Project for APMA120John Flavin

An entrepreneur recently sold his company and wishes to make his newfound wealth work for him.

He has decided to invest in any combination of five different securities with varying risks, prices, and returns.

Because he is new to the world of investments, he wishes to maintain an upper limit on the amount of risk he is taking.

Ultimately, he wants to maximize returns subject to his budget and self-imposed risk constraints.

Given the nature of his previous business endeavors, the lucky entrepreneur wishes to invest in one or more of the five following securities (due to his familiarity with their pricing systems): U.S. Treasury Bonds Domestic Corporate Bonds Closed-ended mutual funds: Mutual fund enrollment

with a high liquidity (comparably to common stock). Domestic technology equity: Stocks in Microsoft,

Apple, Sun Microsystems, etc. Domestic oil equity: Stocks in companies such as

Exxon, Chevron, etc.

Because they are backed by the United States federal government, Treasury bonds (T-bonds) are generally regarded as the safest security for an investor.

The bond will (almost) always be either paid out or sold, with little to no chance of a default.

Thus, the lowest risk value will be assigned to T-bonds.

Based on historical data, the average return on T-bonds between 2000-2007 was 3.32% (due to the economic meltdown, 2008 and 2009

will be excluded from the calculated average returns).

Coporate bonds are debt issued by large companies to fund investment projects.

Since debt holders take unanimous precedence in the case of bankruptcy, corporate bonds are considered to be only slightly more risky then T-bonds.

Furthermore, large companies rarely file Chapter 11 bankruptcy, and only large companies can generally get SEC approval for debt issuance.

The average annual return on corporate bonds is roughly 4.8%

Mutual funds are financial institutions that pool investors’ money to purchase securities. Reduces transaction costs. Decrease equity risk by diversifying an individual

investor’s portfolio. Closed-ended funds are mutual funds that

have an initial issuance of shares (the number of which remains constant).

These shares can be traded openly on the market. Because they are based on common stock, they carry more risk than bonds.

The average annual return on a closed-ended index mutual fund is roughly 6.4%

This category consists of equity (stocks) in technology companies.

For this specific example, we use the average annual risk and return of stock in Microsoft, the largest technology company in the world.

Because it only represents a single industry (no diversification), Microsoft stock commands a higher risk than diversified mutual funds.

However, technology companies (especially Microsoft) generally exhibit predictable growth, making them less risky than other common-stock alternatives.

The average annual return on Microsoft common stock is roughly 7.2%

Common stock in oil companies (for this example, Exxon was analyzed).

Several concerns about equity in oil companies United States has increased dependence on foreign

oil Oil is a non-renewable resource (growth may be large,

but is still limited) Technological advancements may limit the demand

for oil throughout the next several years. Thus, equity in oil will show a high level of risk

and volatility. However, oil stocks also show the highest

average annual returns compared to the other four securities.

Oil stocks exhibit an annual return of about 8.1%.

The retired entrepreneur has decided to perform his own stock analysis, and has assigned risk values in the following manner: T-Bonds = 0 Corporate Bonds = 1 Closed-Ended Mutual Funds = 2 Technology Equity = 3 Oil Equity = 4

Security T-Bonds

C-Bonds Mutual Tech Oil

Risk 0 1 2 3 4

Return 3.32% 4.8% 6.4% 7.2% 8.1%

Price $121.50 $772.72 $9.95 $30.36 $68.21

Price*Return

$4.04 $37.09 $0.64 $2.19 $5.53Because this is his first attempt at personal trading, the entrepreneur will invest only $50,000 dollars, and wants to keep the sum of his risk below 600. These constraints will dictate the linear programming problem.

The objective function will represent the monetary return on the investment portfolio, and is defined as:

Where: x1 = # of treasury bonds x2 = # of corporate bonds x3 = # of mutual fund shares x4 = # of technology equity shares x5 = # of oil equity shares

54321 53.519.264.009.3704.4 xxxxxZ

The constraint on risk is defined by:

The pricing constraint is defined by:

500432 5432 xxxx

000,5021.6836.3095.972.77250.121 54321 xxxxx

With these constraints on pricing and risk, maximum return can be calculated in Excel via the following procedure:Var. # Purchased Price Risk Return Constraints

x1 = 0 $121.50 0 $4.04 Risk = 600 ≤ 600x2 = 52.62698211 $772.72 1 $37.09 Price= $50,000.00 ≤ 50,000x3 = 0 $9.95 2 $0.64x4 = 0 $30.36 3 $2.19x5 = 136.8432545 $68.21 4 $5.53

Z = $2,708.68

Since buying fractional securities is impossible, the entrepreneur chooses to round down the values given by the excel solver.

Thus, the solution becomes X= (0,52,0,0,136) Z= $2,680.76

Var. # Purchased Price Risk Return Constraintsx1 = 0 $121.50 0 $4.04 Risk = 596 ≤ 600x2 = 52 $772.72 1 $37.09 Price= $49,458.00 ≤ 50,000x3 = 0 $9.95 2 $0.64x4 = 0 $30.36 3 $2.19x5 = 136 $68.21 4 $5.53

Z = $2,680.76

Based on this model, it is apparent that both general corporate debt and oil company equity shares are the best investment choices for our entrepreneur.

While the pricing and returns on the securities used in this model are accurate, the entrepreneur chose to forego the assistance of an actuarial firm in assessing the actual risk associated with these securities.

Rather than the arbitrary values, the entrepreneur might want to calculate the standard deviations or variances of these securities and use those numbers to analyze the risk.

These calculations will lead to a more accurate representation of his returns. However, his capital might be reduced as this information comes at a price.

If the entrepreneur is willing to accept higher variability in order to avoid paying analyst fees, then this programming problem will sufficiently meet his needs.