Quantitative Insights into Portfolio Performance: Analyzing Risk and Reward Dynamics
Prashant Kumar
2024-09-09
In this project we are going to analyze & compare two portfolios using few risk metrics( VAR, Beta, Sharpe, Rolling, Drawdown etc) over the period of 3 montha;May 2024-August 2024. The stocks in both the portfolio are picked uding GPT-4o, all the stocks have equal weightage in their portfolios. In the first portfolio, we have:
- Goldman Sachs Group – GS (Financial)
- Apple Inc. – AAPL (Technology)
- Johnson & Johnson – JNJ (Healthcare)
- Exxon Mobil Corporation – XOM (Energy)
- Procter & Gamble Co. – PG (Consumer Staples).
In the second portfolio we have;
- JPMorgan Chase & Co. – JPM (Financial)
- Microsoft Corporation – MSFT (Technology)
- Pfizer Inc. – PFE (Healthcare)
- Chevron Corporation – CVX (Energy)
- The Coca-Cola Company – KO (Consumer Staples).
Now lets start with our analysis, first we start with loading all the libraies
library(quantmod)
library(dygraphs)
library(PerformanceAnalytics)
options(scipen = 999)We will retrive the stock data using the library called ‘quantmod’, the default source is Yahoo.
symbolslist<- c('AAPL','GS','JNJ','XOM','PG','JPM','MSFT','PFE','CVX','KO','^GSPC')
#Setting the time period for August 2024
getSymbols(symbolslist,from='2024-05-01', to='2024-08-1',)## [1] "AAPL" "GS" "JNJ" "XOM" "PG" "JPM" "MSFT" "PFE" "CVX" "KO"
## [11] "GSPC"get## function (x, pos = -1L, envir = as.environment(pos), mode = "any",
## inherits = TRUE)
## .Internal(get(x, envir, mode, inherits))
## <bytecode: 0x0000027d42d53908>
## <environment: namespace:base>Lets ceate the portfolios by merging the stocks into their bags and calculate their returns.
m2<-merge.xts(dailyReturn(JPM),dailyReturn(MSFT),dailyReturn(PFE),dailyReturn(CVX),dailyReturn(KO))
m1<- merge.xts(dailyReturn(GS),dailyReturn(AAPL),dailyReturn(JNJ),dailyReturn(XOM),dailyReturn(PG))
m1## daily.returns daily.returns.1 daily.returns.2 daily.returns.3
## 2024-05-01 0.0006093646 -0.00165113089 0.0164043774 -0.0190226583
## 2024-05-02 0.0131631220 0.02203187041 -0.0083343998 0.0018098689
## 2024-05-03 0.0129689652 0.05981625254 -0.0043356050 -0.0020646754
## 2024-05-06 0.0125291452 -0.00910676259 -0.0046225124 0.0064655172
## 2024-05-07 0.0002929528 0.00379718869 0.0009422492 -0.0049678958
## 2024-05-08 0.0070978470 0.00186409873 0.0015465017 -0.0001721326
## 2024-05-09 0.0192638665 0.01001423758 0.0060423577 0.0197158923
## 2024-05-10 -0.0018219040 -0.00823538068 0.0004003841 -0.0040527132
## 2024-05-13 -0.0025729848 0.01764542843 0.0087385600 -0.0004238337
## 2024-05-14 0.0108254778 0.00617346953 0.0010580853 -0.0020354973
## 2024-05-15 0.0166204879 0.01221794075 0.0085215566 0.0077335232
## 2024-05-16 -0.0033684639 0.00063248533 0.0105456254 -0.0059875112
## 2024-05-17 0.0068888579 0.00015802139 0.0023334237 0.0150165148
## 2024-05-20 -0.0102197870 0.00616210143 -0.0217925190 -0.0081076665
## 2024-05-21 0.0161360029 0.00685727001 -0.0001983128 -0.0069099158
## 2024-05-22 -0.0170702126 -0.00753840479 0.0149430999 -0.0201102685
## 2024-05-23 -0.0091483432 -0.02105808875 -0.0247557202 -0.0170592411
## 2024-05-24 0.0066135519 0.01658813551 -0.0182364448 -0.0007929166
## 2024-05-28 -0.0029706300 0.00005268852 -0.0176226190 0.0126961952
## 2024-05-29 -0.0057414674 0.00157896618 0.0004155531 -0.0107087180
## 2024-05-30 -0.0151803536 0.00525513708 0.0058155381 0.0031681829
## 2024-05-31 0.0139705881 0.00501859348 0.0095677272 0.0286867649
## 2024-06-03 -0.0033732981 0.00925877128 0.0072953388 -0.0239638848
## 2024-06-04 0.0007032766 0.00164926726 0.0004061023 -0.0155526328
## 2024-06-05 0.0140127500 0.00782088483 -0.0123816089 0.0039940054
## 2024-06-06 -0.0077542597 -0.00709654069 0.0030828043 0.0075141306
## 2024-06-07 -0.0069635503 0.01239203885 0.0045076060 -0.0107045820
## 2024-06-10 -0.0029896372 -0.01914776923 0.0003399718 0.0029268455
## 2024-06-11 -0.0204608070 0.07264912559 -0.0025148533 -0.0080474323
## 2024-06-12 0.0099714662 0.02857839055 -0.0091986297 -0.0110546303
## 2024-06-13 -0.0052373658 0.00549114436 0.0002750381 -0.0080230721
## 2024-06-14 0.0002464106 -0.00816840905 0.0006187442 -0.0084514749
## 2024-06-17 0.0083322163 0.01967147898 0.0028171202 -0.0068737970
## 2024-06-18 0.0161046695 -0.01098446902 -0.0020555194 0.0094130365
## 2024-06-20 0.0013553880 -0.02151290660 0.0146241330 0.0215761626
## 2024-06-21 -0.0171815202 -0.01044442607 0.0065638194 -0.0087703217
## 2024-06-24 0.0264560928 0.00313265159 0.0024873621 0.0297038719
## 2024-06-25 -0.0101928012 0.00446818457 -0.0129425479 0.0028057842
## 2024-06-26 -0.0033233187 0.01999326795 -0.0025137245 0.0003497501
## 2024-06-27 -0.0217171812 0.00398596063 -0.0069473111 0.0042828236
## 2024-06-28 0.0142614046 -0.01625413773 0.0024691399 0.0019147190
## 2024-07-01 0.0250707379 0.02910457233 0.0019157004 -0.0013898858
## 2024-07-02 0.0042056284 0.01623992744 -0.0027998064 -0.0067849581
## 2024-07-03 0.0049612941 0.00581104442 -0.0023282636 0.0050797147
## 2024-07-05 -0.0067746908 0.02162037111 0.0054224262 -0.0121122287
## 2024-07-08 0.0001506344 0.00653888403 -0.0068268708 -0.0104966253
## 2024-07-09 0.0172324322 0.00377484560 0.0107919121 -0.0110536447
## 2024-07-10 0.0128165054 0.01880358225 0.0161849002 0.0088335650
## 2024-07-11 0.0007099675 -0.02322082798 0.0018068948 0.0118835048
## 2024-07-12 0.0013563297 0.01305086728 0.0012024578 0.0001765708
## 2024-07-15 0.0257356130 0.01674330148 -0.0042700785 0.0171272402
## 2024-07-16 0.0219206017 0.00179186621 0.0118600171 0.0072042517
## 2024-07-17 -0.0016699065 -0.02529598099 0.0368850243 0.0137883356
## 2024-07-18 -0.0318013490 -0.02053483095 -0.0074083769 0.0098606228
## 2024-07-19 -0.0026326048 0.00057991296 -0.0046969228 -0.0229798256
## 2024-07-22 0.0043511763 -0.00156029980 -0.0029090241 -0.0068924188
## 2024-07-23 0.0104919211 0.00468828256 -0.0122536263 -0.0161359680
## 2024-07-24 -0.0110738225 -0.02875428371 0.0257958157 0.0141080894
## 2024-07-25 0.0102937726 -0.00480455672 0.0214998761 0.0210416322
## 2024-07-26 0.0148868387 0.00216102446 0.0062640942 -0.0008515582
## 2024-07-29 -0.0126445255 0.00128463374 -0.0129482186 -0.0104832808
## 2024-07-30 0.0262827005 0.00256597115 0.0174697548 0.0178294550
## 2024-07-31 0.0066446205 0.01499085344 -0.0215706669 0.0035541861
## daily.returns.4
## 2024-05-01 0.0007349040
## 2024-05-02 0.0026927935
## 2024-05-03 0.0037842431
## 2024-05-06 -0.0001216361
## 2024-05-07 0.0080271956
## 2024-05-08 -0.0041625676
## 2024-05-09 0.0058762096
## 2024-05-10 0.0048784200
## 2024-05-13 -0.0058736047
## 2024-05-14 -0.0006631737
## 2024-05-15 0.0045246140
## 2024-05-16 0.0081076581
## 2024-05-17 -0.0013106233
## 2024-05-20 -0.0019685149
## 2024-05-21 0.0062160574
## 2024-05-22 -0.0032076538
## 2024-05-23 -0.0138251123
## 2024-05-24 -0.0009668479
## 2024-05-28 -0.0134276973
## 2024-05-29 -0.0089510558
## 2024-05-30 0.0057532197
## 2024-05-31 0.0120555507
## 2024-06-03 0.0006685342
## 2024-06-04 0.0143334388
## 2024-06-05 -0.0057481078
## 2024-06-06 0.0145739122
## 2024-06-07 -0.0083694643
## 2024-06-10 0.0017359544
## 2024-06-11 0.0007767530
## 2024-06-12 -0.0137330016
## 2024-06-13 0.0074464889
## 2024-06-14 0.0022834542
## 2024-06-17 0.0042568904
## 2024-06-18 0.0063283436
## 2024-06-20 -0.0052800154
## 2024-06-21 0.0035187949
## 2024-06-24 0.0011292193
## 2024-06-25 -0.0094983133
## 2024-06-26 0.0035959893
## 2024-06-27 -0.0049567145
## 2024-06-28 -0.0102028388
## 2024-07-01 -0.0133397828
## 2024-07-02 0.0072516757
## 2024-07-03 -0.0004270413
## 2024-07-05 0.0084233954
## 2024-07-08 0.0079292870
## 2024-07-09 -0.0051645483
## 2024-07-10 0.0068815608
## 2024-07-11 -0.0075540152
## 2024-07-12 0.0064637391
## 2024-07-15 -0.0121841352
## 2024-07-16 0.0144002618
## 2024-07-17 0.0149146783
## 2024-07-18 -0.0059017941
## 2024-07-19 -0.0028496540
## 2024-07-22 0.0017265615
## 2024-07-23 -0.0096879934
## 2024-07-24 0.0082823486
## 2024-07-25 -0.0065476554
## 2024-07-26 0.0132415027
## 2024-07-29 0.0048488680
## 2024-07-30 -0.0484316841
## 2024-07-31 -0.0058132496m2## daily.returns daily.returns.1 daily.returns.2 daily.returns.3
## 2024-05-01 -0.0021324370 0.0059346863 0.0322825820 -0.0071525930
## 2024-05-02 -0.0010424109 0.0073428720 0.0191317311 0.0068908777
## 2024-05-03 -0.0060002564 0.0221697351 0.0039710722 -0.0029863482
## 2024-05-06 0.0078211408 0.0169183220 0.0125854149 0.0127925307
## 2024-05-07 -0.0013020833 -0.0101562415 -0.0138494102 0.0022796988
## 2024-05-08 0.0203389512 0.0029315782 0.0180050411 -0.0007991940
## 2024-05-09 0.0094556921 0.0043357498 -0.0031835922 0.0179033086
## 2024-05-10 0.0064304014 0.0058691862 -0.0060326499 0.0022363879
## 2024-05-13 -0.0002012806 -0.0024593457 0.0153516709 -0.0077795711
## 2024-05-14 0.0139888232 0.0068645372 -0.0021097529 -0.0055916743
## 2024-05-15 0.0029775501 0.0156519806 0.0155038952 -0.0034227587
## 2024-05-16 0.0017812113 -0.0049399556 0.0034698259 -0.0120208935
## 2024-05-17 0.0114584484 -0.0018527727 -0.0096819048 0.0098081934
## 2024-05-20 -0.0449728588 0.0122081935 -0.0038407369 -0.0094055376
## 2024-05-21 0.0201452214 0.0086989520 0.0010514819 -0.0072607557
## 2024-05-22 -0.0060645885 0.0034495162 0.0364145986 -0.0150027748
## 2024-05-23 -0.0070092250 -0.0081761338 -0.0307432377 -0.0039982538
## 2024-05-24 0.0192464380 0.0074004770 0.0066224686 0.0051611925
## 2024-05-28 -0.0060286317 0.0003719631 -0.0200831004 0.0081774535
## 2024-05-29 -0.0069674155 -0.0026724156 -0.0169611150 -0.0134557311
## 2024-05-30 0.0061582011 -0.0337861443 0.0136592765 0.0086679456
## 2024-05-31 0.0165554760 0.0011092952 0.0163120238 0.0255276677
## 2024-06-03 -0.0039974216 -0.0038783414 0.0226796798 -0.0298212954
## 2024-06-04 -0.0131800791 0.0061666144 0.0061412592 -0.0084466009
## 2024-06-05 -0.0095401141 0.0190833329 0.0020345699 -0.0073657152
## 2024-06-06 -0.0017742617 0.0012027529 -0.0253807113 0.0061298037
## 2024-06-07 0.0154384908 -0.0015782129 -0.0076388652 0.0009620289
## 2024-06-10 -0.0017004068 0.0094844614 -0.0178446547 0.0042286241
## 2024-06-11 -0.0263012874 0.0112417267 -0.0014249736 -0.0015949980
## 2024-06-12 -0.0145606186 0.0193676736 -0.0132001723 -0.0145057460
## 2024-06-13 0.0111209988 0.0011789530 -0.0003615412 -0.0089482873
## 2024-06-14 0.0006196174 0.0022419964 -0.0043399253 -0.0017664814
## 2024-06-17 0.0061925738 0.0131052437 -0.0199782467 0.0040636763
## 2024-06-18 0.0103600591 -0.0045275081 0.0159377432 0.0009138938
## 2024-06-20 0.0084771481 -0.0014338489 0.0120393990 0.0215874096
## 2024-06-21 -0.0119293056 0.0091541092 0.0000000000 -0.0086823328
## 2024-06-24 0.0131431574 -0.0046911498 0.0223504270 0.0259531093
## 2024-06-25 -0.0040727953 0.0073268226 -0.0130465737 -0.0053354520
## 2024-06-26 -0.0032312547 0.0026832053 -0.0203644051 -0.0158400206
## 2024-06-27 0.0088132784 0.0015260139 0.0138584668 0.0023726219
## 2024-06-28 0.0155143665 -0.0130285830 0.0064748313 0.0006396548
## 2024-07-01 0.0157717914 0.0218816389 0.0085775474 0.0006393435
## 2024-07-02 0.0164517154 0.0055831404 -0.0138199645 0.0014694334
## 2024-07-03 -0.0006703988 0.0032441871 -0.0046711880 -0.0002551406
## 2024-07-05 -0.0186880498 0.0147362213 0.0126353236 -0.0153149707
## 2024-07-08 0.0018555833 -0.0028231828 -0.0042780369 0.0001296369
## 2024-07-09 0.0119900899 -0.0143702424 -0.0075188324 -0.0087475286
## 2024-07-10 0.0008187553 0.0146015392 0.0227273118 0.0140541850
## 2024-07-11 -0.0016843412 -0.0247720918 0.0109347253 0.0008379399
## 2024-07-12 -0.0120992747 -0.0025291937 0.0090718852 0.0021254788
## 2024-07-15 0.0249341297 0.0009039878 0.0062240769 0.0157464940
## 2024-07-16 0.0169959153 -0.0097806030 0.0137456912 -0.0017083588
## 2024-07-17 0.0152139316 -0.0133475711 0.0179661250 0.0219306038
## 2024-07-18 -0.0317701828 -0.0071022591 -0.0106560638 0.0045897507
## 2024-07-19 -0.0009524571 -0.0074028880 0.0087512702 -0.0174106767
## 2024-07-22 0.0023834493 0.0133376434 -0.0123456437 -0.0135720294
## 2024-07-23 0.0002377927 0.0043121047 -0.0033783912 -0.0184725718
## 2024-07-24 -0.0082727404 -0.0358548095 0.0162711709 0.0063599910
## 2024-07-25 0.0003835363 -0.0244812314 0.0066711396 0.0159281992
## 2024-07-26 0.0171083882 0.0164196826 0.0195493753 0.0019042977
## 2024-07-29 -0.0065491866 0.0034331648 -0.0016249965 -0.0078559951
## 2024-07-30 0.0205833351 -0.0089283562 0.0218098988 0.0189655243
## 2024-07-31 -0.0111064611 -0.0108058431 -0.0270786394 0.0056401194
## daily.returns.4
## 2024-05-01 0.0021035772
## 2024-05-02 0.0009688580
## 2024-05-03 0.0029036375
## 2024-05-06 0.0028952921
## 2024-05-07 0.0043304004
## 2024-05-08 0.0036729407
## 2024-05-09 0.0004773683
## 2024-05-10 0.0060432132
## 2024-05-13 0.0050585444
## 2024-05-14 -0.0075495965
## 2024-05-15 0.0004754769
## 2024-05-16 0.0030096408
## 2024-05-17 -0.0045799260
## 2024-05-20 -0.0072980976
## 2024-05-21 0.0054339165
## 2024-05-22 0.0014306176
## 2024-05-23 -0.0144444420
## 2024-05-24 -0.0014495112
## 2024-05-28 -0.0029032307
## 2024-05-29 -0.0019411021
## 2024-05-30 0.0043760203
## 2024-05-31 0.0154913517
## 2024-06-03 0.0000000000
## 2024-06-04 0.0160495521
## 2024-06-05 -0.0003128004
## 2024-06-06 0.0035983004
## 2024-06-07 -0.0037412576
## 2024-06-10 -0.0050070364
## 2024-06-11 -0.0006290441
## 2024-06-12 -0.0105428509
## 2024-06-13 0.0017493735
## 2024-06-14 -0.0069852743
## 2024-06-17 0.0011190999
## 2024-06-18 0.0001597275
## 2024-06-20 -0.0071850671
## 2024-06-21 0.0094885839
## 2024-06-24 0.0191174248
## 2024-06-25 -0.0020322193
## 2024-06-26 0.0032895191
## 2024-06-27 -0.0021858423
## 2024-06-28 -0.0040681947
## 2024-07-01 -0.0058130831
## 2024-07-02 -0.0020543182
## 2024-07-03 0.0028503611
## 2024-07-05 0.0067897754
## 2024-07-08 -0.0125470398
## 2024-07-09 -0.0042884444
## 2024-07-10 0.0022332622
## 2024-07-11 0.0042972566
## 2024-07-12 0.0095087528
## 2024-07-15 -0.0045526046
## 2024-07-16 0.0135624791
## 2024-07-17 0.0146258362
## 2024-07-18 -0.0003066500
## 2024-07-19 0.0015339541
## 2024-07-22 -0.0079645316
## 2024-07-23 0.0029334947
## 2024-07-24 0.0130849521
## 2024-07-25 0.0039508000
## 2024-07-26 0.0148328040
## 2024-07-29 -0.0032811515
## 2024-07-30 0.0127188157
## 2024-07-31 -0.0138889249Let create a dataframe where we have both the portfolios along with a change in columns names.
gsr<- as.data.frame(dailyReturn(GS))
appler<- as.data.frame(dailyReturn(AAPL))
JNJR<- as.data.frame(dailyReturn(JNJ))
xomr<- as.data.frame(dailyReturn(XOM))
pgr<- as.data.frame(dailyReturn(PG))
jpmr<- as.data.frame(dailyReturn(JPM))
MSFTR<- as.data.frame(dailyReturn(MSFT))
pfer<- as.data.frame(dailyReturn(PFE))
cvxr<- as.data.frame(dailyReturn(CVX))
kor<- as.data.frame(dailyReturn(KO))
b1<- dailyReturn(GSPC)
port1<-as.data.frame( c(gsr,appler,JNJR,xomr,pgr))
port2<- as.data.frame((c(jpmr,MSFTR,pfer,cvxr,kor)))
colnames(port1)<-c('GS','APPl','JNJ','XOM','PG')
colnames(port2)<- c('JPM','MSFT','PFE','CVX','KO')
port1## GS APPl JNJ XOM PG
## 1 0.0006093646 -0.00165113089 0.0164043774 -0.0190226583 0.0007349040
## 2 0.0131631220 0.02203187041 -0.0083343998 0.0018098689 0.0026927935
## 3 0.0129689652 0.05981625254 -0.0043356050 -0.0020646754 0.0037842431
## 4 0.0125291452 -0.00910676259 -0.0046225124 0.0064655172 -0.0001216361
## 5 0.0002929528 0.00379718869 0.0009422492 -0.0049678958 0.0080271956
## 6 0.0070978470 0.00186409873 0.0015465017 -0.0001721326 -0.0041625676
## 7 0.0192638665 0.01001423758 0.0060423577 0.0197158923 0.0058762096
## 8 -0.0018219040 -0.00823538068 0.0004003841 -0.0040527132 0.0048784200
## 9 -0.0025729848 0.01764542843 0.0087385600 -0.0004238337 -0.0058736047
## 10 0.0108254778 0.00617346953 0.0010580853 -0.0020354973 -0.0006631737
## 11 0.0166204879 0.01221794075 0.0085215566 0.0077335232 0.0045246140
## 12 -0.0033684639 0.00063248533 0.0105456254 -0.0059875112 0.0081076581
## 13 0.0068888579 0.00015802139 0.0023334237 0.0150165148 -0.0013106233
## 14 -0.0102197870 0.00616210143 -0.0217925190 -0.0081076665 -0.0019685149
## 15 0.0161360029 0.00685727001 -0.0001983128 -0.0069099158 0.0062160574
## 16 -0.0170702126 -0.00753840479 0.0149430999 -0.0201102685 -0.0032076538
## 17 -0.0091483432 -0.02105808875 -0.0247557202 -0.0170592411 -0.0138251123
## 18 0.0066135519 0.01658813551 -0.0182364448 -0.0007929166 -0.0009668479
## 19 -0.0029706300 0.00005268852 -0.0176226190 0.0126961952 -0.0134276973
## 20 -0.0057414674 0.00157896618 0.0004155531 -0.0107087180 -0.0089510558
## 21 -0.0151803536 0.00525513708 0.0058155381 0.0031681829 0.0057532197
## 22 0.0139705881 0.00501859348 0.0095677272 0.0286867649 0.0120555507
## 23 -0.0033732981 0.00925877128 0.0072953388 -0.0239638848 0.0006685342
## 24 0.0007032766 0.00164926726 0.0004061023 -0.0155526328 0.0143334388
## 25 0.0140127500 0.00782088483 -0.0123816089 0.0039940054 -0.0057481078
## 26 -0.0077542597 -0.00709654069 0.0030828043 0.0075141306 0.0145739122
## 27 -0.0069635503 0.01239203885 0.0045076060 -0.0107045820 -0.0083694643
## 28 -0.0029896372 -0.01914776923 0.0003399718 0.0029268455 0.0017359544
## 29 -0.0204608070 0.07264912559 -0.0025148533 -0.0080474323 0.0007767530
## 30 0.0099714662 0.02857839055 -0.0091986297 -0.0110546303 -0.0137330016
## 31 -0.0052373658 0.00549114436 0.0002750381 -0.0080230721 0.0074464889
## 32 0.0002464106 -0.00816840905 0.0006187442 -0.0084514749 0.0022834542
## 33 0.0083322163 0.01967147898 0.0028171202 -0.0068737970 0.0042568904
## 34 0.0161046695 -0.01098446902 -0.0020555194 0.0094130365 0.0063283436
## 35 0.0013553880 -0.02151290660 0.0146241330 0.0215761626 -0.0052800154
## 36 -0.0171815202 -0.01044442607 0.0065638194 -0.0087703217 0.0035187949
## 37 0.0264560928 0.00313265159 0.0024873621 0.0297038719 0.0011292193
## 38 -0.0101928012 0.00446818457 -0.0129425479 0.0028057842 -0.0094983133
## 39 -0.0033233187 0.01999326795 -0.0025137245 0.0003497501 0.0035959893
## 40 -0.0217171812 0.00398596063 -0.0069473111 0.0042828236 -0.0049567145
## 41 0.0142614046 -0.01625413773 0.0024691399 0.0019147190 -0.0102028388
## 42 0.0250707379 0.02910457233 0.0019157004 -0.0013898858 -0.0133397828
## 43 0.0042056284 0.01623992744 -0.0027998064 -0.0067849581 0.0072516757
## 44 0.0049612941 0.00581104442 -0.0023282636 0.0050797147 -0.0004270413
## 45 -0.0067746908 0.02162037111 0.0054224262 -0.0121122287 0.0084233954
## 46 0.0001506344 0.00653888403 -0.0068268708 -0.0104966253 0.0079292870
## 47 0.0172324322 0.00377484560 0.0107919121 -0.0110536447 -0.0051645483
## 48 0.0128165054 0.01880358225 0.0161849002 0.0088335650 0.0068815608
## 49 0.0007099675 -0.02322082798 0.0018068948 0.0118835048 -0.0075540152
## 50 0.0013563297 0.01305086728 0.0012024578 0.0001765708 0.0064637391
## 51 0.0257356130 0.01674330148 -0.0042700785 0.0171272402 -0.0121841352
## 52 0.0219206017 0.00179186621 0.0118600171 0.0072042517 0.0144002618
## 53 -0.0016699065 -0.02529598099 0.0368850243 0.0137883356 0.0149146783
## 54 -0.0318013490 -0.02053483095 -0.0074083769 0.0098606228 -0.0059017941
## 55 -0.0026326048 0.00057991296 -0.0046969228 -0.0229798256 -0.0028496540
## 56 0.0043511763 -0.00156029980 -0.0029090241 -0.0068924188 0.0017265615
## 57 0.0104919211 0.00468828256 -0.0122536263 -0.0161359680 -0.0096879934
## 58 -0.0110738225 -0.02875428371 0.0257958157 0.0141080894 0.0082823486
## 59 0.0102937726 -0.00480455672 0.0214998761 0.0210416322 -0.0065476554
## 60 0.0148868387 0.00216102446 0.0062640942 -0.0008515582 0.0132415027
## 61 -0.0126445255 0.00128463374 -0.0129482186 -0.0104832808 0.0048488680
## 62 0.0262827005 0.00256597115 0.0174697548 0.0178294550 -0.0484316841
## 63 0.0066446205 0.01499085344 -0.0215706669 0.0035541861 -0.0058132496table.Stats(m1)## daily.returns daily.returns.1 daily.returns.2 daily.returns.3
## Observations 63.0000 63.0000 63.0000 63.0000
## NAs 0.0000 0.0000 0.0000 0.0000
## Minimum -0.0318 -0.0288 -0.0248 -0.0240
## Quartile 1 -0.0043 -0.0032 -0.0045 -0.0083
## Median 0.0014 0.0038 0.0009 -0.0004
## Arithmetic Mean 0.0029 0.0044 0.0010 0.0001
## Geometric Mean 0.0028 0.0043 0.0009 0.0000
## Quartile 3 0.0129 0.0123 0.0064 0.0076
## Maximum 0.0265 0.0726 0.0369 0.0297
## SE Mean 0.0016 0.0022 0.0014 0.0015
## LCL Mean (0.95) -0.0003 0.0001 -0.0018 -0.0030
## UCL Mean (0.95) 0.0061 0.0088 0.0038 0.0032
## Variance 0.0002 0.0003 0.0001 0.0001
## Stdev 0.0126 0.0172 0.0113 0.0122
## Skewness -0.2221 1.1893 0.2709 0.3012
## Kurtosis -0.2105 3.8479 0.9854 -0.3024
## daily.returns.4
## Observations 63.0000
## NAs 0.0000
## Minimum -0.0484
## Quartile 1 -0.0058
## Median 0.0008
## Arithmetic Mean -0.0002
## Geometric Mean -0.0002
## Quartile 3 0.0063
## Maximum 0.0149
## SE Mean 0.0012
## LCL Mean (0.95) -0.0027
## UCL Mean (0.95) 0.0023
## Variance 0.0001
## Stdev 0.0099
## Skewness -1.8032
## Kurtosis 7.2615table.Stats(m2)## daily.returns daily.returns.1 daily.returns.2 daily.returns.3
## Observations 63.0000 63.0000 63.0000 63.0000
## NAs 0.0000 0.0000 0.0000 0.0000
## Minimum -0.0450 -0.0359 -0.0307 -0.0298
## Quartile 1 -0.0060 -0.0046 -0.0076 -0.0078
## Median 0.0006 0.0022 0.0035 0.0006
## Arithmetic Mean 0.0017 0.0011 0.0025 0.0000
## Geometric Mean 0.0016 0.0010 0.0024 0.0000
## Quartile 3 0.0117 0.0080 0.0138 0.0059
## Maximum 0.0249 0.0222 0.0364 0.0260
## SE Mean 0.0017 0.0015 0.0019 0.0014
## LCL Mean (0.95) -0.0016 -0.0020 -0.0013 -0.0028
## UCL Mean (0.95) 0.0050 0.0041 0.0062 0.0029
## Variance 0.0002 0.0001 0.0002 0.0001
## Stdev 0.0132 0.0121 0.0149 0.0114
## Skewness -0.8540 -0.8223 -0.1328 0.1978
## Kurtosis 1.4584 1.1043 -0.5527 0.0266
## daily.returns.4
## Observations 63.0000
## NAs 0.0000
## Minimum -0.0144
## Quartile 1 -0.0035
## Median 0.0011
## Arithmetic Mean 0.0012
## Geometric Mean 0.0012
## Quartile 3 0.0043
## Maximum 0.0191
## SE Mean 0.0009
## LCL Mean (0.95) -0.0006
## UCL Mean (0.95) 0.0031
## Variance 0.0001
## Stdev 0.0073
## Skewness 0.2822
## Kurtosis 0.0289Lets create multi-plots for both the portfolios
plot(port1)
plot(port2)
Risk Analytics
Lets startb with risk analysis we will calculate & visualize the following;
- Performance Summary Chart
- Standard Deviation
- Portfolio Variance
- Average Portfolio Return
- Volatility
- Wealth Index Visualization
- Sharpe Ratio
- Sortino Ratio
- Treynor Ratio
- Beta
- Alpha
- VAR
- Drawdown Table & Chart
- Rolling Return Table & Chart
Lets start with running the weights of each stock
w1<- c(0.20,0.20,0.20,0.20,0.20)
w2<- c(0.20,0.20,0.20,0.20,0.20)We create the performance summary chart
# portfolio returns
r2<-Return.portfolio(m2,weights = w2)
r1<-Return.portfolio(m1, weights = w1)
r3<- cbind(r1,r2)
colnames(r3)<- c("Portfolio1", "Portfolio2")
charts.PerformanceSummary(r1) # Portfolio 1
charts.PerformanceSummary(r2) #Portfolio 2
Portfolio one has more cummulative returns
Standard Deviation of each stock & Portfolio
A measure of the dispersion of returns around the average.
sapply(port1, sd)## GS APPl JNJ XOM PG
## 0.012646018 0.017227933 0.011265835 0.012203117 0.009851581sapply(port2, sd)## JPM MSFT PFE CVX KO
## 0.013194791 0.012094461 0.014896498 0.011404871 0.007337365StdDev(r1) # Standard deviation of 1st portfolio## [,1]
## StdDev 0.006229384StdDev(r2) # Standard deviation of 2nd portfolio## [,1]
## StdDev 0.006424229Portfolio Covariance
Covariance measures the relationship between the returns of two assets.
#calculating intra-portfolio covariance
cov1<- cov(port1)
cov2<- cov(port2)
cov1## GS APPl JNJ XOM
## GS 0.00015992178 0.000038075488 0.00001754701 0.000055889271
## APPl 0.00003807549 0.000296801678 -0.00004634752 -0.000040549112
## JNJ 0.00001754701 -0.000046347519 0.00012691903 0.000036610389
## XOM 0.00005588927 -0.000040549112 0.00003661039 0.000148916075
## PG -0.00001745396 -0.000001536586 0.00002306568 -0.000007533705
## PG
## GS -0.000017453963
## APPl -0.000001536586
## JNJ 0.000023065676
## XOM -0.000007533705
## PG 0.000097053646cov2## JPM MSFT PFE CVX KO
## JPM 0.00017410250 -0.00001617804 0.00004864279 0.00005838190 0.00001660993
## MSFT -0.00001617804 0.00014627599 -0.00001286670 -0.00003191048 -0.00001504970
## PFE 0.00004864279 -0.00001286670 0.00022190566 0.00002449304 0.00005712185
## CVX 0.00005838190 -0.00003191048 0.00002449304 0.00013007107 0.00002070341
## KO 0.00001660993 -0.00001504970 0.00005712185 0.00002070341 0.00005383693Portfolio Volatility
A measure of the overall risk of a portfolio. It quantifies the dispersion of returns around the average portfolio return.
port1vol<- sqrt(t(w1)%*%cov1%*%w1)
port2vol<- sqrt(t(w2)%*%cov2%*%w2)
Portfolio<- (c('Portfolio1', 'Portfolio2'))
volatilitytable<- rbind(Portfolio, (c(port1vol,port2vol)))
volatilitytable## [,1] [,2]
## Portfolio "Portfolio1" "Portfolio2"
## "0.00614864575178647" "0.00640652213795473"Wealth Index
Charts illustrating the growth of the portfolio’s value over time.
d1<- Return.portfolio(m1, weights = w1, wealth.index = TRUE)
plot(d1)
d2 <- Return.portfolio(m2,weights = w2, wealth.index = TRUE)
plot(d2)
We
clearly see that portfolio 1 has a better wealth index
Sortino Ratio
Similar to Sharpe, but focuses on downside risk, using the Minimum Acceptable Return.
SortinoRatio(r1, MAR = 0.0513) #Portfolio1## portfolio.returns
## Sortino Ratio (MAR = 5.13%) -0.9923338SortinoRatio(r2, MAR= 0.0513) #Portfolio2## portfolio.returns
## Sortino Ratio (MAR = 5.13%) -0.9919832The Sortino ratio of Portfolio 2 is higher than portfolio one, hence it is better risk adjusted
Treynor Ratio
Measures excess return per unit of systematic risk (beta)
TreynorRatio(r1,b1, Rf= 0.0513)## [1] -2.434699TreynorRatio(r2,b1, Rf=0.0513)## [1] -5.5196The Treynor ratio of portfolio 2 is more than portfolio 1 hence its better in terms of risk adjustment
Beta
Measures the portfolio’s sensitivity to market movements
CAPM.beta(r1,b1)## [1] 0.4107273CAPM.beta(r2,b1)## [1] 0.1811721Portfolio 1’s beta is more than that of its counterpart hence it is more volatile
Alpha
The excess return of a portfolio compared to its expected return based on beta.
CAPM.alpha(r1,b1)## [1] 0.001060269CAPM.alpha(r2,b1)## [1] 0.0009994462The alpha of portfolio 1 ia better than alpha of portfolio2, hence return of portfolio 1 is better than portfolio 2
Var
The maximum potential loss over a specified period at a given confidence level.
VaR(r1)## portfolio.returns
## VaR -0.008760184VaR(r2)## portfolio.returns
## VaR -0.009016698The Var of r1 is better than var of portfolio 2
Drawdown Table & Chart
A table and visual representation of the largest decline in portfolio value from a peak.
table.Drawdowns(r1)## From Trough To Depth Length To Trough Recovery
## 1 2024-05-20 2024-05-29 2024-06-24 -0.0337 24 7 17
## 2 2024-07-18 2024-07-24 <NA> -0.0232 11 5 NA
## 3 2024-06-25 2024-06-28 2024-07-01 -0.0077 5 4 1
## 4 2024-07-11 2024-07-11 2024-07-12 -0.0047 2 1 1
## 5 2024-05-10 2024-05-10 2024-05-13 -0.0019 2 1 1chart.Drawdown(r1)
table.Drawdowns(r2)## From Trough To Depth Length To Trough Recovery
## 1 2024-05-16 2024-06-14 2024-06-24 -0.0223 26 21 5
## 2 2024-07-18 2024-07-24 2024-07-30 -0.0203 9 5 4
## 3 2024-07-31 2024-07-31 <NA> -0.0120 2 1 NA
## 4 2024-06-25 2024-06-26 2024-07-01 -0.0097 5 2 3
## 5 2024-07-08 2024-07-09 2024-07-10 -0.0082 3 2 1chart.Drawdown(r2)
Portfolio 2 is more volatile than Portfolio 1
Rolling return
table.RollingPeriods(r3)## Portfolio1 Portfolio2
## Last 12 day Average 0.0005 0.0008
## Last 36 day Average 0.0019 0.0011
## Last 60 day Average 0.0014 0.0011
## Last 12 day Std Dev 0.0068 0.0085
## Last 36 day Std Dev 0.0060 0.0065
## Last 60 day Std Dev 0.0061 0.0065chart.RollingPerformance(r1)
chart.RollingPerformance(r2)
Portfolio 1 has more returns than portfolio 2
Conclusion: Portfolio 1 is more riskier than Portfolio 2 but it is more rewarding too.