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[Solved] Assignment 2 FIN 421 Spring 2021

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In this assignment you will apply mean variance analysis for an asset allocation decision. Mean Variance Analysis in Practice Assume you are a portfolio manager for a large pension fund and in charge of allocating funds across major asset classes. Specifically, today is 12/31/2014 and you are assembling a portfolio for January of 2015. Your investment universe consists of T-bonds (Barclays U.S. Treasury index), investment grade corporate bonds (Barclays U.S. Corp index), domestic stocks (S&P 500), international stocks (MSCI World index), commodities (Goldman Sachs Commodity In- dex), and gold. Asset allocation decisions are made based on mean variance analysis. On Canvas, you will find an Excel file containing historical monthly net returns for these assets. Assume that the risk-free rate for 1/2015 equals 25 basis points per month. QUESTIONS: A Report the mean and variance-covariance matrix for all assets. B Based on the moments you estimated in A, find the tangency portfolio and the minimum variance portfolio. Report the mean, standard deviation, and portfolio weights for both portfolios. C Compute the optimal share invested in risky assets for an investor with the utility function U = μ − ασ2 and values for risk aversion, α, between 10 and 40.1 Plot the optimal risky asset share as a function of α. Is the function increasing or decreasing? Explain economically why you find the slope that you do. D Plot the frontier of risky assets. To do so, use the minimum variance portfolio and the tangency portfolio found above, along with the two fund separation property. Use weights between -25 and 15 on the minimum variance portfolio (i.e. -2500% to 1500%). Add the individual assets as ’dots’ to the plot. E Suppose you form a portfolio that invests in both the minimum variance portfolio and the tangency portfolio. If the weight on the minimum variance portfolio equals 40%, what are the weights on the individual assets (T-bonds, corporate bonds, etc.)? 1Start by computing the optimal share in risky assets for a value of α = 10. Repeat for α = 11, α = 12 etc.

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Fixed Income Equities Commodities
Date T-Bonds Corp. Bonds S&P 500 MSCI World GSCI Gold
197301 -0.010 -0.002 -0.0168 0.003 0.034 0.020
197302 -0.003 0.004 -0.0338 0.008 0.043 0.292
197303 0.000 0.000 -0.0011 0.002 -0.024 0.058
197304 0.009 0.010 -0.0401 -0.050 0.060 0.005
197305 0.002 -0.004 -0.0140 -0.002 0.182 0.262
197306 0.003 -0.011 -0.0052 0.007 -0.017 0.079
197307 -0.021 -0.035 0.0391 0.025 0.258 -0.067
197308 0.020 0.037 -0.0315 -0.041 0.025 -0.097
197309 0.022 0.032 0.0422 0.030 -0.050 -0.036
197310 0.008 -0.011 0.0003 0.011 -0.053 -0.030
197311 0.006 0.011 -0.1072 -0.129 0.052 0.031
197312 -0.001 -0.013 0.0180 -0.007 0.105 0.120
197401 0.007 0.001 -0.0081 0.009 0.112 0.187
197402 0.003 0.002 0.0020 0.016 -0.005 0.272
197403 -0.016 -0.030 -0.0218 -0.024 -0.115 0.021
197404 -0.008 -0.030 -0.0376 -0.016 0.011 -0.026
197405 0.012 0.007 -0.0269 -0.039 -0.068 -0.071
197406 0.000 -0.045 -0.0128 -0.030 0.124 -0.062
197407 0.001 -0.009 -0.0767 -0.058 0.238 0.049
197408 0.001 -0.025 -0.0822 -0.095 -0.049 0.008
197409 0.025 0.012 -0.1175 -0.092 0.121 -0.050
197410 0.012 0.073 0.1681 0.097 0.090 0.128
197411 0.020 -0.003 -0.0457 -0.014 0.019 0.094
197412 0.012 -0.008 -0.0180 -0.015 -0.083 0.030
197501 0.012 0.068 0.1236 0.147 -0.156 -0.060
197502 0.012 0.020 0.0675 0.090 -0.104 0.031
197503 -0.004 -0.032 0.0240 0.008 0.084 -0.022
197504 -0.014 -0.009 0.0494 0.043 -0.046 -0.058
197505 0.020 0.026 0.0512 0.025 -0.015 0.002
197506 0.004 0.027 0.0462 0.014 0.016 -0.010
197507 -0.003 -0.002 -0.0655 -0.054 0.078 0.002
197508 0.004 -0.005 -0.0157 -0.014 0.096 -0.029
197509 -0.002 -0.012 -0.0323 -0.041 0.011 -0.144
197510 0.031 0.048 0.0649 0.070 -0.080 0.037
197511 -0.001 -0.005 0.0301 0.028 -0.012 -0.036
197512 0.019 0.035 -0.0105 0.002 -0.026 0.014
197601 0.010 0.029 0.1201 0.090 -0.048 -0.087
197602 0.002 0.010 -0.0058 -0.007 0.057 0.034
197603 0.010 0.015 0.0326 0.013 0.002 -0.021
197604 0.007 0.004 -0.0096 -0.006 0.038 -0.010
197605 -0.007 -0.009 -0.0081 -0.016 0.018 -0.023
197606 0.013 0.015 0.0440 0.032 -0.017 -0.012
197607 0.010 0.014 -0.0072 -0.008 -0.089 -0.092

,197608 0.014 0.022 0.0016 -0.001 -0.028 -0.083
197609 0.009 0.017 0.0244 0.009 -0.099 0.127
197610 0.012 0.010 -0.0202 -0.034 -0.012 0.053
197611 0.023 0.025 -0.0010 -0.003 0.014 0.064
197612 0.009 0.028 0.0538 0.076 0.050 0.034
197701 -0.017 -0.022 -0.0497 -0.033 -0.003 -0.018
197702 0.005 0.003 -0.0156 -0.003 -0.002 0.077
197703 0.007 0.008 -0.0125 -0.005 0.036 0.053
197704 0.006 0.011 0.0006 0.012 0.052 -0.022
197705 0.006 0.009 -0.0151 -0.013 -0.034 -0.023
197706 0.011 0.016 0.0478 0.039 -0.024 -0.002
197707 -0.004 0.003 -0.0155 -0.012 -0.085 0.011
197708 0.008 0.011 -0.0123 0.005 0.010 0.010
197709 0.000 -0.001 -0.0008 0.014 0.036 0.054
197710 -0.004 -0.006 -0.0420 -0.016 0.029 0.045
197711 0.009 0.009 0.0368 0.014 0.043 -0.006
197712 0.000 -0.008 0.0056 0.021 0.051 0.036
197801 0.001 -0.004 -0.0606 -0.028 0.032 0.058
197802 0.002 0.005 -0.0163 -0.006 0.016 0.039
197803 0.003 0.002 0.0269 0.047 0.103 -0.007
197804 0.002 0.000 0.0890 0.046 0.021 -0.059
197805 0.001 -0.009 0.0137 0.014 0.076 0.088
197806 -0.002 0.002 -0.0166 0.011 -0.093 -0.009
197807 0.009 0.013 0.0570 0.073 0.027 0.086
197808 0.009 0.022 0.0336 0.024 0.027 0.042
197809 0.002 -0.004 -0.0052 0.013 0.056 0.049
197810 -0.011 -0.020 -0.0896 -0.018 0.010 0.120
197811 0.009 0.011 0.0268 -0.034 0.026 -0.205
197812 -0.006 -0.015 0.0166 0.034 -0.012 0.159
197901 0.018 0.020 0.0427 0.027 0.072 0.038
197902 -0.001 -0.010 -0.0286 -0.018 0.059 0.077
197903 0.011 0.011 0.0574 0.043 -0.018 -0.045
197904 0.001 -0.006 0.0042 0.000 0.060 0.016
197905 0.017 0.023 -0.0168 -0.016 -0.047 0.138
197906 0.020 0.023 0.0403 0.030 0.013 -0.003
197907 -0.001 0.002 0.0121 0.009 -0.042 0.068
197908 -0.003 0.000 0.0619 0.041 0.115 0.076
197909 -0.001 -0.021 0.0014 0.024 0.043 0.249
197910 -0.040 -0.081 -0.0656 -0.073 -0.032 -0.043
197911 0.030 0.026 0.0528 0.032 0.069 0.099
197912 0.007 -0.004 0.0183 0.028 0.016 0.256
198001 -0.017 -0.048 0.0613 0.061 0.060 0.275
198002 -0.049 -0.069 0.0026 0.002 -0.009 -0.042
198003 0.011 -0.008 -0.0975 -0.106 -0.140 -0.214
198004 0.095 0.129 0.0424 0.067 0.037 0.032

,198005 0.036 0.058 0.0556 0.051 0.061 0.023
198006 0.014 0.025 0.0297 0.049 0.056 0.247
198007 -0.012 -0.027 0.0682 0.032 0.047 -0.067
198008 -0.030 -0.041 0.0135 0.021 0.016 0.025
198009 -0.004 -0.019 0.0279 0.031 0.056 0.057
198010 -0.012 -0.010 0.0178 0.030 0.031 -0.051
198011 -0.002 -0.005 0.1099 0.043 -0.014 -0.023
198012 0.031 0.028 -0.0306 -0.021 -0.074 -0.051
198101 0.001 -0.002 -0.0434 -0.028 -0.064 -0.139
198102 -0.013 -0.024 0.0213 0.004 -0.029 -0.034
198103 0.025 0.023 0.0383 0.037 -0.002 0.049
198104 -0.024 -0.052 -0.0202 0.002 -0.014 -0.065
198105 0.029 0.044 0.0065 -0.019 0.005 -0.005
198106 0.001 -0.001 -0.0083 -0.001 -0.064 -0.120
198107 -0.016 -0.023 0.0007 -0.016 0.045 -0.039
198108 -0.011 -0.026 -0.0555 -0.019 -0.033 0.050
198109 0.005 -0.017 -0.0505 -0.074 -0.001 0.002
198110 0.054 0.059 0.0521 0.032 0.003 0.006
198111 0.067 0.107 0.0438 0.076 -0.045 -0.031
198112 -0.026 -0.047 -0.0271 -0.020 -0.056 -0.037
198201 0.006 0.001 -0.0154 -0.014 0.080 -0.029
198202 0.014 0.023 -0.0504 -0.060 -0.022 -0.064
198203 0.011 0.016 -0.0068 -0.026 0.037 -0.118
198204 0.024 0.036 0.0416 0.050 0.036 0.113
198205 0.015 0.019 -0.0295 -0.024 0.002 -0.088
198206 -0.012 -0.024 -0.0158 -0.044 -0.030 -0.035
198207 0.040 0.046 -0.0202 -0.012 0.022 0.091
198208 0.044 0.071 0.1274 0.074 -0.002 0.196
198209 0.035 0.051 0.0105 0.006 -0.029 -0.036
198210 0.046 0.067 0.1139 0.070 -0.006 0.069
198211 0.007 0.016 0.0458 0.054 0.040 0.015
198212 0.020 0.018 0.0168 0.046 -0.011 0.046
198301 -0.002 0.005 0.0353 0.022 0.007 0.123
198302 0.026 0.035 0.0257 0.022 -0.011 -0.166
198303 -0.003 0.013 0.0355 0.036 0.067 -0.013
198304 0.022 0.041 0.0757 0.072 0.010 0.034
198305 -0.011 -0.020 -0.0057 -0.009 0.005 0.025
198306 0.003 0.000 0.0370 0.032 0.013 -0.051
198307 -0.019 -0.032 -0.0312 -0.017 0.035 0.013
198308 0.007 0.005 0.0159 0.006 0.018 -0.018
198309 0.030 0.036 0.0142 0.021 -0.027 -0.025
198310 0.003 -0.001 -0.0131 -0.011 -0.012 -0.051
198311 0.011 0.012 0.0238 0.027 0.001 0.058
198312 0.002 -0.003 -0.0057 0.014 0.050 -0.060
198401 0.017 0.028 -0.0039 0.009 0.010 -0.025

, 198402 -0.004 -0.012 -0.0340 -0.016 0.005 0.066
198403 -0.008 -0.013 0.0173 0.048 0.049 -0.020
198404 0.000 -0.009 0.0068 -0.003 -0.011 -0.032
198405 -0.023 -0.037 -0.0531 -0.074 0.029 0.019
198406 0.011 0.014 0.0229 0.009 -0.023 -0.021
198407 0.039 0.055 -0.0138 -0.034 -0.067 -0.090
198408 0.015 0.022 0.1124 0.101 0.043 0.018
198409 0.021 0.030 -0.0001 -0.003 -0.008 -0.010
198410 0.039 0.051 0.0033 0.011 0.005 -0.028
198411 0.017 0.017 -0.0098 -0.003 0.004 -0.018
198412 0.014 0.013 0.0256 0.021 -0.020 -0.060
198501 0.021 0.029 0.0769 0.056 0.013 -0.013
198502 -0.018 -0.025 0.0142 0.002 -0.013 -0.047
198503 0.019 0.019 -0.0006 0.035 0.043 0.135
198504 0.020 0.022 -0.0037 -0.002 -0.032 -0.016
198505 0.047 0.064 0.0627 0.052 0.000 -0.035
198506 0.010 0.008 0.0161 0.018 -0.029 0.011
198507 -0.003 -0.004 -0.0033 0.021 -0.022 0.037
198508 0.017 0.024 -0.0065 0.009 0.015 0.023
198509 0.008 0.001 -0.0332 0.008 0.057 -0.028
198510 0.020 0.024 0.0451 0.054 0.072 -0.002
198511 0.022 0.026 0.0719 0.056 0.017 0.005
198512 0.031 0.033 0.0482 0.047 -0.018 -0.001
198601 0.005 0.008 0.0047 0.015 -0.091 0.083
198602 0.043 0.048 0.0765 0.090 -0.035 -0.044
198603 0.042 0.024 0.0558 0.098 -0.002 0.021
198604 0.004 0.005 -0.0133 0.028 0.056 -0.002
198605 -0.025 -0.011 0.0553 -0.003 -0.038 -0.004
198606 0.034 0.019 0.0157 0.040 0.038 0.006
198607 0.006 0.005 -0.0575 0.008 0.010 0.035
198608 0.029 0.021 0.0744 0.088 0.086 0.079
198609 -0.016 -0.003 -0.0832 -0.039 -0.025 0.091
198610 0.014 0.017 0.0565 -0.017 0.011 -0.047
198611 0.011 0.014 0.0249 0.043 0.030 -0.029
198612 0.001 0.009 -0.0275 0.020 -0.007 0.002
198701 0.011 0.022 0.1352 0.118 0.057 0.042
198702 0.007 0.006 0.0418 0.033 -0.060 -0.004
198703 -0.007 -0.004 0.0263 0.062 0.081 0.033
198704 -0.025 -0.033 -0.0090 0.059 0.050 0.085
198705 -0.004 -0.005 0.0091 0.002 0.046 -0.006
198706 0.012 0.015 0.0501 0.000 0.036 -0.010
198707 -0.003 -0.003 0.0498 0.020 0.045 0.038
198708 -0.006 -0.006 0.0391 0.059 -0.020 -0.018
198709 -0.020 -0.028 -0.0219 -0.017 0.007 0.007
198710 0.040 0.033 -0.2158 -0.170 0.010 0.019

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[Solved] Assignment 2 FIN 421 Spring 2021

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