Asset Allocation using R
Ketki.S
2024-05-30
#Import Libraries
library("quantmod")## Warning: package 'quantmod' was built under R version 4.3.3## Loading required package: xts## Warning: package 'xts' was built under R version 4.3.2## Loading required package: zoo## Warning: package 'zoo' was built under R version 4.3.2##
## Attaching package: 'zoo'## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numeric## Loading required package: TTR## Warning: package 'TTR' was built under R version 4.3.2## Registered S3 method overwritten by 'quantmod':
## method from
## as.zoo.data.frame zoo#Download Monthly Data
start_date = "2016-01-01"
end_date = "2023-12-31"
#BRK
getSymbols("BRK-A", from = start_date, to = end_date, src = "yahoo", periodicity = "monthly")## [1] "BRK-A"BRK = `BRK-A`
BRK_16_24 = BRK$`BRK-A.Adjusted` #Extracted adjusted prices and created new data frame
BRK_16_18 = BRK_16_24[1:36,1] #Extracted 1 to 36 rows and from column 1
Rbrk_16_18 = diff(log(BRK_16_18)) #Calculated returns by taking the log of asset prices
Rbrk_16_24 = diff(log(BRK_16_24))
hist(Rbrk_16_18, xlab="Returns of BRK", main="BRK - Normal Distribution")
#Walmart
getSymbols("WMT", from = start_date, to = end_date, src = "yahoo", periodicity = "monthly")## [1] "WMT"WMT_16_24 = WMT$WMT.Adjusted
WMT_16_18 = WMT_16_24[1:36,1]
Rwmt_16_18 = diff(log(WMT_16_18))
Rwmt_16_24 = diff(log(WMT_16_24))
hist(Rwmt_16_18, xlab="Returns of Walmart", main="Walmart - Normal Distribution")
#Nvidia
getSymbols("NVDA", from=start_date, to=end_date, src = "yahoo" , periodicity="monthly")## [1] "NVDA"NVDA_16_24 = NVDA$NVDA.Adjusted
NVDA_16_18 = NVDA_16_24[1:36,1]
RNVDA_16_18 = diff(log(NVDA_16_18))
RNVDA_16_24 = diff(log(NVDA_16_24))
hist(RNVDA_16_18, xlab="Returns of Starbucks", main="Starbucks- Normal Distribution")
#Mastercard
getSymbols("MA", from=start_date, to=end_date, src = "yahoo" , periodicity="monthly")## [1] "MA"MA_16_24 = MA$MA.Adjusted
MA_16_18 = MA_16_24[1:36,1]
Rma_16_18 = diff(log(MA_16_18))
Rma_16_24 = diff(log(MA_16_24))
hist(Rma_16_18, xlab="Returns of Mastercard", main="Mastercard- Normal Distribution")
#LVMH
getSymbols("LVMUY", from=start_date, to=end_date, src = "yahoo" , periodicity="monthly")## [1] "LVMUY"LV_16_24 = LVMUY$LVMUY.Adjusted
LV_16_18 = LV_16_24[1:36,1]
Rlv_16_18 = diff(log(LV_16_18))
Rlv_16_24 = diff(log(LV_16_24))
hist(Rlv_16_18, xlab="Returns of LVMH", main="LVMH- Normal Distribution")
#Treasury Rate
getSymbols("^TNX", from = start_date, to = end_date, src = "yahoo")## Warning: ^TNX contains missing values. Some functions will not work if objects
## contain missing values in the middle of the series. Consider using na.omit(),
## na.approx(), na.fill(), etc to remove or replace them.## [1] "TNX"mtnx <- to.monthly(TNX)## Warning in to.period(x, "months", indexAt = indexAt, name = name, ...): missing
## values removed from datatnx_16_24 <- mtnx$TNX.Adjusted
tnx_16_18 <- tnx_16_24[1:36,1]
rtnx_16_18<- tnx_16_18/1200#Calculate Excess Returns
Re_brk = Rbrk_16_18 - rtnx_16_18
Re_wmt = Rwmt_16_18 - rtnx_16_18
Re_NVDA = RNVDA_16_18 - rtnx_16_18
Re_ma = Rma_16_18 - rtnx_16_18
Re_lv = Rlv_16_18 - rtnx_16_18#Data Frames & Matrix of Asset Metrics
AssetPrices = data.frame(BRK_16_18, WMT_16_18, NVDA_16_18, MA_16_18, LV_16_18)
AssetReturns = data.frame(Rbrk_16_18,Rwmt_16_18,RNVDA_16_18,Rma_16_18,Rlv_16_18)
AssetExcessR = data.frame(Re_brk,Re_wmt, Re_NVDA, Re_ma, Re_lv)
AssetReturns = AssetReturns[-1,]
AssetExcessR = AssetExcessR[-1,]
AssetPrices_Matrix = matrix(c(BRK_16_18,WMT_16_18, NVDA_16_18, MA_16_18, LV_16_18), nrow = length(MA_16_18), ncol = 5, byrow = TRUE) #Generating a matrix format for statistical purposes instead of a simple table. #Finding Variance-Covariance Matrix
asset.names <- c("BRK", "WMT", "NVDA", "MA", "LVMH")
VCV <- matrix(c(cov(AssetReturns)), nrow = 5, ncol = 5, byrow = TRUE)
dimnames(VCV) = list(asset.names, asset.names) #Calculate Returns
AssetReturns_Matrix <- matrix(colMeans(AssetReturns, na.rm = TRUE))
AssetExcessR_Matrix <- matrix(colMeans(AssetExcessR, na.rm = TRUE))
tnxy_mean <- mean((rtnx_16_18)[-1,])#Create Return and Excess Return Table
Return_Matrix <- matrix(c(AssetReturns_Matrix,AssetExcessR_Matrix), ncol=2)
dimnames(Return_Matrix) = list(asset.names, c("Returns", "Excess Returns"))#Display Data
VCV## BRK WMT NVDA MA LVMH
## BRK 1.456492e-03 6.201981e-04 0.001478205 0.0003922688 -1.218749e-05
## WMT 6.201981e-04 2.867651e-03 0.001383689 0.0001044939 7.673969e-05
## NVDA 1.478205e-03 1.383689e-03 0.018266094 0.0031105174 3.333210e-03
## MA 3.922688e-04 1.044939e-04 0.003110517 0.0022608166 1.398364e-03
## LVMH -1.218749e-05 7.673969e-05 0.003333210 0.0013983640 3.277513e-03Return_Matrix ## Returns Excess Returns
## BRK 0.01296780 0.011002609
## WMT 0.01175084 0.009785649
## NVDA 0.04380277 0.041837577
## MA 0.02205118 0.020085990
## LVMH 0.01868937 0.016724182#Optimum Weights
Z_weight <- solve(VCV,AssetExcessR_Matrix)
W_weight <- Z_weight/sum(Z_weight)
dimnames(W_weight) <- list(asset.names, "Weights")
print(W_weight)## Weights
## BRK 0.30888759
## WMT 0.12725563
## NVDA 0.02044932
## MA 0.40718712
## LVMH 0.13622033#Investing USD 100 in 2018 end
#Positions
BRK_position = W_weight[1,1]*100
WMT_position =W_weight[2,1]*100
NVDA_position = W_weight[3,1]*100
MA_position = W_weight[4,1]*100
LVMH_position = W_weight[5,1]*100
Positions = c(BRK_position, WMT_position, NVDA_position, MA_position, LVMH_position)
labels = c("BRK", "WMT", "NVDA", "MA", "LVMH")
pie(Positions, labels, main = "Position sizes", col = rainbow(length(Positions)))
#Portfolio Value
#BRK
BRK_19_24 = BRK_16_24[37:96]
BRK_shares = BRK_position/BRK_19_24[1,1]
df_brk = data.frame(value = rep(BRK_shares, 60))
BRK_port = df_brk$value*BRK_19_24$`BRK-A.Adjusted`
print(BRK_port)## BRK-A.Adjusted
## 2019-01-01 30.88876
## 2019-02-01 29.96656
## 2019-03-01 29.86888
## 2019-04-01 32.23537
## 2019-05-01 29.45687
## 2019-06-01 31.56801
## 2019-07-01 30.60774
## 2019-08-01 30.05362
## 2019-09-01 30.92168
## 2019-10-01 31.62642
## 2019-11-01 32.77233
## 2019-12-01 33.67420
## 2020-01-01 33.31782
## 2020-02-01 30.65038
## 2020-03-01 26.97189
## 2020-04-01 27.93375
## 2020-05-01 27.63032
## 2020-06-01 26.50583
## 2020-07-01 29.11685
## 2020-08-01 32.48129
## 2020-09-01 31.73173
## 2020-10-01 29.99631
## 2020-11-01 34.08056
## 2020-12-01 34.48980
## 2021-01-01 34.12142
## 2021-02-01 36.15224
## 2021-03-01 38.24673
## 2021-04-01 40.90406
## 2021-05-01 43.23435
## 2021-06-01 41.50904
## 2021-07-01 41.53869
## 2021-08-01 42.62946
## 2021-09-01 40.79290
## 2021-10-01 42.92715
## 2021-11-01 41.33799
## 2021-12-01 44.68825
## 2022-01-01 46.58650
## 2022-02-01 47.22113
## 2022-03-01 52.44852
## 2022-04-01 48.02781
## 2022-05-01 47.00744
## 2022-06-01 40.55203
## 2022-07-01 44.79118
## 2022-08-01 41.77747
## 2022-09-01 40.30611
## 2022-10-01 44.13176
## 2022-11-01 47.62521
## 2022-12-01 46.47801
## 2023-01-01 46.90332
## 2023-02-01 45.96376
## 2023-03-01 46.16952
## 2023-04-01 49.86626
## 2023-05-01 48.39312
## 2023-06-01 51.34674
## 2023-07-01 53.09098
## 2023-08-01 54.21399
## 2023-09-01 52.70197
## 2023-10-01 51.34822
## 2023-11-01 54.13218
## 2023-12-01 53.80743#WMT
WMT_19_24 = WMT_16_24[37:96]
WMT_shares = WMT_position/WMT_19_24[1,1]
df_wmt = data.frame(value = rep(WMT_shares, 60))
WMT_port = df_wmt$value*WMT_19_24$WMT.Adjusted
print(WMT_port)## WMT.Adjusted
## 2019-01-01 12.72556
## 2019-02-01 13.14519
## 2019-03-01 12.95131
## 2019-04-01 13.72992
## 2019-05-01 13.54301
## 2019-06-01 14.82962
## 2019-07-01 14.81486
## 2019-08-01 15.33561
## 2019-09-01 16.00726
## 2019-10-01 15.81574
## 2019-11-01 16.06257
## 2019-12-01 16.02885
## 2020-01-01 15.51139
## 2020-02-01 14.58875
## 2020-03-01 15.39352
## 2020-04-01 16.54077
## 2020-05-01 16.88233
## 2020-06-01 16.37160
## 2020-07-01 17.68646
## 2020-08-01 18.97810
## 2020-09-01 19.20160
## 2020-10-01 19.04240
## 2020-11-01 20.96928
## 2020-12-01 19.78351
## 2021-01-01 19.35167
## 2021-02-01 17.89572
## 2021-03-01 18.70979
## 2021-04-01 19.35225
## 2021-05-01 19.64549
## 2021-06-01 19.58238
## 2021-07-01 19.79484
## 2021-08-01 20.56553
## 2021-09-01 19.42587
## 2021-10-01 20.82518
## 2021-11-01 19.60009
## 2021-12-01 20.16595
## 2022-01-01 19.56426
## 2022-02-01 18.91356
## 2022-03-01 20.83906
## 2022-04-01 21.49140
## 2022-05-01 18.06941
## 2022-06-01 17.14114
## 2022-07-01 18.61727
## 2022-08-01 18.68776
## 2022-09-01 18.36559
## 2022-10-01 20.15400
## 2022-11-01 21.58275
## 2022-12-01 20.07754
## 2023-01-01 20.44886
## 2023-02-01 20.20155
## 2023-03-01 20.95770
## 2023-04-01 21.54597
## 2023-05-01 20.96083
## 2023-06-01 22.51745
## 2023-07-01 22.90139
## 2023-08-01 23.29535
## 2023-09-01 22.99286
## 2023-10-01 23.49318
## 2023-11-01 22.38329
## 2023-12-01 22.66507#NVDA
NVDA_19_24 = NVDA_16_24[37:96]
NVDA_shares = NVDA_position/NVDA_19_24[1,1]
df_nvda = data.frame(value = rep(NVDA_shares, 60))
NVDA_port = df_nvda$value*NVDA_19_24$NVDA.Adjusted
print(NVDA_port)## NVDA.Adjusted
## 2019-01-01 2.044932
## 2019-02-01 2.194443
## 2019-03-01 2.556984
## 2019-04-01 2.577490
## 2019-05-01 1.928988
## 2019-06-01 2.341350
## 2019-07-01 2.405362
## 2019-08-01 2.388111
## 2019-09-01 2.484091
## 2019-10-01 2.868684
## 2019-11-01 3.093019
## 2019-12-01 3.360359
## 2020-01-01 3.376497
## 2020-02-01 3.856916
## 2020-03-01 3.766769
## 2020-04-01 4.176597
## 2020-05-01 5.073134
## 2020-06-01 5.428806
## 2020-07-01 6.070038
## 2020-08-01 7.648200
## 2020-09-01 7.737407
## 2020-10-01 7.169704
## 2020-11-01 7.665931
## 2020-12-01 7.467727
## 2021-01-01 7.432598
## 2021-02-01 7.847293
## 2021-03-01 7.637727
## 2021-04-01 8.591241
## 2021-05-01 9.298141
## 2021-06-01 11.449169
## 2021-07-01 11.163531
## 2021-08-01 12.815818
## 2021-09-01 11.862378
## 2021-10-01 14.640152
## 2021-11-01 18.710902
## 2021-12-01 16.841300
## 2022-01-01 14.022869
## 2022-02-01 13.965027
## 2022-03-01 15.626396
## 2022-04-01 10.623476
## 2022-05-01 10.695074
## 2022-06-01 8.682873
## 2022-07-01 10.405725
## 2022-08-01 8.647471
## 2022-09-01 6.954528
## 2022-10-01 7.734834
## 2022-11-01 9.698201
## 2022-12-01 8.377106
## 2023-01-01 11.199092
## 2023-02-01 13.307986
## 2023-03-01 15.922462
## 2023-04-01 15.909115
## 2023-05-01 21.691067
## 2023-06-01 24.252669
## 2023-07-01 26.793541
## 2023-08-01 28.299238
## 2023-09-01 24.941517
## 2023-10-01 23.384419
## 2023-11-01 26.819259
## 2023-12-01 28.397333#MA
MA_19_24 = MA_16_24[37:96]
MA_shares = MA_position/MA_19_24[1,1]
df_ma= data.frame(value = rep(MA_shares, 60))
MA_port = df_ma$value*MA_19_24$MA.Adjusted
print(MA_port)## MA.Adjusted
## 2019-01-01 40.71871
## 2019-02-01 43.42428
## 2019-03-01 45.48759
## 2019-04-01 49.11771
## 2019-05-01 48.65428
## 2019-06-01 51.17705
## 2019-07-01 52.67446
## 2019-08-01 54.50108
## 2019-09-01 52.60282
## 2019-10-01 53.61780
## 2019-11-01 56.67335
## 2019-12-01 57.90677
## 2020-01-01 61.27152
## 2020-02-01 56.36446
## 2020-03-01 46.90922
## 2020-04-01 53.39721
## 2020-05-01 58.52103
## 2020-06-01 57.51162
## 2020-07-01 60.00695
## 2020-08-01 69.75851
## 2020-09-01 65.85957
## 2020-10-01 56.21347
## 2020-11-01 65.61258
## 2020-12-01 69.59603
## 2021-01-01 61.67010
## 2021-02-01 69.08098
## 2021-03-01 69.51048
## 2021-04-01 74.58833
## 2021-05-01 70.47843
## 2021-06-01 71.35996
## 2021-07-01 75.43527
## 2021-08-01 67.75332
## 2021-09-01 68.03709
## 2021-10-01 65.65751
## 2021-11-01 61.70419
## 2021-12-01 70.40374
## 2022-01-01 75.70578
## 2022-02-01 70.79042
## 2022-03-01 70.11551
## 2022-04-01 71.29269
## 2022-05-01 70.30910
## 2022-06-01 61.98093
## 2022-07-01 69.50752
## 2022-08-01 63.82518
## 2022-09-01 55.94861
## 2022-10-01 64.57486
## 2022-11-01 70.24076
## 2022-12-01 68.53204
## 2023-01-01 73.03934
## 2023-02-01 70.13564
## 2023-03-01 71.73856
## 2023-04-01 75.01941
## 2023-05-01 72.16942
## 2023-06-01 77.76075
## 2023-07-01 77.95452
## 2023-08-01 81.70252
## 2023-09-01 78.39000
## 2023-10-01 74.51712
## 2023-11-01 82.05692
## 2023-12-01 84.57120#LVMH
LV_19_24 = LV_16_24[37:96]
LVMH_shares = LVMH_position/LV_19_24[1,1]
df_lv= data.frame(value = rep(LVMH_shares, 60))
LV_port = df_lv$value*LV_19_24$LVMUY.Adjusted
print(LV_port)## LVMUY.Adjusted
## 2019-01-01 13.62203
## 2019-02-01 14.54643
## 2019-03-01 15.62771
## 2019-04-01 16.66023
## 2019-05-01 16.19028
## 2019-06-01 18.25348
## 2019-07-01 17.74305
## 2019-08-01 17.11250
## 2019-09-01 17.01814
## 2019-10-01 18.30495
## 2019-11-01 19.15639
## 2019-12-01 20.00355
## 2020-01-01 18.80268
## 2020-02-01 17.84076
## 2020-03-01 16.04849
## 2020-04-01 16.60278
## 2020-05-01 18.39228
## 2020-06-01 19.32774
## 2020-07-01 18.86001
## 2020-08-01 20.62513
## 2020-09-01 20.73294
## 2020-10-01 20.71094
## 2020-11-01 25.39527
## 2020-12-01 27.55358
## 2021-01-01 26.96155
## 2021-02-01 28.05724
## 2021-03-01 29.56603
## 2021-04-01 33.32364
## 2021-05-01 35.73675
## 2021-06-01 35.08529
## 2021-07-01 35.66115
## 2021-08-01 32.93749
## 2021-09-01 31.85691
## 2021-10-01 34.98747
## 2021-11-01 34.81182
## 2021-12-01 36.79731
## 2022-01-01 36.48911
## 2022-02-01 32.54766
## 2022-03-01 31.83976
## 2022-04-01 28.99254
## 2022-05-01 29.13014
## 2022-06-01 27.59911
## 2022-07-01 31.33409
## 2022-08-01 29.23402
## 2022-09-01 26.53327
## 2022-10-01 28.50237
## 2022-11-01 34.54970
## 2022-12-01 32.95038
## 2023-01-01 39.73287
## 2023-02-01 37.89965
## 2023-03-01 41.78900
## 2023-04-01 43.66772
## 2023-05-01 40.12715
## 2023-06-01 43.27838
## 2023-07-01 42.68481
## 2023-08-01 38.79562
## 2023-09-01 34.63141
## 2023-10-01 32.84152
## 2023-11-01 34.78725
## 2023-12-01 37.52659#No. of Shares
Shares = c(BRK_shares, WMT_shares, NVDA_shares, MA_shares, LVMH_shares)
print(Shares)## BRK-A.Adjusted
## 2019-01-01 9.916135e-05
## 2019-01-01 4.358847e-01
## 2019-01-01 5.735060e-02
## 2019-01-01 1.988742e-01
## 2019-01-01 2.332116e-01#Total Portfolio
Portfolio = data.frame(BRK_port, WMT_port, NVDA_port, MA_port, LV_port)
Portfolio$Total = rowSums(Portfolio)
print(Portfolio$Total)## [1] 100.0000 103.2769 106.4925 114.3207 109.7734 118.1695 118.2455 119.3909
## [9] 119.0340 122.2336 127.7577 130.9737 132.2799 123.3013 109.0899 118.6511
## [17] 126.4991 125.1456 131.7403 149.4912 145.2632 133.1328 153.7236 158.8906
## [25] 149.5373 159.0335 163.6708 176.7595 178.3932 178.9858 183.5935 176.7016
## [33] 171.9751 179.0375 176.1650 188.8965 192.3685 183.4378 190.8693 180.4279
## [41] 175.2112 155.9561 174.6558 162.1719 148.1081 165.0978 183.6966 176.4151
## [49] 191.3235 187.5086 196.5772 206.0085 203.3416 219.1560 223.4252 226.3067
## [57] 213.6578 205.5845 220.1789 226.9676Total_Portfolio = data.frame(Portfolio$Total)
print(Total_Portfolio)## Portfolio.Total
## 1 100.0000
## 2 103.2769
## 3 106.4925
## 4 114.3207
## 5 109.7734
## 6 118.1695
## 7 118.2455
## 8 119.3909
## 9 119.0340
## 10 122.2336
## 11 127.7577
## 12 130.9737
## 13 132.2799
## 14 123.3013
## 15 109.0899
## 16 118.6511
## 17 126.4991
## 18 125.1456
## 19 131.7403
## 20 149.4912
## 21 145.2632
## 22 133.1328
## 23 153.7236
## 24 158.8906
## 25 149.5373
## 26 159.0335
## 27 163.6708
## 28 176.7595
## 29 178.3932
## 30 178.9858
## 31 183.5935
## 32 176.7016
## 33 171.9751
## 34 179.0375
## 35 176.1650
## 36 188.8965
## 37 192.3685
## 38 183.4378
## 39 190.8693
## 40 180.4279
## 41 175.2112
## 42 155.9561
## 43 174.6558
## 44 162.1719
## 45 148.1081
## 46 165.0978
## 47 183.6966
## 48 176.4151
## 49 191.3235
## 50 187.5086
## 51 196.5772
## 52 206.0085
## 53 203.3416
## 54 219.1560
## 55 223.4252
## 56 226.3067
## 57 213.6578
## 58 205.5845
## 59 220.1789
## 60 226.9676plot(Portfolio$Total, main = "Hypothetical Path of USD 100", type="l", col= "black")
#Calculate Stats
Return_Portfolio <- t(W_weight)%*%AssetReturns_Matrix
Variance_Portfolio <- t(W_weight)%*%VCV%*%(W_weight)
SD_Portfolio <- Variance_Portfolio^0.5
Sharpe_Ratio <- ((Return_Portfolio - tnxy_mean)/SD_Portfolio)Monthly Optimal Stats table indicate strong performance
#Optimal Stats Table
PortfolioStats_Matrix <- matrix(c(Return_Portfolio, Variance_Portfolio, SD_Portfolio, Sharpe_Ratio))
PortfolioStats.names <- c("Return", "Variance", "SD", "Sharpe Ratio")
dimnames(PortfolioStats_Matrix) <- list(PortfolioStats.names, "Opt. Portfolio")
PortfolioStats_Matrix## Opt. Portfolio
## Return 0.017921519
## Variance 0.001039977
## SD 0.032248670
## Sharpe Ratio 0.494790279#Global Minimum Variance Portfolio
ZGMV <- solve(VCV,matrix(c(1,1,1,1,1), byrow = TRUE))
WGMV <- ZGMV/sum(ZGMV)
dimnames(WGMV) <- list(asset.names, "Weights")
print(WGMV)## Weights
## BRK 0.45824952
## WMT 0.18731268
## NVDA -0.08898693
## MA 0.22720437
## LVMH 0.21622037#Calculate GMV Portfolio Stats
RGMV <- t(WGMV)%*%AssetReturns_Matrix
VGMV <- t(WGMV)%*%VCV%*%WGMV
SDGMV <- VGMV^0.5 #Create GMV Stats Table
GTBL <- matrix(c(RGMV, VGMV, SDGMV), nrow = 3)
gmvstat.names <- c("Return", "Variance", "Std Dev")
dimnames(GTBL) <- list(gmvstat.names, "GMV Portfolio")#Efficient Frontier and CAL
j <- 0
return_p <- rep(0, 50000)
sd_p <- rep(0, 50000)
vect_0 <- rep(0, 50000) #create a matrix of 0
fractions <- matrix(vect_0, 10000,5)
for (a in seq(-.2, 1, 0.1)) { #iterate through weights for asset 1 from -20% to 100% by 10%
for (b in seq(-.2, 1, 0.1)) { #iterate through weights for asset 2 from -20% to 100% by 10%
for(c in seq(-.2, 1, 0.1)){ #iterate through weights for asset 3 from -20% to 100% by 10%
for(d in seq(-.2, 1, 0.1)){ #iterate through weights for asset 4 from -20% to 100% by 10%
for(e in seq(-.2, 1, 0.1)){ #iterate through weights for asset 5 from -20% to 100% by 10%
if(a+b+c+d+e==1) { #test that the weights are equal to 1
j=j+1 #increment j by 1 if a+b+c+d+e is equal to 1 (valid weights)
fractions[j,] <- c(a,b,c,d,e) #load a,b,c,d,e values into row j of the matrix
sd_p[j] <- (t(fractions[j,])%*%VCV%*%fractions[j,])^.5 #calculate the std dev of the portfolio at a given weight of assets
return_p[j] <- fractions[j,]%*%AssetReturns_Matrix #calcuate the return of the portfolio at a given weight of assets
}
}
}
}
}
}
Rport <- return_p[1:j] #assign filled vector spots in return_p to the R_p matrix to omit empty spots
Stddev_p <- sd_p[1:j] #assign filled vector spots in sd_p to the sigma_p matrix to omit empty spots
##Create Capital Asset Line
f <- seq(0,.24, .24) #create x-coordinates for CAL points
CAL <- tnxy_mean+Sharpe_Ratio*f## Warning in Sharpe_Ratio * f: Recycling array of length 1 in array-vector arithmetic is deprecated.
## Use c() or as.vector() instead.Sharpe_Ratio## [,1]
## Weights 0.4947903#Plot
plot(Stddev_p, Rport, col="yellow1", xlab="Portfolio Standard Deviation", ylab= "Portfolio expected return", xlim=c(0, .12), ylim= c(0, .035))
points(SDGMV, RGMV, col="blue3", pch=17)
points(SD_Portfolio, Return_Portfolio, col= "black", pch=16, bg="black")
points(f, CAL, col= "cadetblue", type="l")
legend("bottomright",c("SD/R", "GMV", "Tangency Portfolio"),cex=.8,col=c("yellow1","blue3", "black","cadetblue"),lty = c(0,0,0,1),pch=c(1,17,16,NA_integer_))