Problem Description

An investor has $100,000 to invest in four assets. Below is a list of the assets’ expected annual returns and the minimum and maximum amounts the investor is comfortable allocating to each investment.

Table 3. Portfolio Allocation Expected Returns and Investment Bounds

Investment

Annual Return

Lower Bound

Upper Bound

Money market fund

3%

$0

$50,000

Income fund

5%

$10,000

$25,000

Growth and income fund

7%

$0

$80,000

Aggressive growth fund

11%

$10,000

$100,000

The source of uncertainty in this problem is the annual return of each asset. The more conservative assets, the Income and Money Market funds, have relatively stable annual returns, while the Aggressive Growth fund has higher volatility.

The decision problem, then, is to determine how much to invest in each asset to maximize the total expected annual return while maintaining the risk at an acceptable level and keeping within the minimum and maximum limits for each investment.