MUTUAL "FUN" MODELING!! - The table below depicts the attributes of 10 mutual funds that you have chosen for investment of your client's money. She has $100,000 to invest, though you do not have to invest it all (Warren Buffet doesn't tie up all of his money either!). Attributes: 1) A Measure of the riskiness of the fund (low is better than high). 2) Investment Category_{STOCK, BAL (anced). INTL, BOND) 3) Investment Company (VAN, FID, JPM, TRP) 4) RET1 - anticipated annual return under market conditions Election Results 1+| 5) RET2 - anticipated annual return under market conditions "Election Results 2" 6) RET3 - anticipated annual return under market conditions "Election Results 3" 7) Green - a measure of how 'green' the companies in which the fund invests Social - a measure of how the funds are invested in socially conscious companies 1.7 Type STOCK BOND Company RET1 -0.036 0.151 0.212 0.122 0.117 Risk Measure 1.4 22 3.1 BAL VAN 1.2 STOCK FID -0.042 VAN -0.013 INTL FID 0.071 JPM 0.063 0.203 -0.052 2.4 BAL JPM -0.021 0.247 0.022 5.5 3.8 1.81 INTL VAN 0.046 0.122 -0.033 6.5 3.2 1.8 BOND FID -0.021 0.106 0.069 7.5 6.1 27 INTL TRP 0.071 0.137 -0.022 1 3 RET2 RET3 Green Social STOCK TRP -0.044 0.188 0.051 4.4 5 0.04 4 0.053 5 7.1 0.02 61 4.2 -0.04 3 4.4 4 3 5.2 Invest the model optimally (minimizing risk - amount invested in a fund times the risk measure) such that: a) Under market conditions RET1 and RET3, the model shows no loss. b) Under market conditions RET2, there is a return of at least $14,000. (This is a number). c) No more than 40% of the funds invested can be with any one company. d) At least 10% of the invested funds must be with each company. e) No more than 40% of the funds invested can be with any one investment category. f) At least 10% of the invested funds must be within each investment category. g) The invested funds must average at least 5.0 on the green measure. h) The invested funds must average at least 4.75 on the social measure. 1) Investments must be in integer dollars. Create and solve an LP model that addresses this investment situation. Keep in mind we do not know in advance how much the model will decide to invest - it will be between $0 and $100,000. Only the model knows . Follow up: The model may decide not to invest in every fund. Re-run the analysis with a requirement that each fund must have at least 2.5% of the total money invested allocated. Compare how this solution alters the original solution. MUTUAL "FUN" MODELING!! - The table below depicts the attributes of 10 mutual funds that you have chosen for investment of your client's money. She has $100,000 to invest, though you do not have to invest it all (Warren Buffet doesn't tie up all of his money either!). Attributes: 1) A Measure of the riskiness of the fund (low is better than high). 2) Investment Category_{STOCK, BAL (anced). INTL, BOND) 3) Investment Company (VAN, FID, JPM, TRP) 4) RET1 - anticipated annual return under market conditions Election Results 1+| 5) RET2 - anticipated annual return under market conditions "Election Results 2" 6) RET3 - anticipated annual return under market conditions "Election Results 3" 7) Green - a measure of how 'green' the companies in which the fund invests Social - a measure of how the funds are invested in socially conscious companies 1.7 Type STOCK BOND Company RET1 -0.036 0.151 0.212 0.122 0.117 Risk Measure 1.4 22 3.1 BAL VAN 1.2 STOCK FID -0.042 VAN -0.013 INTL FID 0.071 JPM 0.063 0.203 -0.052 2.4 BAL JPM -0.021 0.247 0.022 5.5 3.8 1.81 INTL VAN 0.046 0.122 -0.033 6.5 3.2 1.8 BOND FID -0.021 0.106 0.069 7.5 6.1 27 INTL TRP 0.071 0.137 -0.022 1 3 RET2 RET3 Green Social STOCK TRP -0.044 0.188 0.051 4.4 5 0.04 4 0.053 5 7.1 0.02 61 4.2 -0.04 3 4.4 4 3 5.2 Invest the model optimally (minimizing risk - amount invested in a fund times the risk measure) such that: a) Under market conditions RET1 and RET3, the model shows no loss. b) Under market conditions RET2, there is a return of at least $14,000. (This is a number). c) No more than 40% of the funds invested can be with any one company. d) At least 10% of the invested funds must be with each company. e) No more than 40% of the funds invested can be with any one investment category. f) At least 10% of the invested funds must be within each investment category. g) The invested funds must average at least 5.0 on the green measure. h) The invested funds must average at least 4.75 on the social measure. 1) Investments must be in integer dollars. Create and solve an LP model that addresses this investment situation. Keep in mind we do not know in advance how much the model will decide to invest - it will be between $0 and $100,000. Only the model knows . Follow up: The model may decide not to invest in every fund. Re-run the analysis with a requirement that each fund must have at least 2.5% of the total money invested allocated. Compare how this solution alters the original solution