## Loading required package: lubridate
##
## Attaching package: 'lubridate'
## The following object is masked from 'package:base':
##
## date
## Loading required package: PerformanceAnalytics
## Loading required package: xts
## Loading required package: zoo
##
## Attaching package: 'zoo'
## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numeric
## Registered S3 method overwritten by 'xts':
## method from
## as.zoo.xts zoo
##
## Attaching package: 'PerformanceAnalytics'
## The following object is masked from 'package:graphics':
##
## legend
## Loading required package: quantmod
## Loading required package: TTR
## Registered S3 method overwritten by 'quantmod':
## method from
## as.zoo.data.frame zoo
## Version 0.4-0 included new data defaults. See ?getSymbols.
## Loading required package: tidyverse
## ── Attaching packages ──────────────────────────────────────────── tidyverse 1.2.1 ──
## ✔ ggplot2 3.2.1 ✔ purrr 0.3.2
## ✔ tibble 2.1.3 ✔ dplyr 0.8.3
## ✔ tidyr 0.8.3 ✔ stringr 1.4.0
## ✔ readr 1.3.1 ✔ forcats 0.4.0
## ── Conflicts ─────────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ lubridate::as.difftime() masks base::as.difftime()
## ✖ lubridate::date() masks base::date()
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::first() masks xts::first()
## ✖ lubridate::intersect() masks base::intersect()
## ✖ dplyr::lag() masks stats::lag()
## ✖ dplyr::last() masks xts::last()
## ✖ lubridate::setdiff() masks base::setdiff()
## ✖ lubridate::union() masks base::union()
## # A tibble: 3,777 x 8
## symbol date open high low close volume adjusted
## <chr> <date> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 NFLX 2014-12-01 49.3 49.6 48.2 48.8 11964400 48.8
## 2 NFLX 2014-12-02 48.8 50.5 48.7 50.3 14271600 50.3
## 3 NFLX 2014-12-03 50.2 50.7 49.2 50.7 13819400 50.7
## 4 NFLX 2014-12-04 50.4 51.1 49.9 50.1 11853800 50.1
## 5 NFLX 2014-12-05 50.1 50.6 49.7 50.1 9930200 50.1
## 6 NFLX 2014-12-08 49.9 50.0 48.3 48.5 13621300 48.5
## 7 NFLX 2014-12-09 47.8 49.3 47.0 49.1 17976700 49.1
## 8 NFLX 2014-12-10 49.0 49.2 47.7 47.8 12644800 47.8
## 9 NFLX 2014-12-11 48.0 48.7 47.7 47.8 11769100 47.8
## 10 NFLX 2014-12-12 47.4 48.3 47.0 47.8 13521200 47.8
## # … with 3,767 more rows## # A tibble: 180 x 3
## # Groups: symbol [3]
## symbol date Ra
## <chr> <date> <dbl>
## 1 NFLX 2014-12-31 -0.000585
## 2 NFLX 2015-01-30 0.293
## 3 NFLX 2015-02-27 0.0749
## 4 NFLX 2015-03-31 -0.123
## 5 NFLX 2015-04-30 0.336
## 6 NFLX 2015-05-29 0.121
## 7 NFLX 2015-06-30 0.0527
## 8 NFLX 2015-07-31 0.218
## 9 NFLX 2015-08-31 0.00630
## 10 NFLX 2015-09-30 -0.102
## # … with 170 more rows
## # A tibble: 60 x 2
## date Rb
## <date> <dbl>
## 1 2014-12-31 0.00184
## 2 2015-01-30 -0.0213
## 3 2015-02-27 0.0708
## 4 2015-03-31 -0.0126
## 5 2015-04-30 0.00827
## 6 2015-05-29 0.0260
## 7 2015-06-30 -0.0164
## 8 2015-07-31 0.0284
## 9 2015-08-31 -0.0686
## 10 2015-09-30 -0.0327
## # … with 50 more rows## Ungrouping data frame groups: symbol
## # A tibble: 18,000 x 4
## # Groups: portfolio [100]
## portfolio symbol date Ra
## <int> <chr> <date> <dbl>
## 1 1 NFLX 2014-12-31 -0.000585
## 2 1 NFLX 2015-01-30 0.293
## 3 1 NFLX 2015-02-27 0.0749
## 4 1 NFLX 2015-03-31 -0.123
## 5 1 NFLX 2015-04-30 0.336
## 6 1 NFLX 2015-05-29 0.121
## 7 1 NFLX 2015-06-30 0.0527
## 8 1 NFLX 2015-07-31 0.218
## 9 1 NFLX 2015-08-31 0.00630
## 10 1 NFLX 2015-09-30 -0.102
## # … with 17,990 more rows
## [1] 3
## [1] 0.06385721 0.32707606 0.60906672
## [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
## Ungrouping data frame groups: symbol
## # 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
## # A tibble: 6,000 x 3
## # Groups: portfolio [100]
## portfolio date Ra
## <int> <date> <dbl>
## 1 1 2014-12-31 -0.0423
## 2 1 2015-01-30 0.0780
## 3 1 2015-02-27 0.0520
## 4 1 2015-03-31 -0.0428
## 5 1 2015-04-30 0.165
## 6 1 2015-05-29 0.0508
## 7 1 2015-06-30 0.0313
## 8 1 2015-07-31 0.163
## 9 1 2015-08-31 -0.0436
## 10 1 2015-09-30 -0.0125
## # … with 5,990 more rows## # A tibble: 6,000 x 4
## # Groups: portfolio [100]
## portfolio date Ra Rb
## <int> <date> <dbl> <dbl>
## 1 1 2014-12-31 -0.0423 0.00184
## 2 1 2015-01-30 0.0780 -0.0213
## 3 1 2015-02-27 0.0520 0.0708
## 4 1 2015-03-31 -0.0428 -0.0126
## 5 1 2015-04-30 0.165 0.00827
## 6 1 2015-05-29 0.0508 0.0260
## 7 1 2015-06-30 0.0313 -0.0164
## 8 1 2015-07-31 0.163 0.0284
## 9 1 2015-08-31 -0.0436 -0.0686
## 10 1 2015-09-30 -0.0125 -0.0327
## # … with 5,990 more rows
## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
## portfolio 1.0000 2.0000 3.0000 4.0000 5.0000 6.0000 7.0000 8.0000
## ActivePremium 0.2062 0.2922 0.3111 0.2191 0.1287 0.2628 0.2858 0.2891
## Alpha 0.0129 0.0191 0.0218 0.0140 0.0094 0.0173 0.0172 0.0178
## AnnualizedAlpha 0.1666 0.2543 0.2949 0.1812 0.1185 0.2288 0.2276 0.2357
## Beta 1.2742 1.4214 1.4435 1.3104 1.1293 1.3839 1.4062 1.4133
## Beta- 1.6334 1.6272 1.6176 1.5592 1.3751 1.5781 1.7440 1.6897
## Beta+ 1.1036 1.4827 1.5359 1.2069 0.7553 1.3922 1.4616 1.4705
## Correlation 0.7287 0.5734 0.4958 0.6662 0.6498 0.5810 0.6947 0.6546
## Correlationp-value 0.0000 0.0000 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000
## InformationRatio 1.1593 0.9729 0.8368 1.0088 0.6696 0.9182 1.3054 1.1856
## R-squared 0.5310 0.3288 0.2458 0.4438 0.4222 0.3376 0.4826 0.4286
## TrackingError 0.1779 0.3004 0.3718 0.2172 0.1922 0.2862 0.2189 0.2438
## TreynorRatio 0.2630 0.2963 0.3048 0.2655 0.2281 0.2830 0.2949 0.2957
## [,9] [,10] [,11] [,12] [,13] [,14] [,15]
## portfolio 9.0000 10.0000 11.0000 12.0000 13.0000 14.0000 15.0000
## ActivePremium 0.2269 0.2794 0.1262 0.2871 0.2688 0.2582 0.2885
## Alpha 0.0143 0.0177 0.0092 0.0173 0.0163 0.0157 0.0201
## AnnualizedAlpha 0.1864 0.2347 0.1166 0.2281 0.2137 0.2051 0.2701
## Beta 1.3224 1.4032 1.1204 1.4076 1.3812 1.3644 1.4188
## Beta- 1.5790 1.6351 1.3806 1.7603 1.7206 1.7122 1.5846
## Beta+ 1.2361 1.4394 0.7269 1.4681 1.3930 1.3476 1.4790
## Correlation 0.6709 0.6170 0.6550 0.6985 0.7055 0.7136 0.5098
## Correlationp-value 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## InformationRatio 1.0466 1.0515 0.6714 1.3226 1.2899 1.2844 0.8196
## R-squared 0.4501 0.3806 0.4290 0.4879 0.4977 0.5092 0.2599
## TrackingError 0.2167 0.2657 0.1880 0.2170 0.2084 0.2010 0.3520
## TreynorRatio 0.2690 0.2909 0.2277 0.2955 0.2879 0.2837 0.2942
## [,16] [,17] [,18] [,19] [,20] [,21] [,22]
## portfolio 16.0000 17.0000 18.0000 19.0000 20.0000 21.0000 22.0000
## ActivePremium 0.3075 0.1341 0.1647 0.2244 0.2649 0.1952 0.2513
## Alpha 0.0205 0.0098 0.0113 0.0144 0.0166 0.0124 0.0160
## AnnualizedAlpha 0.2759 0.1239 0.1438 0.1872 0.2182 0.1598 0.2099
## Beta 1.4397 1.1494 1.2141 1.3212 1.3815 1.2604 1.3637
## Beta- 1.6341 1.3586 1.4338 1.5550 1.6329 1.5629 1.5950
## Beta+ 1.5263 0.8203 0.9759 1.2354 1.3858 1.0732 1.3408
## Correlation 0.5406 0.6281 0.6447 0.6495 0.6477 0.7096 0.6343
## Correlationp-value 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## InformationRatio 0.9297 0.6467 0.7814 0.9807 1.0956 1.0541 1.0200
## R-squared 0.2922 0.3945 0.4156 0.4218 0.4195 0.5035 0.4023
## TrackingError 0.3307 0.2073 0.2108 0.2288 0.2418 0.1851 0.2464
## TreynorRatio 0.3031 0.2287 0.2418 0.2673 0.2850 0.2571 0.2788
## [,23] [,24] [,25] [,26] [,27] [,28] [,29]
## portfolio 23.0000 24.0000 25.0000 26.0000 27.0000 28.0000 29.0000
## ActivePremium 0.1577 0.1765 0.2977 0.1354 0.1706 0.2728 0.2852
## Alpha 0.0110 0.0117 0.0191 0.0096 0.0112 0.0165 0.0189
## AnnualizedAlpha 0.1400 0.1504 0.2547 0.1214 0.1431 0.2166 0.2518
## Beta 1.2017 1.2342 1.4271 1.1335 1.2027 1.3868 1.4134
## Beta- 1.4100 1.4738 1.6493 1.4411 1.5685 1.7364 1.6064
## Beta+ 0.9495 1.0196 1.4982 0.7445 0.9117 1.4095 1.4633
## Correlation 0.6333 0.6635 0.5904 0.6809 0.7178 0.7064 0.5610
## Correlationp-value 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## InformationRatio 0.7347 0.8635 1.0290 0.7624 0.9949 1.3060 0.9262
## R-squared 0.4011 0.4402 0.3485 0.4636 0.5153 0.4990 0.3147
## TrackingError 0.2147 0.2044 0.2893 0.1776 0.1715 0.2089 0.3079
## TreynorRatio 0.2384 0.2474 0.2989 0.2331 0.2490 0.2896 0.2929
## [,30] [,31] [,32] [,33] [,34] [,35] [,36]
## portfolio 30.0000 31.0000 32.0000 33.0000 34.0000 35.0000 36.0000
## ActivePremium 0.2419 0.1988 0.2687 0.0929 0.2537 0.2790 0.1727
## Alpha 0.0149 0.0127 0.0162 0.0081 0.0159 0.0168 0.0116
## AnnualizedAlpha 0.1936 0.1634 0.2129 0.1016 0.2082 0.2218 0.1479
## Beta 1.3408 1.2704 1.3792 1.0557 1.3648 1.3947 1.2271
## Beta- 1.6559 1.5495 1.7611 1.2163 1.6197 1.8115 1.4644
## Beta+ 1.2822 1.1022 1.3923 0.6076 1.3433 1.4414 1.0028
## Correlation 0.7077 0.6950 0.7131 0.5676 0.6575 0.7033 0.6611
## Correlationp-value 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## InformationRatio 1.2095 1.0230 1.3175 0.4185 1.0909 1.3162 0.8454
## R-squared 0.5009 0.4831 0.5085 0.3221 0.4323 0.4947 0.4371
## TrackingError 0.2000 0.1943 0.2039 0.2219 0.2326 0.2120 0.2043
## TreynorRatio 0.2765 0.2579 0.2882 0.2100 0.2803 0.2924 0.2458
## [,37] [,38] [,39] [,40] [,41] [,42] [,43]
## portfolio 37.0000 38.0000 39.0000 40.0000 41.0000 42.0000 43.0000
## ActivePremium 0.2944 0.1305 0.2758 0.1320 0.1104 0.1767 0.1489
## Alpha 0.0182 0.0101 0.0166 0.0099 0.0086 0.0131 0.0106
## AnnualizedAlpha 0.2416 0.1284 0.2188 0.1250 0.1078 0.1686 0.1353
## Beta 1.4207 1.1556 1.3900 1.1509 1.0728 1.2547 1.1859
## Beta- 1.6893 1.2994 1.7866 1.3305 1.3720 1.3864 1.3795
## Beta+ 1.4887 0.8660 1.4250 0.8368 0.5880 1.1100 0.9164
## Correlation 0.6437 0.5677 0.7085 0.6023 0.6448 0.5409 0.6184
## Correlationp-value 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## InformationRatio 1.1678 0.5356 1.3244 0.5946 0.5984 0.6201 0.6771
## R-squared 0.4143 0.3223 0.5020 0.3628 0.4157 0.2926 0.3824
## TrackingError 0.2521 0.2437 0.2083 0.2220 0.1845 0.2849 0.2199
## TreynorRatio 0.2979 0.2245 0.2912 0.2266 0.2230 0.2435 0.2342
## [,44] [,45] [,46] [,47] [,48] [,49] [,50]
## portfolio 44.0000 45.0000 46.0000 47.0000 48.0000 49.0000 50.0000
## ActivePremium 0.2271 0.2758 0.0636 0.2986 0.2612 0.2085 0.2432
## Alpha 0.0144 0.0167 0.0071 0.0196 0.0163 0.0136 0.0161
## AnnualizedAlpha 0.1876 0.2203 0.0883 0.2617 0.2135 0.1765 0.2110
## Beta 1.3240 1.3925 0.9799 1.4292 1.3752 1.2964 1.3559
## Beta- 1.5713 1.7135 1.0927 1.6333 1.6379 1.5163 1.5486
## Beta+ 1.2410 1.4215 0.4375 1.5016 1.3701 1.1768 1.3253
## Correlation 0.6620 0.6936 0.5112 0.5648 0.6606 0.6399 0.5917
## Correlationp-value 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## InformationRatio 1.0227 1.2709 0.2667 0.9674 1.1222 0.9082 0.8924
## R-squared 0.4383 0.4811 0.2613 0.3190 0.4364 0.4094 0.3501
## TrackingError 0.2221 0.2170 0.2386 0.3087 0.2327 0.2295 0.2725
## TreynorRatio 0.2689 0.2906 0.1964 0.2991 0.2836 0.2602 0.2744
## [,51] [,52] [,53] [,54] [,55] [,56] [,57]
## portfolio 51.0000 52.0000 53.0000 54.0000 55.0000 56.0000 57.0000
## ActivePremium 0.2604 0.1710 0.1657 0.2300 0.1735 0.1809 0.2010
## Alpha 0.0173 0.0120 0.0110 0.0141 0.0113 0.0118 0.0143
## AnnualizedAlpha 0.2288 0.1541 0.1404 0.1836 0.1449 0.1517 0.1863
## Beta 1.3813 1.2351 1.2046 1.3177 1.2089 1.2387 1.2956
## Beta- 1.5684 1.4106 1.4897 1.6687 1.5746 1.5035 1.4415
## Beta+ 1.3867 1.0426 0.9340 1.2209 0.9282 1.0248 1.1981
## Correlation 0.5726 0.5984 0.6938 0.7247 0.7196 0.6843 0.5489
## Correlationp-value 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## InformationRatio 0.8928 0.7069 0.9031 1.2290 1.0112 0.9313 0.6956
## R-squared 0.3279 0.3581 0.4814 0.5252 0.5179 0.4682 0.3013
## TrackingError 0.2917 0.2419 0.1835 0.1872 0.1716 0.1943 0.2890
## TreynorRatio 0.2818 0.2428 0.2445 0.2724 0.2501 0.2501 0.2546
## [,58] [,59] [,60] [,61] [,62] [,63] [,64]
## portfolio 58.0000 59.0000 60.0000 61.0000 62.0000 63.0000 64.0000
## ActivePremium 0.2152 0.1944 0.1477 0.1650 0.2923 0.2719 0.2783
## Alpha 0.0134 0.0127 0.0106 0.0110 0.0178 0.0165 0.0180
## AnnualizedAlpha 0.1734 0.1633 0.1354 0.1408 0.2362 0.2167 0.2381
## Beta 1.2872 1.2682 1.1850 1.2067 1.4167 1.3864 1.4031
## Beta- 1.6840 1.5081 1.3705 1.4705 1.7130 1.7124 1.6164
## Beta+ 1.1366 1.1035 0.9176 0.9447 1.4829 1.4056 1.4382
## Correlation 0.7280 0.6631 0.6104 0.6804 0.6678 0.6984 0.5951
## Correlationp-value 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## InformationRatio 1.1926 0.9216 0.6586 0.8656 1.2357 1.2748 0.9918
## R-squared 0.5299 0.4397 0.3726 0.4630 0.4459 0.4877 0.3541
## TrackingError 0.1804 0.2109 0.2243 0.1906 0.2365 0.2133 0.2806
## TreynorRatio 0.2673 0.2549 0.2334 0.2435 0.2973 0.2890 0.2902
## [,65] [,66] [,67] [,68] [,69] [,70] [,71]
## portfolio 65.0000 66.0000 67.0000 68.0000 69.0000 70.0000 71.0000
## ActivePremium 0.0709 0.2732 0.0593 0.2566 0.2421 0.2583 0.3053
## Alpha 0.0073 0.0180 0.0069 0.0156 0.0154 0.0159 0.0195
## AnnualizedAlpha 0.0912 0.2391 0.0861 0.2043 0.2018 0.2086 0.2611
## Beta 0.9988 1.3980 0.9658 1.3628 1.3495 1.3689 1.4361
## Beta- 1.1278 1.5919 1.0778 1.6947 1.5825 1.6546 1.6629
## Beta+ 0.4776 1.4262 0.4003 1.3420 1.3056 1.3552 1.5213
## Correlation 0.5278 0.5726 0.5051 0.7090 0.6409 0.6815 0.5892
## Correlationp-value 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## InformationRatio 0.3046 0.9244 0.2480 1.2626 1.0110 1.1767 1.0452
## R-squared 0.2785 0.3278 0.2551 0.5027 0.4108 0.4644 0.3472
## TrackingError 0.2328 0.2956 0.2391 0.2032 0.2395 0.2195 0.2921
## TreynorRatio 0.2000 0.2876 0.1948 0.2828 0.2749 0.2828 0.3023
## [,72] [,73] [,74] [,75] [,76] [,77] [,78]
## portfolio 72.0000 73.0000 74.0000 75.0000 76.0000 77.0000 78.0000
## ActivePremium 0.2978 0.2424 0.3002 0.2850 0.2572 0.2267 0.1365
## Alpha 0.0191 0.0155 0.0187 0.0191 0.0167 0.0147 0.0109
## AnnualizedAlpha 0.2542 0.2024 0.2488 0.2548 0.2199 0.1913 0.1387
## Beta 1.4272 1.3502 1.4285 1.4137 1.3746 1.3269 1.1765
## Beta- 1.6514 1.5805 1.6862 1.5987 1.5825 1.5456 1.2889
## Beta+ 1.4986 1.3075 1.5072 1.4641 1.3688 1.2515 0.9357
## Correlation 0.5929 0.6378 0.6286 0.5488 0.6029 0.6320 0.5323
## Correlationp-value 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## InformationRatio 1.0358 1.0035 1.1397 0.8975 0.9562 0.9431 0.5014
## R-squared 0.3515 0.4068 0.3952 0.3012 0.3635 0.3995 0.2833
## TrackingError 0.2875 0.2415 0.2634 0.3175 0.2690 0.2403 0.2722
## TreynorRatio 0.2989 0.2749 0.3003 0.2927 0.2808 0.2679 0.2255
## [,79] [,80] [,81] [,82] [,83] [,84] [,85]
## portfolio 79.0000 80.0000 81.0000 82.0000 83.0000 84.0000 85.0000
## ActivePremium 0.2515 0.2757 0.2448 0.0437 0.2672 0.1722 0.3197
## Alpha 0.0156 0.0166 0.0150 0.0065 0.0172 0.0116 0.0219
## AnnualizedAlpha 0.2034 0.2187 0.1952 0.0803 0.2268 0.1481 0.2974
## Beta 1.3590 1.3907 1.3390 0.9198 1.3879 1.2272 1.4526
## Beta- 1.6412 1.7514 1.7486 1.0012 1.6052 1.4585 1.6383
## Beta+ 1.3290 1.4221 1.2812 0.2953 1.4009 1.0045 1.5567
## Correlation 0.6823 0.7072 0.7203 0.4698 0.6082 0.6559 0.5083
## Correlationp-value 0.0000 0.0000 0.0000 0.0002 0.0000 0.0000 0.0000
## InformationRatio 1.1582 1.3183 1.2677 0.1743 0.9960 0.8314 0.8822
## R-squared 0.4655 0.5001 0.5188 0.2207 0.3699 0.4302 0.2583
## TrackingError 0.2172 0.2092 0.1931 0.2506 0.2683 0.2072 0.3624
## TreynorRatio 0.2799 0.2909 0.2791 0.1876 0.2854 0.2453 0.3088
## [,86] [,87] [,88] [,89] [,90] [,91] [,92]
## portfolio 86.0000 87.0000 88.0000 89.0000 90.0000 91.0000 92.0000
## ActivePremium 0.2461 0.2290 0.2182 0.0457 0.2527 0.2022 0.0893
## Alpha 0.0169 0.0141 0.0136 0.0064 0.0154 0.0140 0.0080
## AnnualizedAlpha 0.2230 0.1828 0.1761 0.0800 0.2007 0.1822 0.0999
## Beta 1.3637 1.3142 1.3016 0.9145 1.3553 1.2946 1.0469
## Beta- 1.5279 1.6844 1.6081 1.0426 1.7079 1.4585 1.2024
## Beta+ 1.3497 1.2113 1.1796 0.2512 1.3231 1.1881 0.5875
## Correlation 0.5483 0.7277 0.7100 0.4855 0.7173 0.5737 0.5613
## Correlationp-value 0.0000 0.0000 0.0000 0.0001 0.0000 0.0000 0.0000
## InformationRatio 0.8047 1.2370 1.1362 0.1913 1.2796 0.7460 0.3993
## R-squared 0.3006 0.5295 0.5041 0.2357 0.5145 0.3291 0.3151
## TrackingError 0.3058 0.1851 0.1920 0.2388 0.1975 0.2711 0.2236
## TreynorRatio 0.2750 0.2723 0.2666 0.1909 0.2815 0.2557 0.2084
## [,93] [,94] [,95] [,96] [,97] [,98] [,99]
## portfolio 93.0000 94.0000 95.0000 96.0000 97.0000 98.0000 99.0000
## ActivePremium 0.2977 0.0135 0.2317 0.1691 0.2523 0.2305 0.1776
## Alpha 0.0204 0.0058 0.0143 0.0111 0.0162 0.0142 0.0122
## AnnualizedAlpha 0.2741 0.0724 0.1851 0.1422 0.2120 0.1845 0.1571
## Beta 1.4291 0.8245 1.3219 1.2095 1.3658 1.3209 1.2454
## Beta- 1.6060 0.8175 1.6582 1.5078 1.5897 1.6466 1.4338
## Beta+ 1.5015 0.0867 1.2322 0.9434 1.3465 1.2294 1.0624
## Correlation 0.5208 0.3909 0.7202 0.7019 0.6253 0.7165 0.6118
## Correlationp-value 0.0000 0.0020 0.0000 0.0000 0.0000 0.0000 0.0000
## InformationRatio 0.8631 0.0477 1.2181 0.9377 0.9992 1.2010 0.7528
## R-squared 0.2712 0.1528 0.5187 0.4927 0.3910 0.5134 0.3743
## TrackingError 0.3449 0.2823 0.1902 0.1803 0.2525 0.1919 0.2359
## TreynorRatio 0.2985 0.1726 0.2728 0.2463 0.2790 0.2721 0.2460
## [,100]
## portfolio 100.0000
## ActivePremium 0.3064
## Alpha 0.0200
## AnnualizedAlpha 0.2677
## Beta 1.4380
## Beta- 1.6484
## Beta+ 1.5236
## Correlation 0.5663
## Correlationp-value 0.0000
## InformationRatio 0.9893
## R-squared 0.3207
## TrackingError 0.3097
## TreynorRatio 0.3027## # A tibble: 100 x 13
## # Groups: portfolio [100]
## portfolio ActivePremium Alpha AnnualizedAlpha Beta `Beta-` `Beta+`
## <int> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 85 0.320 0.0219 0.297 1.45 1.64 1.56
## 2 3 0.311 0.0218 0.295 1.44 1.62 1.54
## 3 16 0.308 0.0205 0.276 1.44 1.63 1.53
## 4 93 0.298 0.0204 0.274 1.43 1.61 1.50
## 5 15 0.288 0.0201 0.270 1.42 1.58 1.48
## 6 100 0.306 0.02 0.268 1.44 1.65 1.52
## 7 47 0.299 0.0196 0.262 1.43 1.63 1.50
## 8 71 0.305 0.0195 0.261 1.44 1.66 1.52
## 9 2 0.292 0.0191 0.254 1.42 1.63 1.48
## 10 25 0.298 0.0191 0.255 1.43 1.65 1.50
## # … 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 least affected, it has the highest Alpha.
The weights of the stocks for the least affected portfolio(85) are NFLX 0.9296928791, TSLA 0.0003363329, AMZN 0.0699707880
## [,1] [,2] [,3]
## symbol "NFLX" "TSLA" "AMZN"
## ESSharpe(Rf=0.2%,p=99%) "0.1958779" "0.0405976" "0.1457544"
## StdDevSharpe(Rf=0.2%,p=99%) "0.29753614" "0.09310117" "0.36692880"
## VaRSharpe(Rf=0.2%,p=99%) "0.19587789" "0.04779468" "0.18695785"Netflix, due to the much higher Sharpe Ratio. ## Q8 Hide the messages, but display the code and its results on the webpage. Hint: Use message, echo and results in the chunk options. Refer to the RMarkdown Reference Guide.