# Load packages
library(tidyquant)
library(tidyverse)
from <- today() - years(5)
stock_prices <- c("NFLX", "TSLA", "AMZN") %>%
tq_get(get = "stock.prices",
from = from)
stock_prices
## # A tibble: 3,774 x 8
## symbol date open high low close volume adjusted
## <chr> <date> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 NFLX 2014-11-26 50.2 50.5 49.7 50.2 10063200 50.2
## 2 NFLX 2014-11-28 50.5 50.6 49.4 49.5 6702500 49.5
## 3 NFLX 2014-12-01 49.3 49.6 48.2 48.8 11964400 48.8
## 4 NFLX 2014-12-02 48.8 50.5 48.7 50.3 14271600 50.3
## 5 NFLX 2014-12-03 50.2 50.7 49.2 50.7 13819400 50.7
## 6 NFLX 2014-12-04 50.4 51.1 49.9 50.1 11853800 50.1
## 7 NFLX 2014-12-05 50.1 50.6 49.7 50.1 9930200 50.1
## 8 NFLX 2014-12-08 49.9 50.0 48.3 48.5 13621300 48.5
## 9 NFLX 2014-12-09 47.8 49.3 47.0 49.1 17976700 49.1
## 10 NFLX 2014-12-10 49.0 49.2 47.7 47.8 12644800 47.8
## # … with 3,764 more rowsHint: Use NASDAQ Compsite Index as baseline.
stock_returns_monthly <- stock_prices %>%
group_by(symbol) %>%
tq_transmute(select = adjusted,
mutate_fun = periodReturn,
period = "monthly",
col_rename = "Ra")
stock_returns_monthly
## # A tibble: 183 x 3
## # Groups: symbol [3]
## symbol date Ra
## <chr> <date> <dbl>
## 1 NFLX 2014-11-28 -0.0130
## 2 NFLX 2014-12-31 -0.0144
## 3 NFLX 2015-01-30 0.293
## 4 NFLX 2015-02-27 0.0749
## 5 NFLX 2015-03-31 -0.123
## 6 NFLX 2015-04-30 0.336
## 7 NFLX 2015-05-29 0.121
## 8 NFLX 2015-06-30 0.0527
## 9 NFLX 2015-07-31 0.218
## 10 NFLX 2015-08-31 0.00630
## # … with 173 more rows
baseline_returns_monthly <- "^IXIC" %>%
tq_get(get = "stock.prices",
from <- today() - years(5)) %>%
tq_transmute(select = adjusted,
mutate_fun = periodReturn,
period = "monthly",
col_rename = "Rb")
baseline_returns_monthly
## # A tibble: 131 x 2
## date Rb
## <date> <dbl>
## 1 2009-01-30 -0.0954
## 2 2009-02-27 -0.0668
## 3 2009-03-31 0.109
## 4 2009-04-30 0.123
## 5 2009-05-29 0.0332
## 6 2009-06-30 0.0342
## 7 2009-07-31 0.0782
## 8 2009-08-31 0.0154
## 9 2009-09-30 0.0564
## 10 2009-10-30 -0.0364
## # … with 121 more rowsHint: Create 100 portfolios.
# scaling a single portfolio to num_port number
num_port = 100
stock_returns_monthly_multi <- stock_returns_monthly %>%
tq_repeat_df(n = num_port)
stock_returns_monthly_multi
## # A tibble: 18,300 x 4
## # Groups: portfolio [100]
## portfolio symbol date Ra
## <int> <chr> <date> <dbl>
## 1 1 NFLX 2014-11-28 -0.0130
## 2 1 NFLX 2014-12-31 -0.0144
## 3 1 NFLX 2015-01-30 0.293
## 4 1 NFLX 2015-02-27 0.0749
## 5 1 NFLX 2015-03-31 -0.123
## 6 1 NFLX 2015-04-30 0.336
## 7 1 NFLX 2015-05-29 0.121
## 8 1 NFLX 2015-06-30 0.0527
## 9 1 NFLX 2015-07-31 0.218
## 10 1 NFLX 2015-08-31 0.00630
## # … with 18,290 more rows
# Create Vector of Weights
# not all symbols need to be specified. Any symbol not specified by default gets a weight of zero.
# The following is what I tried based on the info on the Web.
# https://stackoverflow.com/questions/5622608/choosing-n-numbers-with-fixed-sum
# n = number of stocks in the portfolio
# Choose n - 1 numbers between 0 and 1
# Sort them and calculate the distance between each number
# Create a data frame # of columns = # of stocks in the portfolio and # of rows = # of portfolio
# n = # of stocks in the portfolio
# Case of two portfolios with three stocks
num_stocks <- stock_returns_monthly %>%
distinct(symbol) %>%
n_distinct()
num_stocks
## [1] 3
# Initialize data frame
weights <- list()
# Set the seed of random numbers so that they can be reproduced
set.seed(06182019)
# Loop through the values 1 to number of portfolios, to generate weights for stocks in the portfolio
for(i in 1:num_port){
# Generate n-1 number of random numbers b/t 0 and 1
weights[[i]] = runif(num_stocks-1, 0, 1)
# Add 0 and 1
weights[[i]] = append(weights[[i]], c(0, 1))
# Sort the random numbers
weights[[i]] = sort(weights[[i]])
# Calculate the differences b/t the random numbers
weights[[i]] = diff(weights[[i]])
}
weights[[1]]
## [1] 0.06385721 0.32707606 0.60906672
# Convert the list to a vector
weights <- unlist(weights)
weights
## [1] 0.0638572143 0.3270760642 0.6090667215 0.6674315634 0.0835250188
## [6] 0.2490434179 0.9486860994 0.0501059340 0.0012079666 0.3082285074
## [11] 0.3311331158 0.3606383768 0.1122350958 0.6053920568 0.2823728474
## [16] 0.5903503322 0.2067945255 0.2028551423 0.2308615067 0.0173753274
## [21] 0.7517631659 0.4117328513 0.0418477936 0.5464193551 0.3082213739
## [26] 0.2995600218 0.3922186042 0.5221402226 0.1136128758 0.3642469016
## [31] 0.0857777279 0.6071222641 0.3071000080 0.1944349897 0.0029123276
## [36] 0.8026526826 0.1962747315 0.0904070712 0.7133181973 0.1588861502
## [41] 0.1306861357 0.7104277140 0.8440541434 0.1414887353 0.0144571213
## [46] 0.7966482679 0.0351519424 0.1681997897 0.1807254998 0.6042723870
## [51] 0.2150021133 0.2389462919 0.5176046358 0.2434490724 0.3562180211
## [56] 0.3205262697 0.3232557091 0.4174840255 0.1583388411 0.4241771335
## [61] 0.1504051252 0.3887717656 0.4608231091 0.4359975604 0.2236178115
## [66] 0.3403846282 0.2422919362 0.5420307070 0.2156773568 0.2298394081
## [71] 0.4745642522 0.2955963397 0.6258799869 0.0470416916 0.3270783215
## [76] 0.0375024606 0.5680024794 0.3944950600 0.0067017451 0.4451984253
## [81] 0.5480998296 0.1778505542 0.0676041283 0.7545453175 0.6894674809
## [86] 0.1230664686 0.1874660505 0.2058625557 0.2131162025 0.5810212418
## [91] 0.2013536913 0.3865516332 0.4120946755 0.0952859495 0.0685476365
## [96] 0.8361664140 0.1381823656 0.7144982803 0.1473193541 0.3775856681
## [101] 0.2000978957 0.4223164362 0.0258709076 0.0040990973 0.9700299951
## [106] 0.2257158658 0.4868523953 0.2874317388 0.4520090686 0.0244057050
## [111] 0.5235852264 0.2803844183 0.6376286114 0.0819869703 0.0697063785
## [116] 0.0290425441 0.9012510774 0.2231925349 0.6202506609 0.1565568042
## [121] 0.0009567274 0.6347501962 0.3642930763 0.4652535468 0.5267369885
## [126] 0.0080094647 0.2455690326 0.5717535003 0.1826774671 0.3309030798
## [131] 0.3034736423 0.3656232778 0.2554464112 0.0708831192 0.6736704696
## [136] 0.1052531952 0.7828613615 0.1118854433 0.7046088497 0.0596986255
## [141] 0.2356925248 0.3761585231 0.1659869477 0.4578545291 0.3481856456
## [146] 0.3822073762 0.2696069782 0.5244447065 0.2792275760 0.1963277175
## [151] 0.6065907234 0.2213197036 0.1720895730 0.3427638044 0.5191903980
## [156] 0.1380457976 0.1276013840 0.4892495682 0.3831490478 0.1110758134
## [161] 0.2420915307 0.6468326559 0.0106872793 0.4357936298 0.5535190909
## [166] 0.1927190754 0.4503961648 0.3568847599 0.5162877000 0.4488447069
## [171] 0.0348675931 0.0060355372 0.2789414194 0.7150230433 0.2701046988
## [176] 0.4184351300 0.3114601711 0.2568394218 0.5781026899 0.1650578883
## [181] 0.1619223342 0.4994306306 0.3386470352 0.3610243672 0.0146180678
## [186] 0.6243575651 0.2348479216 0.0849322565 0.6802198219 0.5817097924
## [191] 0.1324886060 0.2858016016 0.1098506262 0.7657505460 0.1243988278
## [196] 0.6334049297 0.1678676454 0.1987274250 0.0912114033 0.7903820183
## [201] 0.1184065784 0.1932190827 0.1458225858 0.6609583315 0.4054246263
## [206] 0.2570355292 0.3375398444 0.3087824071 0.1639304662 0.5272871268
## [211] 0.6402869809 0.0111529650 0.3485600541 0.6183618691 0.0447616260
## [216] 0.3368765048 0.4133743953 0.2577889026 0.3288367020 0.5067144651
## [221] 0.0076246934 0.4856608415 0.7231894799 0.1317818118 0.1450287083
## [226] 0.5244801973 0.2174437300 0.2580760727 0.4000706738 0.3209665995
## [231] 0.2789627267 0.3616019287 0.6374677932 0.0009302781 0.3023019873
## [236] 0.1927107023 0.5049873104 0.1554450225 0.0488181734 0.7957368041
## [241] 0.0097467289 0.1565462507 0.8337070204 0.0703802700 0.8226276855
## [246] 0.1069920445 0.5283486014 0.1723249501 0.2993264485 0.2353959384
## [251] 0.4908058548 0.2737982068 0.9296928791 0.0003363329 0.0699707880
## [256] 0.6333949310 0.2909886991 0.0756163700 0.0715088164 0.2376923505
## [261] 0.6907988330 0.1826897927 0.3067737606 0.5105364467 0.0269268886
## [266] 0.8082488808 0.1648242306 0.1397872302 0.1511347455 0.7090780244
## [271] 0.4692959369 0.4335684299 0.0971356332 0.1340574222 0.7232535251
## [276] 0.1426890527 0.8350737332 0.0936780574 0.0712482093 0.0399914719
## [281] 0.8819474026 0.0780611255 0.1437206552 0.2424383720 0.6138409728
## [286] 0.1119870632 0.4740645280 0.4139484088 0.4601041367 0.2248874852
## [291] 0.3150083781 0.1636324150 0.2519571851 0.5844103999 0.3345076842
## [296] 0.4942367005 0.1712556153 0.7141235650 0.0222984271 0.2635780079
#
weights_table <- stock_returns_monthly %>%
distinct(symbol) %>%
tq_repeat_df(n = num_port) %>%
bind_cols(tibble(weights)) %>%
group_by(portfolio)
weights_table
## # A tibble: 300 x 3
## # Groups: portfolio [100]
## portfolio symbol weights
## <int> <chr> <dbl>
## 1 1 NFLX 0.0639
## 2 1 TSLA 0.327
## 3 1 AMZN 0.609
## 4 2 NFLX 0.667
## 5 2 TSLA 0.0835
## 6 2 AMZN 0.249
## 7 3 NFLX 0.949
## 8 3 TSLA 0.0501
## 9 3 AMZN 0.00121
## 10 4 NFLX 0.308
## # … with 290 more rows
# Aggregate a Portfolio using Vector of Weights
portfolio_returns_monthly_multi <-
stock_returns_monthly_multi %>%
tq_portfolio(assets_col = symbol,
returns_col = Ra,
weights = weights_table,
col_rename = "Ra")
portfolio_returns_monthly_multi
## # A tibble: 6,100 x 3
## # Groups: portfolio [100]
## portfolio date Ra
## <int> <date> <dbl>
## 1 1 2014-11-28 0.00327
## 2 1 2014-12-31 -0.0814
## 3 1 2015-01-30 0.0804
## 4 1 2015-02-27 0.0527
## 5 1 2015-03-31 -0.0424
## 6 1 2015-04-30 0.165
## 7 1 2015-05-29 0.0500
## 8 1 2015-06-30 0.0308
## 9 1 2015-07-31 0.166
## 10 1 2015-08-31 -0.0434
## # … with 6,090 more rows# Merging Ra and Rb
RaRb_multi_portfolio <- left_join(portfolio_returns_monthly_multi ,
baseline_returns_monthly,
by = "date")
RaRb_multi_portfolio
## # A tibble: 6,100 x 4
## # Groups: portfolio [100]
## portfolio date Ra Rb
## <int> <date> <dbl> <dbl>
## 1 1 2014-11-28 0.00327 0.0347
## 2 1 2014-12-31 -0.0814 -0.0116
## 3 1 2015-01-30 0.0804 -0.0213
## 4 1 2015-02-27 0.0527 0.0708
## 5 1 2015-03-31 -0.0424 -0.0126
## 6 1 2015-04-30 0.165 0.00827
## 7 1 2015-05-29 0.0500 0.0260
## 8 1 2015-06-30 0.0308 -0.0164
## 9 1 2015-07-31 0.166 0.0284
## 10 1 2015-08-31 -0.0434 -0.0686
## # … with 6,090 more rows
RaRb_multi_portfolio %>%
tq_performance(Ra = Ra, Rb = Rb, performance_fun = table.CAPM)
## # A tibble: 100 x 13
## # Groups: portfolio [100]
## portfolio ActivePremium Alpha AnnualizedAlpha Beta `Beta-` `Beta+`
## <int> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 1 0.188 0.0117 0.150 1.28 1.51 1.04
## 2 2 0.275 0.018 0.239 1.41 1.56 1.44
## 3 3 0.294 0.0208 0.280 1.43 1.57 1.51
## 4 4 0.202 0.0129 0.166 1.31 1.47 1.15
## 5 5 0.113 0.0082 0.103 1.14 1.28 0.695
## 6 6 0.246 0.0163 0.214 1.38 1.51 1.35
## 7 7 0.267 0.016 0.210 1.40 1.63 1.40
## 8 8 0.271 0.0167 0.219 1.41 1.59 1.42
## 9 9 0.210 0.0132 0.171 1.32 1.48 1.18
## 10 10 0.262 0.0166 0.219 1.40 1.55 1.39
## # … with 90 more rows, and 6 more variables: Correlation <dbl>,
## # `Correlationp-value` <dbl>, InformationRatio <dbl>, `R-squared` <dbl>,
## # TrackingError <dbl>, TreynorRatio <dbl>Hint: Sort the portfolios based on the relevant measure you calcualted in Q4. Use dplyr::arrange(). Discuss your answer based on the measure you used to sort.
RaRb_multi_portfolio %>%
tq_performance(Ra = Ra, Rb = Rb, performance_fun = table.CAPM) %>%
arrange(desc(Alpha))
## # A tibble: 100 x 13
## # Groups: portfolio [100]
## portfolio ActivePremium Alpha AnnualizedAlpha Beta `Beta-` `Beta+`
## <int> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 85 0.302 0.0209 0.282 1.44 1.59 1.52
## 2 3 0.294 0.0208 0.280 1.43 1.57 1.51
## 3 16 0.290 0.0195 0.260 1.43 1.58 1.49
## 4 93 0.281 0.0194 0.259 1.42 1.55 1.47
## 5 15 0.272 0.0191 0.256 1.41 1.53 1.45
## 6 100 0.289 0.0189 0.252 1.43 1.58 1.48
## 7 47 0.281 0.0185 0.246 1.42 1.57 1.46
## 8 71 0.287 0.0184 0.245 1.43 1.59 1.48
## 9 75 0.268 0.0181 0.240 1.40 1.54 1.43
## 10 2 0.275 0.018 0.239 1.41 1.56 1.44
## # … with 90 more rows, and 6 more variables: Correlation <dbl>,
## # `Correlationp-value` <dbl>, InformationRatio <dbl>, `R-squared` <dbl>,
## # TrackingError <dbl>, TreynorRatio <dbl>Portfolio 85 is the portfolio that is the least effected by adverse market movements by having the highest Alpha at .0209.
Portfolio 85
NFLX 0.9296928791 93%
TSLA 0.0003363329 <1%
AMZN 0.0699707880 7%Hint: Use SharpeRatio for the performance_fun argument, instead of SharpeRatio.annualized, which doesn’t work with the Rf and p arguments. Sort the results using dplyr::arrange().
stock_returns_monthly %>%
tq_performance(Ra = Ra,
performance_fun = SharpeRatio,
Rf = 0.02/12, p =.99)
## # A tibble: 3 x 4
## # Groups: symbol [3]
## symbol `ESSharpe(Rf=0.2%,p=… `StdDevSharpe(Rf=0.2%… `VaRSharpe(Rf=0.2%,p…
## <chr> <dbl> <dbl> <dbl>
## 1 NFLX 0.193 0.291 0.193
## 2 TSLA 0.0370 0.0851 0.0438
## 3 AMZN 0.141 0.353 0.180Netflix has the greatest return per risk when VaR is used at .193, then Amazon at .179, then Tesla at .043.
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