.5729412807 -1.5785787404
## [191] -1.9505387694 1.6065361853 -1.1125431363 0.9519850754 1.1826454536
## [196] 0.2206439322 -0.5020209910 0.5200886182 -0.8774301331 -0.1916952260
## [201] 1.5828916315 -1.0692640845 -0.6847901834 -0.4333111715 1.1810770930
## [206] 0.9934757023 0.4640787402 1.2082768278 -0.1905985889 0.0923001468
## [211] -0.3233053079 -0.1890971335 0.3855040109 -0.2283214542 -1.8256126678
## [216] 0.0566683760 -0.4391626982 0.3211407935 0.9408517674 -0.0473660471
## [221] -1.5745078232 0.5360050803 -1.1901449041 -1.2046569469 -1.4210499698
## [226] -1.6424446889 1.2352182752 -0.2333588546 -1.3270029844 -1.2343185500
## [231] 2.2060877762 1.8899759440 0.5967429621 0.5034555832 -1.2781691809
## [236] 0.3957300239 -0.4855991303 0.9267820088 0.8836634216 -1.0796741160
## [241] -1.9446212152 -0.2479245106 0.9434951299 0.4322452028 -1.7010608468
## [246] -0.8142123050 -0.6457915138 -2.2990007177 3.1986894163 2.0070357177
## [251] 0.4540479560 -1.3036567543 1.4801409258 -0.8592856153 -0.3051504713
## [256] -2.9100910027 -0.7604697917 1.2971462643 0.1639067186 -1.7569795865
## [261] -0.7052557663 1.7577831987 1.6258733236 1.5318383352 1.2656222441
## [266] -0.0273334212 0.9511929627 -0.8203659496 1.1226040385 0.4455074642
## [271] 0.7581919091 0.6243995088 -0.4703516085 -1.4918365867 0.1220186964
## [276] 0.7623163793 -1.0351141314 -0.2897091066 0.5712191825 -0.1306168534
## [281] -1.1228857812 -0.9045371441 1.1899515597 -1.2705944535 0.1381798910
## [286] 1.6302917813 -0.2864227702 -2.1275595998 -2.6004266225 0.9583317651
## [291] -2.4061844193 -0.0611500383 1.5374467902 -2.8638219035 0.5996697909
## [296] 0.3774285208 2.8458411523 -2.8933866966 -0.1170028903 -2.2059317042
## [301] -0.8458082016 -1.3759159067 0.6693253571 1.5134083027 -0.1248438767
## [306] 0.9094298533 -3.1663544600 0.0459102093 -0.6721363392 1.3861765059
## [311] -0.0370272172 1.2505093783 1.8380763048 1.9818931064 -0.4562643094
## [316] -1.1699368931 1.9878330584 -0.7016143869 -0.3214253534 1.5674460589
## [321] -0.7559486287 -2.0438076379 -1.8500898790 -2.3063200183 -0.7450482239
## [326] 0.6891497475 -1.6471820898 0.2438742406 1.3317860337 0.6963247645
## [331] 0.5568644942 2.3546801919 -0.5266811101 -2.3370802753 -0.1636565315
## [336] -0.0161148715 1.1724432194 1.0225091443 0.3418623720 1.1342762332
## [341] 0.2859858399 -0.6830821957 -0.8606005468 0.5849745581 0.7011148448
## [346] 1.1828159274 -1.3630999841 1.9675025532 0.6245955490 1.0992367731
## [351] -0.9203624787 0.0282449895 -0.8137650349 1.8266849477 1.1499889516
## [356] 1.0510519120 0.1519801229 -0.3172357081 1.1492312823 -0.0700423886
## [361] 0.7123602880 -0.3818667907 -0.2574247671 0.6988776592 -0.4761764507
## [366] 1.3048431145 0.6504476953 0.3435583716 -0.1485810538 0.2483039798
## [371] -0.8867165678 -1.3608761379 -0.1054867774 0.3446030102 1.1042013780
## [376] -3.3600631235 -0.0983986097 -1.3631942565 -1.1415568584 0.7651049815
## [381] -1.7623503350 -0.5774761388 1.8018019706 1.1676942307 1.1041717416
## [386] 0.6548089069 -2.5867492854 0.1339860717 -0.7898417293 -0.1963404100
## [391] 1.2982116883 -0.4980362179 -2.1044059709 -0.6443098091 -0.9098105541
## [396] -0.7516165188 -1.0619975631 1.8373822881 -1.2622704831 -1.3171907796
## [401] 1.9017752269 1.7300593963 0.8001073549 -0.7277351460 -1.8096785397
## [406] -0.9628518385 -0.1952250455 -0.3843136135 4.2478429808 -2.9086157448
## [411] 1.0800722763 -0.7015004092 -0.2146896820 -0.6307862247 2.6154575973
## [416] 0.9391277012 1.5704989929 0.1210183820 -0.7142661596 2.4368096871
## [421] -0.2542632234 -1.1709994887 -2.4192157414 -0.3578680084 0.0947726927
## [426] 0.6900843535 0.2905430895 -1.6366007863 2.4995589847 0.7369330112
## [431] -0.5208679516 -0.3664111252 -0.4533780505 0.6965613090 -0.0264675112
## [436] -0.1589907334 0.9600295615 0.6739484691 0.0690975467 -1.0341184040
## [441] -0.1654829534 3.1065096332 -0.2586117553 0.7804134456 -1.3124301308
## [446] -1.3854140781 0.0162686758 0.3981967265 -0.5004852966 1.3015040533
## [451] -1.2220530376 -0.5035429981 -1.5819672070 -0.9907657992 -0.9375219352
## [456] 0.2926186683 1.0144563802 -0.8011428533 0.7787445212 -0.3666104890
## [461] -1.2100629624 1.1517712409 0.2726502391 -0.7565001905 0.3283510642
## [466] -0.8240113304 1.8755694254 -0.4789271851 0.7889772102 0.9475252417
## [471] 0.1407857918 0.9718221806 -0.2077888653 -1.8337158493 -0.3320685392
## [476] 1.6262322136 1.0474786493 0.3800836880 0.8413871483 0.6033045193
## [481] 0.4154230685 -0.7779179913 1.3865227165 1.2073475825 0.5068817258
## [486] -0.0050755783 -0.2060833159 1.4286212125 -0.8573638360 -1.5141461061
## [491] 0.5293797734 0.9927677137 0.2285043026 0.6821239873 -0.5915326056
## [496] 0.0416981294 -1.3574841374 -0.2693774870 -0.1562740543 -0.0805375759
## [501] -0.2534870832 -0.1770103809 -0.3015182913 1.0833621101 1.1910864081
## [506] -0.1659613240 -1.5288023108 0.1118471463 -2.0091692096 -1.3080229961
## [511] 0.5381811246 0.6492029870 0.3918225479 2.0972303983 -1.0622213270
## [516] 0.8704622604 0.6785958701 -1.6259224726 -0.2649516024 0.8067614982
## [521] -0.1355761321 -0.0719619984 0.7070838096 0.1010711808 1.3098562650
## [526] 0.5438440166 -0.6644740694 -0.1006256487 0.5848870480 0.5852813178
## [531] -0.0328467734 -0.7222776443 1.1263347514 -0.0596536479 0.3420188827
## [536] -0.2254818135 0.3669661786 -0.0167036618 0.0333939016 0.1202839026
## [541] -1.3280315099 -0.7776846806 1.4737615732 0.9649798841 0.0259211075
## [546] -1.0691390333 -0.7641457942 -0.5224694828 1.2612833597 0.0275596383
## [551] -0.1231758047 -0.1472123567 -0.0392067522 -0.3493976330 0.2333583667
## [556] -0.4372701248 0.8712400651 0.9709652306 -0.2894740235 0.0441468593
## [561] -0.7474556604 -0.4287417911 -0.1066045471 1.1859513880 -0.5013341725
## [566] -0.2603395973 0.9081989927 0.9752477322 -0.2148077583 0.2928882825
## [571] -0.4188617447 0.5912876016 -0.1398417539 0.7104939469 0.3767831912
## [576] 0.1442827808 1.3861441069 -0.7061630999 -0.1683284216 -0.3269358971
## [581] 0.6082158922 -0.1341207131 -0.3687136950 0.9464350264 0.2147664753
## [586] 0.4914353177 0.6317766160 0.1148160042 0.1076033785 -0.2494058532
## [591] -0.1269109533 0.3481794252 0.5369650890 0.1000565147 0.4127805647
## [596] -0.2035600347 0.3089511806 0.7342284872 0.0405379121 -0.4283737002
## [601] -0.3037324407 0.2476124581 0.2693635104 0.1708731625 -1.3233182220
## [606] 0.3609479378 0.0903009688 -0.0458653765 -0.8248871684 0.1695518328
## [611] -0.7959790537 0.5980047737 0.0300153116 -0.7521790087 -0.4085006438
## [616] 0.3001751067 0.7086005312 -0.9156383827 -0.6644419487 -1.0406846145
## [621] 0.5714790465 0.4449540972 -0.6291777273 0.9000424149 -1.7698600026
## [626] 0.3720361090 0.1644876738 1.4636485886 0.3228705818 -0.2069866983
## [631] -0.3273314308 -0.2933437758 -0.5538569743 0.3741153615 0.1390701584
## [636] 0.1446107882 -0.2541790935 0.1073362053 0.3859439039 -1.0595902262
## [641] 0.1889686593 -0.0328419850 -1.1365825763 -1.0140881104 -0.4993429964
## [646] 0.6221801850 -0.9123856617 -0.1896058592 0.7038116393 -0.9271880898
## [651] 0.0903279053 -0.9438445972 0.7066868845 -0.0262980899 1.7405812392
## [656] 1.0874310800 0.4260668097 0.2372641336 -0.7151451183 -0.7501553142
## [661] 0.7198779648 0.6436992971 -0.9811008765 -1.0033846903 -1.1626505439
## [666] 0.1577079820 0.2807064706 -1.0785768706 -0.9281691702 -0.8562643023
## [671] 0.6626504532 0.5386705473 0.8709234013 1.1601922622 0.5562663585
## [676] 0.0391809152 0.2787296530 -0.0362727596 -1.0033236939 1.1706823362
## [681] 0.1109604159 0.8237323575 -0.0537127823 0.2481644991 0.0991277408
## [686] 0.7908257631 -0.0127805137 0.0786304995 0.0768244741 -0.0972518943
## [691] 0.2054829984 -0.4650155375 0.2838651195 0.7720198725 0.1185194853
## [696] 0.2178984208 -0.8043673535 0.3666138576 0.6155745088 0.6324262434
## [701] 0.5499944070 1.3105257173 -0.0315658067 0.1052125365 0.3169977065
## [706] 0.5196322976 -1.3931509883 0.4754145226 0.0149342216 0.3339063804
## [711] 0.1703146043 -0.0645541109 -0.2728440815 -0.0499476753 -0.4287717722
## [716] -0.1860541795 0.1422089513 1.2721866034 0.3072551404 0.4939191291
## [721] -0.2481078086 -0.1534089178 -0.1334796705 0.0016897221 0.4378026370
## [726] 0.9075841149 -0.0616008122 0.1606056103 -0.4093281798 0.1534790585
## [731] 0.0421373788 0.7149057128 -0.0186752414 -1.0928345237 0.9273618452
## [736] 0.8655265432 -0.2900813360 0.0822160110 0.4425906591 0.0550532899
## [741] 0.4484248488 -0.0992719924 -0.2973067248 0.4858930494 0.5314631016
## [746] -0.5080381383 -0.2767924102 0.3781967940 0.9565654385 -0.2376064979
## [751] -0.4608328067 0.0705489705 0.0505125161 0.2145404955 0.7565016892
## [756] -0.0007803379 -0.6236178914 -0.0640172370 0.4867133969 -0.7894343230
## [761] 0.1169801899 0.7979708315 -0.1581171590 -0.4765118547 -0.1214100801
## [766] -0.1037892600 0.7670603759 0.8284975803 -0.2265261025 -0.1583182905
## [771] -0.0254827670 -0.4832806269 0.4243945639 0.1204321004 -0.2700699078
## [776] 0.0292070488 0.3295898598 -1.8466614040 0.8798233501 -0.1723151545
## [781] -0.1364690101 -0.1400912223 0.5047383465 -0.9300883408 -1.7059364773
## [786] -0.2602320801 -0.9224803446 -0.4054421381 -0.7633686826 0.4665827039
## [791] 0.8292095851 -0.2601837774 0.5685402784 0.3011034956 0.0398902474
## [796] -1.3341062235 -0.2115646336 0.2947005064 0.0978034215 0.7451805392
## [801] 0.0096391113 0.3615789087 0.4827548502 -0.0537759802 -0.2228163161
## [806] 0.4899365583 0.8528960895 -0.2442477593 0.0032041989 0.0523958854
## [811] 0.4287892874 -0.2306706928 -1.3561123438 0.4405990527 -0.1856712566
## [816] -0.2231556681 -0.4618080063 0.6541756852 -0.2595735490 0.2481813785
## [821] 0.7441895507 -0.0903326725 0.0595113926 0.3663923866 0.4169591672
## [826] 0.2199966095 -0.1504969954 0.1386413811 0.7755342508 0.1986775930
## [831] -0.4876429113 -0.0393267384 -0.2144846448 0.1569355059 0.3147931593
## [836] 0.1695463800 -0.5101594631 0.0732902017 0.8636269686 0.5370930676
## [841] 0.5287154239 0.0017961986 -0.1300132803 0.7628046704 -0.8991665302
## [846] 0.4398388245 -0.1230887597 0.4094610859 -0.3885834824 -1.1405817924
## [851] -0.6921803231 0.3583726882 -0.1717709854 -1.4295722936 -0.5430393908
## [856] 0.4680110523 -0.2375540457 -0.7718949321 0.3035090047 -1.6461232275
## [861] -0.5592690007 0.6831485938 0.6455465327 -1.7688944894 1.2706206030
## [866] 0.5550684170 -0.1399460798 1.0684472608 0.2361126052 0.7651215828
## [871] 0.4294367598 0.9180836444 -0.1028000911 0.3169724991 -1.1907169427
## [876] 0.5733098598 -0.4046398518 0.4088901872 -0.5747983592 -0.2735691738
## [881] 0.6353343729 -1.6885102416 0.2431528255 -0.3019869574 -1.7959729097
## [886] 0.5325176156 0.0912529823 1.0499554575 0.6887975358 0.4047617388
## [891] 0.3184187757 -0.3700760562 -0.4151318300 0.1930732685 -0.1241817674
## [896] 0.1167723873 0.0920099899 -0.1986542065 -0.2924237018 -0.2986770908
## [901] 0.6279548629 -0.8506821375 0.2000635658 0.0307115070 0.2368608483
## [906] -0.7295455524 0.5593453794 0.6996111781 0.0292460395 0.6915899577
## [911] 0.5152833242 -0.8774969863 0.4451092630 -0.5812135853 0.0894241579
## [916] -0.0655507316 0.3171772829 -0.6355313759 -0.1364767038 -0.3197302581
## [921] -0.1784415640 0.2274995480 -0.3254092186 -1.2101391490 0.0974903924
## [926] -0.2176355406 1.0542651984 1.0937954650 0.4353324818 0.3142216548
## [931] -0.1249782121 -0.3266350683 -0.0061833051 -0.6763341734 -0.7131983648
## [936] 0.3311139373 0.7994851380 0.0468356504 0.1368533494 0.4202299498
## [941] -0.0819332232 0.3599998405 -0.2555594968 0.4730179387 0.1165548181
## [946] 0.1143422477 0.2817432604 -0.2286065657 0.1461861763 -0.4958017352
## [951] -0.3744011741 0.3966905019 -0.3793042300 -0.2814700041 0.1696964934
## [956] -0.0320516389 -2.9017841464 -0.7717253698 1.5208849308 0.5693333482
## [961] 0.9258744038 0.2094554571 -0.5882297468 -0.2318991035 -0.6437841874
## [966] -0.5879795624 0.8725136887 -0.1241920721 -1.4054118086 0.1284094086
## [971] -1.0748097744 0.9373920382 -0.2792133359 0.7569619981 -0.4405053337
## [976] 0.0210203477 0.5839610201 0.0818888504 0.6976284650 -0.3298239272
## [981] 0.7244003359 0.6757952838 -0.3035828140 0.3374775338 -0.9227848351
## [986] 0.4174436070 0.6625344722 0.6815069276 0.1869103717 -0.9393133064
## [991] 0.3314375395 0.3170633449 0.4463033913 0.8989220831 -0.0145553725
## [996] 0.1303577552 0.4313692876 -0.2767948564 -1.6514321524 -0.7207927043
## [1001] -0.4593217571 -0.2480385321 -2.0112416322 1.6691839097 -1.9873207703
## [1006] -0.5820749252 1.0597856037 -0.8183747076 0.7717491149 -1.5916593793
## [1011] -0.5635626543 -0.4540580669 -1.3036164991 1.3496022077 0.7012566337
## [1016] -0.7050918542 0.7620223988 0.2828128443 0.6540906464 0.8654958556
## [1021] 0.0119450517 -1.0302055098 -0.0409098551 -1.7301776751 1.5184751386
## [1026] 0.6349236257 1.6164546228 -1.7517707144 -4.1204513290 2.1894339502
## [1031] -4.0588614734 9.9011563992 -1.5897200566 2.0511573169 -0.6613379435
## [1036] -0.2838207553 -1.1254238802 -0.4288043269 -1.4282553771 1.5379208927
## [1041] -0.3717634599 1.9212569819 0.6462973697 -0.0085041801 0.9432054093
## [1046] 1.2659492226 -0.3733240326 0.7224744399 -0.0873503455 0.0185526785
## [1051] 0.3045789205 0.0060004899 -0.3475521631 0.6369635082 0.5534518740
## [1056] -0.0705501020 0.8025859903 0.4940056541 1.0286540816 -0.0706549273
## [1061] -1.1094469297 0.0128396961 0.3619869455 1.1525351912 -0.6242508553
## [1066] -0.4678489290 0.1358480341 0.6657943869 0.5356527219 -0.1359753216
## [1071] -0.7746855038 0.2221424966 0.0208172697 0.4808707883 -0.4486352149
## [1076] 0.5883602698 -0.3931273668 0.4848411606 -0.4895035549 -0.1179048250
## [1081] -0.5305304882 0.9296996438 0.5109576313 -0.1977288578 0.4733270701
## [1086] 0.3636923959 0.1871412656 0.1739022284 0.5415028980 0.5265404233
## [1091] -0.4642893864 -0.1365050524 0.3192156630 0.2179765857 0.0650580609
## [1096] 0.2143858494 -0.8185528088 0.1470972150 0.5421969133 -0.2559842189
## [1101] 0.0136383618 0.0478866502 0.5059389970 -0.0824356989 0.2924700555
## [1106] -0.1237934621 -0.5426524407 -0.2872499217 -1.3634605548 -0.7836460475
## [1111] 0.9284546134 -0.5908494278 0.5667864107 -0.5384076288 0.5386120278
## [1116] -0.2538429490 0.7910633239 0.0605037283 0.2336743114 -0.4257906534
## [1121] 0.0640786654 -0.5409372893 -0.1692051633 -0.1670653523 1.2893594501
## [1126] -0.2841597337 0.4731528745 0.2961833385 0.2779220333 -0.4471993887
## [1131] 0.2191713198 0.0378530811 0.7043951891 -0.7287409184 -0.0452431634
## [1136] 0.1426928211 -0.2786136170 0.5043941073 -0.0966537044 0.1785351437
## [1141] -0.2622248883 -0.0684346467 0.0771084785 0.2595112817 0.5931553244
## [1146] -0.5307484242 -0.4770738514 -0.0525064593 0.4280980533 -0.0055559970
## [1151] 0.4848121796 0.6943860388 -0.2371003683 -0.0944654162 0.0953379192
## [1156] -0.4676791814 0.4439422109 -0.3755659599 -2.7888248809 0.4860745173
## [1161] 0.6333947152 -0.2573155822 -0.8962478082 0.7672414092 0.6738377059
## [1166] -0.0207800845 -0.6221306503 0.5189715986 0.2897211295 0.4338670518
## [1171] -0.0993093016 -0.2946100172 -0.5562299577 -0.5664887916 -0.4409793522
## [1176] -0.2499840141 0.3917418089 -0.9910737254 0.4871378614 0.6937039958
## [1181] 0.4543920445 -0.2453503482 -1.3034551923 0.9287833483 -0.6136744296
## [1186] -0.3594253048 0.2463131148 -2.9559583575 0.7202847980 1.0333709692
## [1191] 1.0280691570 0.2805611078 0.3894429645 0.0048453259 -0.0232740897
## [1196] 0.5051901766 -0.1361703665 0.0594216149 -0.4173031893 -0.0014632856
## [1201] 0.7783715141 0.5786104156 -0.8630932947 -0.6367196266 0.0020536172
## [1206] -1.1972827455 -0.0486908192 0.6165497568 0.1934430777 0.5439122806
## [1211] 0.3930485383 -0.0876594662 0.0310002997 -0.0608614388 -0.7728832696
## [1216] -0.2855384521 0.1430584961 0.5325692014 -0.3475796363 0.1063057690
## [1221] 0.5550036100 0.4773808889 -0.1959168455 -0.1558226824 -0.3585607240
## [1226] -0.2949523072 -0.9960375567 0.9530600572 -0.0157618514 0.1123325711
## [1231] 0.3899913780 0.1814557762 -0.3423338310 -0.1251188559 -0.1186111142
## [1236] 0.8645788057 -0.9683003218 -0.6033617612 -0.5702502504 1.6952321247
## [1241] 0.6875563475 -0.4685672312 -0.5018256445 -1.7934539038 0.0277996383
## [1246] 0.3425341874 0.3767800095 0.0080201969 0.9681058774 -0.9201231661
## [1251] 0.7707598993 0.4480015749 -0.5166553375 0.3258180310mean(btc_returns, na.rm = TRUE)## [1] 0.0005721713mean(sp_returns)## [1] 0.0002495662sd(btc_returns, na.rm = TRUE)## [1] 0.02953908sd(sp_returns)## [1] 0.008971909mean(btc_returns > 0, na.rm = TRUE)## [1] 0.4975342mean(sp_returns > 0, na.rm = TRUE)## [1] 0.5318979