Homework Assignment #2 s2

Homework Assignment #2

1. An electric utility is planning the expansion of its generating capacity for the next five years. Its current capacity is 800 Megawatts (MW), and forecasts of future total demand (capacity needed) for each of the next five years are:

Year Total Capacity Needed (MW) 1 885 2 960 3 1052 4 1160 5 1280

The utility can increase its generating capacity by installing 10-, 50- or 100-MW generators. The cost of installing a generator depends on its size and the year it is brought on line. A generator brought on line in a particular year is available to satisfy demand in that year and each subsequent year. Any number of generators of any type can be added in any year. The costs (in $1,000s) of bringing the different generators on line in each year are: Costs (in $1,000s) 10-MW 50-MW 100-MW Year 1 $300 $1211 $1950 Year 2 $250 $1058 $2191 Year 3 $208 $965 $1759 Year 4 $173 $887 $1649 Year 5 $145 $722 $1458 a. Formulate an integer (linear) decision model that minimizes the cost of bringing generators on line while satisfying the capacity requirements. What is the optimal plan to expand capacity? What is the total cost? b. Assume now that at most one generator of each type can be brought on line in any one year. What is the cost of satisfying the capacity requirements now? How has the optimal plan changed?

Decision Models 2 Prof. Juran 2. InvestCo, a U.S. fund management firm, wants to use scenario-based portfolio optimization on daily data to construct its short-term equity portfolio. Using the actual returns data on nine stocks over 63 days (in the data file posted on the course web site), answer the following: a. Determine the highest return portfolio that invests 100% in long positions (no shorting) in these nine stocks, and has a risk level (as measured by standard- deviation) not greater than the risk of holding the S&P 500 index. What is the optimal portfolio’s expected daily return and standard deviation of returns? What stocks make up the portfolio and what percentage of the portfolio do they represent? b. Assume you can also invest in the S&P 500 index (using the SPDRs index security that trades on the American Stock Exchange). You cannot short the S&P or the individual stocks. What is the new optimal portfolio, and what is its expected daily return and standard deviation of returns? What stocks make up the portfolio and what percentage of the portfolio do they represent? c. Assume you can short any of the nine stocks and the S&P 500, but that the total short position in any one stock (or index) cannot exceed 1% of the portfolio. That is, the amount invested in any one stock (or index) must be at least –1% of the portfolio. What is the optimal portfolio’s expected daily return and standard deviation of returns? What stocks make up the portfolio and what percentage of the portfolio do they represent? d. Using SolverTable, graph the efficient frontier portfolio by varying the maximum risk level of the portfolio from 1x to 3x the S&P risk level (in increments of 0.05), and tracing out an efficient frontier.

Decision Models 3 Prof. Juran