Asset 4 has E[R4] = 7.4% and SD = 21% meaning it is at least as risky as the other risky assets and has a lower expected return than any of the other risky assets. In other words, it appears to be a dominated asset. Why does it have a positive weight in the optimal portfolio?

Reference:

https://docs.google.com/spreadsheets/d/13MYC067MbiADZoFxeEN0QpTn9UBBh9rR/edit#gid=564614616

E[R] sigma[R] w1 E[R] Var[R] sigma[R] Asset 1 0.136 0.154 -1 2 0.164 0.197 0.444 Mean-Variance Frontier of a Portfolio of Two Assets Asset 2 0.15 0.23 -0.9 1.9 0.163 0.177 0.421 0.170 -0.8 1.8 0.161 0.159 0.399 Correlation 0.27 -0.7 1.7 0.160 0.142 0.376 127 -0.6 1.6 0.158 0.126 0.354 Plot Area 0.160 -0.5 1.5 0.157 0.111 0.333 -0.4 1.4 0.156 0.097 0.311 -0.3 1.3 0.154 0.084 0.290 -0.2 1.2 0.153 0.150 0.073 0.269 Asset 2 -0.1 1.1 0.151 0.062 0.249 0 0.150 0.053 0.230 0.1 0.9 0.149 0.045 0.212 0.140 0.2 0.8 0.147 0.038 0.195 Asset 1 0.3 0.7 0.146 0.032 0.179 0.4 0.6 0.144 0.027 0.166 Portfolio Expected Return 0.130 0.5 0.5 0.143 0.024 0.155 0.6 0.4 0.142 0.022 0.147 0.7 0.3 0.140 0.020 0.143 0.120 0.8 0.2 0.139 0.020 0.143 0.9 0.1 0.137 0.021 0.146 1 0 0.136 0.024 0.154 0.110 1.1 -0.1 0.135 0.027 0.165 1.2 -0.2 0.133 0.032 0.178 1.3 -0.3 0.132 0.037 0.193 0.100 1.4 -0.4 0.130 0.044 0.210 1.5 -0.5 0.129 0.052 0.229 1.6 -0.6 0.128 0.061 0.248 0.090 1.7 -0.7 0.126 0.072 0.268 1.8 -0.8 0.125 0.083 0.288 0.100 0.150 0.200 0.250 0.300 0.350 0.400 1.9 -0.9 0.123 0.096 0.309 Portfolio Volatility 2 -1 0.122 0.110 0.331# Mean SD Opt CAL & Eff Frontier Tangency Global Min. 0 4.0% 0.0% 20% # Portfolio Var. Port. 1 10.6% 16.0% = Mean 19.82% 24.27% 16.6% 14.2% 15% W N - 42.16% 27.40% 3 10.0% 17.4% 14.26% 18.66% 4 7.4% 21.0% 10% 12.04% 18.38% 5 12.0% 21.0% 11.72% 11.29% 5% Risky Weights Correlations 1 2 3 4 5 40% 100.0% 0.0% 0.0% -20.0% 0.0% 0% 20% 5% 10% 15% 20% 25% 0.0% 100.0% 0.0% -10.0% 0.0% 0.0% 0.0% 100.0% -10.0% 0.0% 0% -5% SD W NOT A WN- -20.0% -10.0% -10.0% 100.0% 0.0% 2 3 4 5 -20% 0.0% 0.0% 0.0% 0.0% 100.0% Craig Holden's Excel-based Interactive Optimizer (C) Copyright 1997 Craig W. Holden All Rights Reserved You are granted permission to use this spreadsheet for any nonprofit, educational purpose. Comments are welcome. E-mail: CHOLDEN@INDIANA.EDU Mail: Professor Craig W.Holden, School of Business, Indiana University, Bloomington, IN 47405\f