EMP 504 CH 08: Nonlinear LP Investment Portfolio:: Rebecca Paris #106909694

The typical goal of investors is to gain high returns while minimizing their risks; this dilemma presents a trade-off. Generally, the greater the return, the higher the risk investors must be willing to take. Harry Markowitz’s Nobel Prize model measures risk through determining the variance of a portfolio.

The objective of the Markowitz Mean-Variance Portfolio Model is to minimize a portfolios’ variance. Once the model is developed, it can be iterated for different values of return; this iteration process generates variance for each return. These data points can then be graphed into what’s referred to as the efficient frontier by the financial industry. The graph is useful in helping investors pick the region in which they feel they would be most comfortable.

Perlman & Brothers utilized these tools, Markowitz Model and efficient frontier, in making their recent investment decision among three stocks. Their goal is to find a minimum-variance portfolio that yields a twelve percent annual return.

Utilizing the Markowitz model, it was determined that investing in stock options one and three, each at fifty percent total investment met their goal of twelve percent returns with minimal risks.

Iterating the model from ten percent return to fourteen percent return while incrementing by one-half percent generated the following efficient frontier:

0.0600 0.0800 0.1000 0.1200 0.1400 0.1600 0.1800 0.2000 0.22000.0900

0.1000

0.1100

0.1200

0.1300

0.1400

0.1500

Efficient Frontier

Portfolio Std Dev

Po

rtfo

lio

Ret

urn

Noteworthy:: SD = standard deviation which is the square root of the portfolio variance.

As you can see, as return increases from ten percent to fourteen percent, the standard deviation also increases. Initially, the relationship of increase is obviously non-linear, but as increase in return progresses, the increase in variance starts to increase - nearing linearity. Perlman & Brothers goal of twelve percent annual return appears to be right on the pivot point between non-linearity and apparently linearity. If Perlman wants to reconsider its annual return, they should refer to the graph above when determining their new objective.