An investment advisor at RMC Financial Services wants to develop a model that can be used to allocate investment funds among four alternatives: stocks, bonds, mutual funds, and cash. For the coming investment period, the company developed estimates of the annual rate of return and the associated risk for each alternative. Risk is measured between 0 and 1, with higher risk value denoting more volatility and thus more uncertainty. The estimated rate of return for stocks is 10%, for bonds 3%, for mutual funds 4%, and cash 1%. The risk index for the stocks, bonds, and mutual funds investment is estimated as 0.8, 0.2, and 0.3, respectively. Because cash is held in money market funds, the annual return is lower, but it carries essentially no risk (i.e., risk index is zero for cash investment). The objective is to determine the portion of funds allocated to each investment alternatives in order to maximize the total annual return for the portfolio subject to the risk level the client is willing to tolerate. The investment advisor calculates total risk as the sum of risk for all investment alternatives. For example, if 40% of client’s funds are investment in stocks, 30% in bonds, 20% in mutual funds, and 10% in cash, the total risk for the portfolio would be 0.40(0.8) + 0.30(0.2) + 0.20(0.3) + 0.10(0.0). An investment advisor will meet with each client to discuss the client’s investment objectives and to determine a maximum total risk value for the client. A maximum total risk value 0.45 would be assigned to a moderate risk tolerance investor. RMC Financial Services specified additional guidelines that must be applied to all clients. The guidelines are: 1) no more than 75% of the total investment may be in stocks; 2) the amount invested in mutual funds must be at least as much as invested in bonds; 3) the amount of cash must be at least 10%, but no more than 30% of the total investment funds. Determine the optimal allocation of investment funds among stocks, bonds, mutual funds, and cash for a moderate risk tolerance client. What is the annual rate of return and the total risk for the optimal portfolio?
An investment advisor at RMC Financial Services wants to develop a model that can be used to allocate investment funds among four alternatives: stocks, bonds, mutual funds, and cash. For the coming investment period, the company developed estimates of the annual
The investment advisor calculates total risk as the sum of risk for all investment alternatives. For example, if 40% of client’s funds are investment in stocks, 30% in bonds, 20% in mutual funds, and 10% in cash, the total risk for the portfolio would be 0.40(0.8) + 0.30(0.2) + 0.20(0.3) + 0.10(0.0). An investment advisor will meet with each client to discuss the client’s investment objectives and to determine a maximum total risk value for the client. A maximum total risk value 0.45 would be assigned to a moderate risk tolerance investor. RMC Financial Services specified additional guidelines that must be applied to all clients. The guidelines are: 1) no more than 75% of the total investment may be in stocks; 2) the amount invested in mutual funds must be at least as much as invested in bonds; 3) the amount of cash must be at least 10%, but no more than 30% of the total investment funds.
Determine the optimal allocation of investment funds among stocks, bonds, mutual funds, and cash for a moderate risk tolerance client. What is the annual rate of return and the total risk for the optimal portfolio?
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