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 Blackboard, you will find an Excel file containing historical monthly net returns for these

assets. Assume that the risk-free rate for 1/2015 equals 0%.

QUESTIONS:

A Report the mean and variance-covariance matrix for all assets.

B Report the mean, standard deviation, and portfolio weights for both the tangency portfolio

and the minimum variance portfolio

C Compute the optimal share invested in risky assets for an investor with the utility function

U = ? ?? 2 and values for risk aversion, ?, between 10 and 40. 1 Plot the optimal

risky asset share as a function of ?. 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. Add the individual assets as ?dots?

to the plot.

E Food for thought, i.e. no need to hand this part in! Suppose you form a portfolio that invests

in both the minimum variance portfolio and the tangency portfolio. When the weight on

the minimum variance portfolio equals 5, what are the weights on the individual assets

(T-bonds, corporate bonds, etc.)?

PROF. DAVID SCHREINDORFER FIN 421 - SPRING 2016 Assignment 3 Due: Wednesday, 02.03.16 (11:59PM) In this assignment you will apply mean variance analysis for an asset allocation decision using real data. 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. Specically, 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 Index), and gold. Asset allocation decisions are made based on mean variance analysis. On Blackboard, you will nd an Excel le containing historical monthly net returns for these assets. Assume that the risk-free rate for 1/2015 equals 0%. QUESTIONS: A Report the mean and variance-covariance matrix for all assets. B Report the mean, standard deviation, and portfolio weights for both the tangency portfolio and the minimum variance portfolio C Compute the optimal share invested in risky assets for an investor with the utility function U = 2 and values for risk aversion, , between 10 and 40.1 Plot the optimal risky asset share as a function of . Is the function increasing or decreasing? Explain economically why you nd 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. Add the individual assets as 'dots' to the plot. E Food for thought, i.e. no need to hand this part in! Suppose you form a portfolio that invests in both the minimum variance portfolio and the tangency portfolio. When the weight on the minimum variance portfolio equals 5, what are the weights on the individual assets (T-bonds, corporate bonds, etc.)? 1 Start by computing the optimal share in risky assets for a value of = 10. Repeat for = 11, = 12 etc. 1/1 Fixed Income Equities Date T-Bonds Corp. Bonds S&P 500 197301 -0.010 -0.002 -0.0168 197302 -0.003 0.004 -0.0338 197303 0.000 0.000 -0.0011 197304 0.009 0.010 -0.0401 197305 0.002 -0.004 -0.0140 197306 0.003 -0.011 -0.0052 197307 -0.021 -0.035 0.0391 197308 0.020 0.037 -0.0315 197309 0.022 0.032 0.0422 197310 0.008 -0.011 0.0003 197311 0.006 0.011 -0.1072 197312 -0.001 -0.013 0.0180 197401 0.007 0.001 -0.0081 197402 0.003 0.002 0.0020 197403 -0.016 -0.030 -0.0218 197404 -0.008 -0.030 -0.0376 197405 0.012 0.007 -0.0269 197406 0.000 -0.045 -0.0128 197407 0.001 -0.009 -0.0767 197408 0.001 -0.025 -0.0822 197409 0.025 0.012 -0.1175 197410 0.012 0.073 0.1681 197411 0.020 -0.003 -0.0457 197412 0.012 -0.008 -0.0180 197501 0.012 0.068 0.1236 197502 0.012 0.020 0.0675 197503 -0.004 -0.032 0.0240 197504 -0.014 -0.009 0.0494 197505 0.020 0.026 0.0512 197506 0.004 0.027 0.0462 197507 -0.003 -0.002 -0.0655 197508 0.004 -0.005 -0.0157 197509 -0.002 -0.012 -0.0323 197510 0.031 0.048 0.0649 197511 -0.001 -0.005 0.0301 197512 0.019 0.035 -0.0105 197601 0.010 0.029 0.1201 197602 0.002 0.010 -0.0058 197603 0.010 0.015 0.0326 197604 0.007 0.004 -0.0096 197605 -0.007 -0.009 -0.0081 197606 0.013 0.015 0.0440 197607 0.010 0.014 -0.0072 197608 0.014 0.022 0.0016 197609 0.009 0.017 0.0244 197610 0.012 0.010 -0.0202 197611 0.023 0.025 -0.0010 197612 0.009 0.028 0.0538 197701 -0.017 -0.022 -0.0497 197702 0.005 0.003 -0.0156 197703 0.007 0.008 -0.0125 197704 0.006 0.011 0.0006 197705 0.006 0.009 -0.0151 197706 0.011 0.016 0.0478 197707 -0.004 0.003 -0.0155 197708 0.008 0.011 -0.0123 197709 0.000 -0.001 -0.0008 197710 -0.004 -0.006 -0.0420 197711 0.009 0.009 0.0368 197712 0.000 -0.008 0.0056 197801 0.001 -0.004 -0.0606 197802 0.002 0.005 -0.0163 197803 0.003 0.002 0.0269 197804 0.002 0.000 0.0890 197805 0.001 -0.009 0.0137 197806 -0.002 0.002 -0.0166 197807 0.009 0.013 0.0570 197808 0.009 0.022 0.0336 197809 0.002 -0.004 -0.0052 197810 -0.011 -0.020 -0.0896 197811 0.009 0.011 0.0268 197812 -0.006 -0.015 0.0166 197901 0.018 0.020 0.0427 197902 -0.001 -0.010 -0.0286 197903 0.011 0.011 0.0574 197904 0.001 -0.006 0.0042 197905 0.017 0.023 -0.0168 197906 0.020 0.023 0.0403 197907 -0.001 0.002 0.0121 197908 -0.003 0.000 0.0619 197909 -0.001 -0.021 0.0014 197910 -0.040 -0.081 -0.0656 197911 0.030 0.026 0.0528 Commodities MSCI World GSCI 0.003 0.034 0.008 0.043 0.002 -0.024 -0.050 0.060 -0.002 0.182 0.007 -0.017 0.025 0.258 -0.041 0.025 0.030 -0.050 0.011 -0.053 -0.129 0.052 -0.007 0.105 0.009 0.112 0.016 -0.005 -0.024 -0.115 -0.016 0.011 -0.039 -0.068 -0.030 0.124 -0.058 0.238 -0.095 -0.049 -0.092 0.121 0.097 0.090 -0.014 0.019 -0.015 -0.083 0.147 -0.156 0.090 -0.104 0.008 0.084 0.043 -0.046 0.025 -0.015 0.014 0.016 -0.054 0.078 -0.014 0.096 -0.041 0.011 0.070 -0.080 0.028 -0.012 0.002 -0.026 0.090 -0.048 -0.007 0.057 0.013 0.002 -0.006 0.038 -0.016 0.018 0.032 -0.017 -0.008 -0.089 -0.001 -0.028 0.009 -0.099 -0.034 -0.012 -0.003 0.014 0.076 0.050 -0.033 -0.003 -0.003 -0.002 -0.005 0.036 0.012 0.052 -0.013 -0.034 0.039 -0.024 -0.012 -0.085 0.005 0.010 0.014 0.036 -0.016 0.029 0.014 0.043 0.021 0.051 -0.028 0.032 -0.006 0.016 0.047 0.103 0.046 0.021 0.014 0.076 0.011 -0.093 0.073 0.027 0.024 0.027 0.013 0.056 -0.018 0.010 -0.034 0.026 0.034 -0.012 0.027 0.072 -0.018 0.059 0.043 -0.018 0.000 0.060 -0.016 -0.047 0.030 0.013 0.009 -0.042 0.041 0.115 0.024 0.043 -0.073 -0.032 0.032 0.069 Gold 0.020 0.292 0.058 0.005 0.262 0.079 -0.067 -0.097 -0.036 -0.030 0.031 0.120 0.187 0.272 0.021 -0.026 -0.071 -0.062 0.049 0.008 -0.050 0.128 0.094 0.030 -0.060 0.031 -0.022 -0.058 0.002 -0.010 0.002 -0.029 -0.144 0.037 -0.036 0.014 -0.087 0.034 -0.021 -0.010 -0.023 -0.012 -0.092 -0.083 0.127 0.053 0.064 0.034 -0.018 0.077 0.053 -0.022 -0.023 -0.002 0.011 0.010 0.054 0.045 -0.006 0.036 0.058 0.039 -0.007 -0.059 0.088 -0.009 0.086 0.042 0.049 0.120 -0.205 0.159 0.038 0.077 -0.045 0.016 0.138 -0.003 0.068 0.076 0.249 -0.043 0.099 197912 198001 198002 198003 198004 198005 198006 198007 198008 198009 198010 198011 198012 198101 198102 198103 198104 198105 198106 198107 198108 198109 198110 198111 198112 198201 198202 198203 198204 198205 198206 198207 198208 198209 198210 198211 198212 198301 198302 198303 198304 198305 198306 198307 198308 198309 198310 198311 198312 198401 198402 198403 198404 198405 198406 198407 198408 198409 198410 198411 198412 198501 198502 198503 198504 198505 198506 198507 198508 198509 198510 198511 198512 198601 198602 198603 198604 198605 198606 198607 198608 198609 198610 198611 198612 0.007 -0.017 -0.049 0.011 0.095 0.036 0.014 -0.012 -0.030 -0.004 -0.012 -0.002 0.031 0.001 -0.013 0.025 -0.024 0.029 0.001 -0.016 -0.011 0.005 0.054 0.067 -0.026 0.006 0.014 0.011 0.024 0.015 -0.012 0.040 0.044 0.035 0.046 0.007 0.020 -0.002 0.026 -0.003 0.022 -0.011 0.003 -0.019 0.007 0.030 0.003 0.011 0.002 0.017 -0.004 -0.008 0.000 -0.023 0.011 0.039 0.015 0.021 0.039 0.017 0.014 0.021 -0.018 0.019 0.020 0.047 0.010 -0.003 0.017 0.008 0.020 0.022 0.031 0.005 0.043 0.042 0.004 -0.025 0.034 0.006 0.029 -0.016 0.014 0.011 0.001 -0.004 -0.048 -0.069 -0.008 0.129 0.058 0.025 -0.027 -0.041 -0.019 -0.010 -0.005 0.028 -0.002 -0.024 0.023 -0.052 0.044 -0.001 -0.023 -0.026 -0.017 0.059 0.107 -0.047 0.001 0.023 0.016 0.036 0.019 -0.024 0.046 0.071 0.051 0.067 0.016 0.018 0.005 0.035 0.013 0.041 -0.020 0.000 -0.032 0.005 0.036 -0.001 0.012 -0.003 0.028 -0.012 -0.013 -0.009 -0.037 0.014 0.055 0.022 0.030 0.051 0.017 0.013 0.029 -0.025 0.019 0.022 0.064 0.008 -0.004 0.024 0.001 0.024 0.026 0.033 0.008 0.048 0.024 0.005 -0.011 0.019 0.005 0.021 -0.003 0.017 0.014 0.009 0.0183 0.0613 0.0026 -0.0975 0.0424 0.0556 0.0297 0.0682 0.0135 0.0279 0.0178 0.1099 -0.0306 -0.0434 0.0213 0.0383 -0.0202 0.0065 -0.0083 0.0007 -0.0555 -0.0505 0.0521 0.0438 -0.0271 -0.0154 -0.0504 -0.0068 0.0416 -0.0295 -0.0158 -0.0202 0.1274 0.0105 0.1139 0.0458 0.0168 0.0353 0.0257 0.0355 0.0757 -0.0057 0.0370 -0.0312 0.0159 0.0142 -0.0131 0.0238 -0.0057 -0.0039 -0.0340 0.0173 0.0068 -0.0531 0.0229 -0.0138 0.1124 -0.0001 0.0033 -0.0098 0.0256 0.0769 0.0142 -0.0006 -0.0037 0.0627 0.0161 -0.0033 -0.0065 -0.0332 0.0451 0.0719 0.0482 0.0047 0.0765 0.0558 -0.0133 0.0553 0.0157 -0.0575 0.0744 -0.0832 0.0565 0.0249 -0.0275 0.028 0.061 0.002 -0.106 0.067 0.051 0.049 0.032 0.021 0.031 0.030 0.043 -0.021 -0.028 0.004 0.037 0.002 -0.019 -0.001 -0.016 -0.019 -0.074 0.032 0.076 -0.020 -0.014 -0.060 -0.026 0.050 -0.024 -0.044 -0.012 0.074 0.006 0.070 0.054 0.046 0.022 0.022 0.036 0.072 -0.009 0.032 -0.017 0.006 0.021 -0.011 0.027 0.014 0.009 -0.016 0.048 -0.003 -0.074 0.009 -0.034 0.101 -0.003 0.011 -0.003 0.021 0.056 0.002 0.035 -0.002 0.052 0.018 0.021 0.009 0.008 0.054 0.056 0.047 0.015 0.090 0.098 0.028 -0.003 0.040 0.008 0.088 -0.039 -0.017 0.043 0.020 0.016 0.060 -0.009 -0.140 0.037 0.061 0.056 0.047 0.016 0.056 0.031 -0.014 -0.074 -0.064 -0.029 -0.002 -0.014 0.005 -0.064 0.045 -0.033 -0.001 0.003 -0.045 -0.056 0.080 -0.022 0.037 0.036 0.002 -0.030 0.022 -0.002 -0.029 -0.006 0.040 -0.011 0.007 -0.011 0.067 0.010 0.005 0.013 0.035 0.018 -0.027 -0.012 0.001 0.050 0.010 0.005 0.049 -0.011 0.029 -0.023 -0.067 0.043 -0.008 0.005 0.004 -0.020 0.013 -0.013 0.043 -0.032 0.000 -0.029 -0.022 0.015 0.057 0.072 0.017 -0.018 -0.091 -0.035 -0.002 0.056 -0.038 0.038 0.010 0.086 -0.025 0.011 0.030 -0.007 0.256 0.275 -0.042 -0.214 0.032 0.023 0.247 -0.067 0.025 0.057 -0.051 -0.023 -0.051 -0.139 -0.034 0.049 -0.065 -0.005 -0.120 -0.039 0.050 0.002 0.006 -0.031 -0.037 -0.029 -0.064 -0.118 0.113 -0.088 -0.035 0.091 0.196 -0.036 0.069 0.015 0.046 0.123 -0.166 -0.013 0.034 0.025 -0.051 0.013 -0.018 -0.025 -0.051 0.058 -0.060 -0.025 0.066 -0.020 -0.032 0.019 -0.021 -0.090 0.018 -0.010 -0.028 -0.018 -0.060 -0.013 -0.047 0.135 -0.016 -0.035 0.011 0.037 0.023 -0.028 -0.002 0.005 -0.001 0.083 -0.044 0.021 -0.002 -0.004 0.006 0.035 0.079 0.091 -0.047 -0.029 0.002 198701 198702 198703 198704 198705 198706 198707 198708 198709 198710 198711 198712 198801 198802 198803 198804 198805 198806 198807 198808 198809 198810 198811 198812 198901 198902 198903 198904 198905 198906 198907 198908 198909 198910 198911 198912 199001 199002 199003 199004 199005 199006 199007 199008 199009 199010 199011 199012 199101 199102 199103 199104 199105 199106 199107 199108 199109 199110 199111 199112 199201 199202 199203 199204 199205 199206 199207 199208 199209 199210 199211 199212 199301 199302 199303 199304 199305 199306 199307 199308 199309 199310 199311 199312 199401 0.011 0.007 -0.007 -0.025 -0.004 0.012 -0.003 -0.006 -0.020 0.040 0.004 0.012 0.033 0.010 -0.011 -0.006 -0.008 0.023 -0.007 0.002 0.022 0.018 -0.012 0.004 0.013 -0.009 0.007 0.022 0.024 0.034 0.022 -0.017 0.004 0.027 0.010 0.002 -0.015 0.002 0.000 -0.009 0.028 0.016 0.013 -0.014 0.010 0.017 0.022 0.016 0.011 0.005 0.005 0.011 0.004 -0.002 0.012 0.023 0.021 0.009 0.010 0.035 -0.016 0.004 -0.006 0.006 0.018 0.015 0.026 0.010 0.015 -0.015 -0.002 0.017 0.022 0.020 0.003 0.008 -0.001 0.022 0.006 0.022 0.004 0.004 -0.011 0.004 0.014 0.022 0.006 -0.004 -0.033 -0.005 0.015 -0.003 -0.006 -0.028 0.033 0.011 0.019 0.039 0.014 -0.009 -0.007 -0.005 0.024 -0.002 0.004 0.022 0.018 -0.010 0.003 0.015 -0.006 0.003 0.020 0.027 0.030 0.019 -0.011 0.005 0.023 0.007 0.001 -0.013 0.003 0.001 -0.010 0.032 0.017 0.011 -0.016 0.005 0.005 0.021 0.014 0.013 0.017 0.012 0.013 0.007 0.000 0.014 0.023 0.021 0.010 0.010 0.033 -0.013 0.010 -0.004 0.005 0.022 0.016 0.027 0.008 0.012 -0.018 0.002 0.019 0.023 0.023 0.004 0.008 0.001 0.024 0.007 0.025 0.002 0.005 -0.012 0.006 0.019 0.1352 0.0418 0.0263 -0.0090 0.0091 0.0501 0.0498 0.0391 -0.0219 -0.2158 -0.0819 0.0739 0.0427 0.0474 -0.0308 0.0105 0.0080 0.0477 -0.0045 -0.0325 0.0427 0.0269 -0.0144 0.0186 0.0723 -0.0250 0.0230 0.0517 0.0410 -0.0056 0.0901 0.0199 -0.0040 -0.0236 0.0205 0.0227 -0.0677 0.0134 0.0266 -0.0245 0.0974 -0.0068 -0.0045 -0.0908 -0.0490 -0.0036 0.0646 0.0280 0.0450 0.0716 0.0244 0.0023 0.0429 -0.0454 0.0465 0.0239 -0.0169 0.0135 -0.0402 0.1141 -0.0183 0.0129 -0.0195 0.0286 0.0049 -0.0150 0.0409 -0.0206 0.0113 0.0048 0.0338 0.0134 0.0073 0.0135 0.0212 -0.0245 0.0263 0.0035 -0.0046 0.0374 -0.0076 0.0199 -0.0087 0.0126 0.0334 0.118 0.033 0.062 0.059 0.002 0.000 0.020 0.059 -0.017 -0.170 -0.024 0.044 0.025 0.058 0.030 0.013 -0.020 -0.001 0.019 -0.055 0.043 0.067 0.035 0.009 0.036 -0.006 -0.006 0.023 -0.024 -0.011 0.113 -0.024 0.028 -0.033 0.040 0.032 -0.047 -0.043 -0.060 -0.014 0.105 -0.007 0.009 -0.093 -0.105 0.094 -0.016 0.021 0.037 0.093 -0.029 0.008 0.023 -0.062 0.047 -0.003 0.026 0.016 -0.043 0.073 -0.018 -0.017 -0.047 0.014 0.040 -0.033 0.003 0.025 -0.009 -0.027 0.018 0.008 0.004 0.024 0.058 0.047 0.023 -0.008 0.021 0.046 -0.018 0.028 -0.056 0.049 0.066 0.057 -0.060 0.081 0.050 0.046 0.036 0.045 -0.020 0.007 0.010 0.000 -0.028 0.027 -0.011 0.050 0.031 0.035 -0.028 0.006 -0.007 -0.027 0.048 0.057 0.073 0.004 0.043 0.067 0.032 -0.013 0.035 -0.028 0.035 0.060 -0.007 0.016 0.091 -0.004 -0.003 0.007 -0.010 -0.007 -0.016 0.083 0.166 0.229 -0.061 -0.066 -0.020 -0.094 0.014 0.038 0.023 -0.001 -0.024 0.051 0.015 0.008 0.029 -0.040 -0.071 0.027 -0.011 0.011 0.030 0.027 -0.006 -0.014 0.001 0.011 -0.022 -0.013 0.002 0.012 0.012 0.021 -0.011 -0.028 -0.031 -0.009 0.008 0.003 -0.036 -0.050 -0.019 0.081 0.042 -0.004 0.033 0.085 -0.006 -0.010 0.038 -0.018 0.007 0.019 0.055 -0.015 -0.044 -0.089 0.081 -0.018 0.009 -0.038 -0.009 -0.015 -0.071 0.041 0.022 -0.026 -0.037 -0.021 -0.012 -0.003 -0.047 0.021 -0.006 -0.026 0.026 0.019 0.082 -0.014 0.041 -0.020 -0.090 -0.002 -0.021 -0.031 0.053 0.046 0.046 -0.066 0.015 0.016 -0.055 -0.018 -0.025 -0.002 0.023 0.015 -0.009 -0.046 0.010 0.020 0.026 -0.037 0.002 -0.003 -0.033 -0.015 0.004 0.017 0.042 -0.049 0.025 -0.029 -0.015 -0.002 -0.006 -0.006 0.025 0.049 0.078 -0.005 0.065 -0.082 -0.048 0.047 0.005 0.054 -0.032 199402 199403 199404 199405 199406 199407 199408 199409 199410 199411 199412 199501 199502 199503 199504 199505 199506 199507 199508 199509 199510 199511 199512 199601 199602 199603 199604 199605 199606 199607 199608 199609 199610 199611 199612 199701 199702 199703 199704 199705 199706 199707 199708 199709 199710 199711 199712 199801 199802 199803 199804 199805 199806 199807 199808 199809 199810 199811 199812 199901 199902 199903 199904 199905 199906 199907 199908 199909 199910 199911 199912 200001 200002 200003 200004 200005 200006 200007 200008 200009 200010 200011 200012 200101 200102 -0.022 -0.022 -0.008 -0.001 -0.002 0.018 0.000 -0.014 -0.001 -0.002 0.006 0.019 0.021 0.006 0.013 0.040 0.008 -0.004 0.012 0.010 0.016 0.016 0.014 0.006 -0.021 -0.009 -0.006 -0.002 0.013 0.002 -0.002 0.016 0.022 0.017 -0.010 0.001 0.001 -0.011 0.014 0.009 0.011 0.029 -0.010 0.015 0.017 0.005 0.011 0.015 -0.003 0.003 0.005 0.010 0.012 0.002 0.027 0.028 -0.003 0.000 0.002 0.006 -0.026 0.004 0.002 -0.009 -0.002 -0.001 0.000 0.008 0.001 -0.002 -0.007 0.003 0.015 0.020 -0.003 0.002 0.017 0.010 0.015 0.001 0.010 0.021 0.019 0.008 0.012 -0.024 -0.031 -0.010 -0.004 -0.003 0.025 0.001 -0.019 -0.002 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