An investment advisor wants to develop a model that can be used to allocate investment funds among four alternatives : stocks, bonds, mutual funds , and a money market account. for next quater , the advisor used historical data to develop estimates of the project annual ratr of return and the associated risk for each option, which are given in the table below. Risk is measuerd using a index between 0 and 1 , with higher values denoting more volating, which implies more uncertainty for examples, cash held in the money market account has a low annula return of 1.1%, but the risk is extremely low; on the other hand , while stocks yield a higher rate of return , they are highly reflective of market volatility, and thus the associate risk is high.
investment . proj. ror risk
stocks 10.7% 0.82
bonds . 3.2 % 0.22
mutual funds 4.5% 0.33
cash 1.1% 0.02
the advisor has specific guidelines that must be aplied to all clients , regardless of their affinity for or aversion to risk.
* no more than 75% of the total investment may be in stocks.
* the amount invested in mutual funds must be at least as much as invested in bonds.
* the amount of cash held in the money market account must be at least 10% buut no moref than 30% of the total inveetsmnet .
Suppose the maximum risk value for a particular clients is 0.4. Develop a linear program that can be used to determine the optimal allocation of investment funds among stocks, bonds, mutual funds, and money market accounts. solve the LP using the solver feature and determine the annual rate of return for this portfolio.