solution

An investment company manages portfolios of stocks, bonds, and other investment alternatives. One of the company’s clients would like to invest $200,000 in stocks. The client is interested in four specific stocks – A, B, C, and/or D. The company gathered the following relevant financial data for the four stocks:

	Stock A	Stock B	Stock C	Stock D
Price per share	$100	$50	$80	$40
Annual rate of return	0.12	0.08	0.06	0.10
Risk measure per dollar invested	0.10	0.07	0.05	0.08

Based on the above data, the investor has stipulated the following investment guidelines:

1. The entire amount of $200,000 must be invested.

2. The annual rate of return must be at least 9% of the invested capital of $200,000.

3. Not every stock has to be purchased, however, if selected, no one stock can account for more than 50% of the total dollar investment.

4. The total investment in stocks A and B combined must be equal to or greater than the total investment in stocks C and D combined.

question:

Q4. (30 p.) Suppose the investor decides that the annual rate of return no longer has to be at least 9% and agrees to a minimum level of 8%. What does the shadow price associated with this constraint indicate about a possible change in total risk that could occur from this lower rate of return? Show the relevant portion of the Solver’s output. Fully interpret the results.