Question

please help me with this calculations. i used the data analysis to figure out the correlation matrix.

Below there are 10 Assets

row 66: Mean Return

Row 67: Standard Deviation

Row 69: Annual Return

Row 70 Annual ST. deviation

I used the data analysis to calculate the CORRELATION matrix with the DATA ASSET RANGE. now im stuck on how to calculate the covariance matrix

Enr gy Telc 0.0559 0.0508 0.0093 0.0297 0.0352 0.0065 0.0249 0.0646 0.0165 0.0554 0.0524 0.0278 0.0307 0.0533 0.0647 11 0 0.02440.0118 0.0084 0.0009 0.0268 0.0057 0.0256 12 0.0142 0.0027 0.0052 0.05670.0154 0.0115 0.0025 0.0397 0.0094 0.003 0.0094 0.0188 0.0541 0.0128 0.0286 15 0.0431 0.0463 0.0481 0.0358 0.0286 0.0035 0.0046 0.0648 0.023 0.0033 16 0.0554 0.052 0.0461 0.02270.051 0.0427 0.0052 0.0539 0.0515 0.0543 0.034 0.0144 0.0008 18 0.0264 0.0386 0.0309 0.0444 0.0093 0.0129 0.0141 0.06690.0303 0.0576 19 0.0479 0.0474 0 0.0257 0.0424 0.0304 0.00290.0746 0.0267 20 0.0236 0.0058 0.006 0.00410.0064 0.0131 0.0173 0.0185 0.01590.0088 0.0156 0.0913 0.0437 0.0555 0.0431 23 0.02430.0040.0155 0.0264 0.0293 0.0245 0.022 0.00280.0070.0084 0.003 0.0218 0.0139 0.00920.0488 26 0.01320.0149 0.02020.03840.0161 0.03550.0049 0.05370.006 0.0008 27 0.04790.0217 0.0197 0.08970.0242 0.0237 0.0141 0.026 0.0478 0.0366 0.05830.0842 0.0401 0.0534 0.0835 29 0.00620.0323 -0.044 0.0581 0.0386 0.01430.0261 -0.0056 0.0181 0.0729 0.0885 0.0207 0.0452 0.0772 31 0.0098 0.0194 0.0059 0.0109 0.0029 0.0116 0.0192 0.03450.0085 0.0071 32 0 0.037 0.09680.0078 0.0252 0.0302 0.02360.0029 0.0038 33 0.0011 0.1253 0.0612 0.04630.047 0.0605 0.0036 0.0462 0.0417 0.0942 0.0029 9 0.0570.0362 0.0403 0.07040.0466 0.01210.04 10 0.0346 0.0792 0.0527 0.0326 0.0101-0.0009 13 0.0344 0.0064 0.0128 0.0087 0.0121 0.0345 0.0397 14 0.0117 0.0438 0.0226 0.0415 0.0032 0.0296 17 0.00080.0942 0.03090.0802 0.0095 0.0131 0.017 0.02050.0987 21 0.00550.0419 0.0403 0.04390.0353 0.03370.0489 0.0118 0.003 22 0.0503 0.0808 0.06220.0482 0.0623 0.083 24 0.0081 0.0093 0.0071 0.0694 0.0046 0.0139 0.034 25 0.0153 0.0103 0.0114 0.0507 0.0066 0.0201 0.0082-0.005 28 0.04180.0613 0.0485 0.0363 30 0.0664 0.0686 0.08270.1232 0.1135 0.00790.0403 0.02850.0095 0.1076 0.0728 0.1088 0.0597 0.0844 0.0602 0.0792 0.0573 0.0292 36 0.003 0.0146 0.02560.0910.0174 0.0409 0.006 0.00780.006 0.0356 37 0.0072 0.0111 0.007 -0.0090.0067 0.0509 0.003 0.02240.0099 0.0247 0.013 0.01890.0312 0.0737 0.0084 0.0014 39 0.0005 0.0864 0.0474 0.0279 0.0283 00777 0.0228 -0.0022 0.0349 0.0601 40 0.00610.0029 0.013 0.0139 0.0196 0.0191 0.0354 0.0392 0.0144 0.0321 0.0035 42 - 0 0.0283 -0.00610.03970.0744 38 0.0468 0.0569 0.006 0.0267 0.0251 0.0164 0.0015 0.0358 0.0009 0.0277 0.0289 0.0233 -0.0109 0.0293 0.004 0.01750.0068 43 0.0376 0.076 44 0.0353 0.0383 0.0035 0.0213 0.0079 0.0086 0.0468 0.0364 0.0042 0.0086 5 0.0163 0.0277 0.0323 0.04320.0381 0.0471 46 0.0373 0.0068 0.0409 0.0236 0.0419 47 0.0089 0.0005 0.002 0.0121 0.0085 0.0217 0.0084 0.0032 48 0.0051 0.0172 0.027 0.0282 0.0029 0.02790.0011 0.0036 0.0270.0109 49 0.03080.0052 0.01590.0346 0.0083 0.04250.0194 0.0258 0.0161 0.0043 50 0.00980.0351 0.0161 0.0022 0.0063 0.0214 0.0227 -0.01890.019 0.0556 51 0.0012 0.0111 0.0227 0.021 0.0194 0.0383 0.053 0.0299 0.0006 0.0053 52 0.0171 0.0016 0.00350.052 0.0117 0.03030.0256 0.02210.0166 0.0178 53 0.0033 0.0529 0.0503 0.1113 0.0234 0.00590.0168 0.0196 0.025 54 0.001 55 0.041 0.006 0.0337 0.0295 0.0379 0.0108 0.0372 0.0241 56 0.02010.0083 0.0249 0.0511 0.0177 0.0022 0.0459 0.05010.0244 0.0023 57 0.0191 0.0253 0.0617 0.0283 -0.0053 0.0763 0.0318 0.0281 0.094 0.0638 0.0909 0.0956 0.0078 0.0054 0.0627 -0.0284 0.0445 0.0138 0.0109 0.050.0007 0.0402 0.0281 0.071 0.034 0.01 0.0221 0.008 0.0016 0.015 0.0269 0.0224 0.0236 0.012 0.0367 0.003 0.0092 0.0684 0.0574 0.031 0.08 0.0621 0.0602 0.0327 0.1086 0.0576 0.0001 0.0732 0.0452 0.0473 59 0.0107 0.0559 0.0317 0.0296 0.0059 0.03310.0252 0.0320.0254 0.02 60 0.0396 0.0013 0.0359 0.1014 0.0278 0.00120.0241 0.0277 0.039 0.0028 61 0.0051 0.0295 0.0326 0.0348 0.0081 0.06930.0093 0.0021 0.0085 0.0243 62 0.0452 0.0079 -0.0216 0.0055 0.0219 0.0035 0.0623 0.0261 0.0303 0.0152 63 0.028 0.0142 0.0587 0.0107 0.0394 0.0224 0.0268 0.0173 0.0316 0.0612 64 0.01040.0052 0.00910.029 0.0114 0.0733 0.0295 0.0091 65 0.08 0.0446 0.008395 0.005232 0.011533 0.002352 0.0082630.017155 0.007372 0.007802 0.01339 0.01217 67 0.028851 0.043922 0.03614 0.054301 0.031371 0.036616 0.036304 0.03204 0.033658 0.036622 68 0.105524 0.064618 0.147526 0.028588 0.1037930.226438 0.092136 0.097743 0.173058 0.156223 0.099943 0.152152 0.125192 0.188105 0.1086720.126841 0.125761 0.110991 0.116595 0.126863 Annual Ret Annual S. D NoDur Durbl Manuf Enrgy Chems BusEq Telcm Utils 10.55241% 6.46183% 14.75256% 2.85879% 10.37931% 22.64382% 9.21361% 9.77435% 17.30577% 15.62228% 9.99433% 15.21520% 12.51916% 18.81052% 10.86716% 12.68409% 12.57610% 11,09907% 11.65946% 12.68634% 10 12 Hith 13 Correlation Matrix Durbl Manuf Enrgy Chems BusEq Telcm Shops NoDur NoDur 1 0.39493626 0.511977097 0.244246 0.719471 0.453824 0.657706 0.451208 0.58578 0.454882 1 0.82439851 0.501854 0.6925120.649297 0.534854 0.137239 0.616737 0.634625 1 0.561811 0.803162 0.679968 0.6182520.158923 0.662857 0.649035 1 0.528512 0.257657 0.478561 0.1910240.323178 0.239692 1 0.644442 0.700688 0.287812 0.6216260.64474 1 0.515346 077667 0.65046 0.604294 1 0.216198 0.601768 0.517999 1 0.187936 0.17909 1 0.663402 16 18 19 20 21 Durbl Manuf Enrgy Chems BusEq Telcm Utils 0.39493626 0.5119770970.82439851 0.244246167 0.501854182 0.561810927 0.719470961 0.692512001 0.803162325 0.528512 0.453824196 0.649296523 0.679968067 0.257657 0.644442 0.657706079 0.53485414 0.618252021 0.478561 0.700688 0.515346 0.451208472 0.137238688 0.158922541 0.191024 0.287812 0.177667 0.216198 23 24 25 26 27 28 29 30 31 32 0.58578004 0.616737319 0.662857139 0.323178 0.621626 0.65046 0.601768 0.187936 0.454881991 0.634624685 0.649034642 0.239692 0.64474 0.604294 0.517999 0.17909 0.663402 Hith Covariance Matrix NoDur Manuf Enrgy Chems BusEq Telcm Utils Shops Hlth Durbl Manuf Enrgy Chems BusEq Telcm Utils 36 Hith 37 38 39 Bordered Covariance Matrix for Target Returns Durbl Manuf Enrgy Chems BusEq Telcm Utils Shops Hith Weights 41 NoDur 42 Durbl 43 Manuf 44 Enrgy 45 Chems 46 BusEq 47 Telcm 48 Utils 49 Shops 50 Hlth 51 52 53 Formula Bar Port Var Port S.D Port Mean 56 57 58 59 60 61 62 63 Weights Chems Port S. D Durbl Manuf Enrgy Telcm Utils Shops Hith 10 65 12 13 14 15 16 18 20 67 68 69 71 72 73 74 Weights (Case A) 2 Mean Port S. D Durbl Manuf Enrgy Chems Bus Telcm Utils Shops Hith 10 12 13 14 15 16 18 20 13 14 15 16 17 18 19 Mean 20 21 Weights-Case B Port S. D NoDur Durbl Manuf Enrgy Chems BusE Telcm Utils Shops Hith 23 24 25 26 27 28 29 30 10 12 13 14 15 16 18 20 32 34 36 37 38

Answer 1

Hi,

Creation of the correlation matrix is very easy in R studio.

If you don't know R programming language, you can follow this link :https://www.guru99.com/r-programming-introduction-basics.html

To solve this problem in R.

You would need to follow the below code in R

# Import data in working directory data

dataset <- read.csv("data.csv") # here data.csv contains the data that you presented in the above screenshot.

# Creation of correlation matrix

cor(dataset)

# You will get the correlation matrix as you wanted (similar to the screenshot that you have shared)