One of the basic principles of investment management is diversification. By hold

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One of the basic principles of investment management is diversification. By holding a portfolio of several types of securities, for example, you can earn a rate of return that represents the average of the returns from the individual investments, while reducing your overall risk.

LMD Trust Inc. invests client's funds in various types of securities. They have $75 million for immediate investment and wish to maximize the interest earned over the next year. They are considering four investment options including Municipal Bonds, Technology Stocks, Blue Chip Stocks, and CDO's (collateralized debt obligations). The expected return for each security is given in Table 1 below.

Also included in Table 1 are beta values (market-related risk) and the variances for returns for the four securities. To control for market and return related risk. LMD has set a maximum weighted average beta of 0.2 and an average variance level of 4%.   In addition, the maximum amount to be invested for each alternative is set at 40% of the total portfolio. The LP formulation is given below.

Setup and solve the problem in the adjacent ('Solver Solution') worksheet, generate the answer and sensitivity reports, then answer the questions given on the first worksheet. Decision Variables M = amount (in dollars) invested in Municipal Bonds T = amount (in dollars) invested in Technology Stocks Table 1 B = amount (in dollars) invested in Blue Chip Stocks Security Average Rate of Return beta variance C = amount (in dollars) invested in CDOs M 3% 0 0 T 10% 0.32 6% Objective Function B 7% 0.18 3% Maximize average return = 0.03M + 0.10T + 0.07B + 0.05C C 5% 0.05 0 Constraints Total of 75M to invest M + T + B + C < 75,000,000 Average beta of 0.2 or less -0.2M + 0.12T - 0.02B - 0.15C < 0 Average variance of 4% or less -0.04M + 0.02T - 0.01B - 0.04C < 0 No more than 40% in M 0.6M - 0.4T - 0.4B - 0.4C < 0 No more than 40% in T -0.4M + 0.6T - 0.4B - 0.4C < 0 No more than 40% in B -0.4M - 0.4T + 0.6B - 0.4C < 0 No more than 40% in C -0.4M - 0.4T - 0.4B + 0.6C < 0 Non-negativity: M,T,B,C > 0          AFTER FINDING THE SOLUTION, USE THE ANSWER AND SENSITIVITY REPORTS TO ANSWER THE FOLLOWING QUESTIONS What is the minimum rate of return required for Municipal Bonds before we would add them to the portfolio? (specify to 3 decimal places) Based upon the Sensitivity Report, if we could increase our investment by $1,000,000, what would the new total return be (in dollars)? (specify to 2 decimal places) How low could the rate of return on the CDOs be and our current optimal portfolio solution would remain optimal? (specify to 3 decimal places)          One of the basic principles of investment management is diversification. By holding a portfolio of several types of securities, for example, you can earn a rate of return that represents the average of the returns from the individual investments, while reducing your overall risk.

LMD Trust Inc. invests client's funds in various types of securities. They have $75 million for immediate investment and wish to maximize the interest earned over the next year. They are considering four investment options including Municipal Bonds, Technology Stocks, Blue Chip Stocks, and CDO's (collateralized debt obligations). The expected return for each security is given in Table 1 below.

Also included in Table 1 are beta values (market-related risk) and the variances for returns for the four securities. To control for market and return related risk. LMD has set a maximum weighted average beta of 0.2 and an average variance level of 4%.   In addition, the maximum amount to be invested for each alternative is set at 40% of the total portfolio. The LP formulation is given below.

Setup and solve the problem in the adjacent ('Solver Solution') worksheet, generate the answer and sensitivity reports, then answer the questions given on the first worksheet. Decision Variables M = amount (in dollars) invested in Municipal Bonds T = amount (in dollars) invested in Technology Stocks Table 1 B = amount (in dollars) invested in Blue Chip Stocks Security Average Rate of Return beta variance C = amount (in dollars) invested in CDOs M 3% 0 0 T 10% 0.32 6% Objective Function B 7% 0.18 3% Maximize average return = 0.03M + 0.10T + 0.07B + 0.05C C 5% 0.05 0 Constraints Total of 75M to invest M + T + B + C < 75,000,000 Average beta of 0.2 or less -0.2M + 0.12T - 0.02B - 0.15C < 0 Average variance of 4% or less -0.04M + 0.02T - 0.01B - 0.04C < 0 No more than 40% in M 0.6M - 0.4T - 0.4B - 0.4C < 0 No more than 40% in T -0.4M + 0.6T - 0.4B - 0.4C < 0 No more than 40% in B -0.4M - 0.4T + 0.6B - 0.4C < 0 No more than 40% in C -0.4M - 0.4T - 0.4B + 0.6C < 0 Non-negativity: M,T,B,C > 0          AFTER FINDING THE SOLUTION, USE THE ANSWER AND SENSITIVITY REPORTS TO ANSWER THE FOLLOWING QUESTIONS What is the minimum rate of return required for Municipal Bonds before we would add them to the portfolio? (specify to 3 decimal places) Based upon the Sensitivity Report, if we could increase our investment by $1,000,000, what would the new total return be (in dollars)? (specify to 2 decimal places) How low could the rate of return on the CDOs be and our current optimal portfolio solution would remain optimal? (specify to 3 decimal places)         

Explanation / Answer

1) The minimum rate of return for M bonds before they enter solution is 0.0123

2) Increase in investment by $1000,000 will increase return by shadow price X $1,000,000 = 0.076462 * 1000,000 = $76,462

3) The allowable decrease for CDOs is 0.00786 and so return could be as low as 0.05-0.00786 = 0.0421

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