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Teaching Students About the Value of Diversification – A Retirement Portfolio's Efficient Frontier

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2015 ASEE Annual Conference & Exposition


Seattle, Washington

Publication Date

June 14, 2015

Start Date

June 14, 2015

End Date

June 17, 2015





Conference Session

Engineering Economics Teaching Tools

Tagged Division

Engineering Economy

Page Count


Page Numbers

26.1491.1 - 26.1491.19



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Paper Authors


Ted Eschenbach P.E. University of Alaska Anchorage

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Dr. Ted Eschenbach, P.E. is the principal of TGE Consulting, an emeritus professor of engineering management at the University of Alaska Anchorage, and the founding editor emeritus of the Engineering Management Journal. He is the author or coauthor of over 250 publications and presentations, including 19 books. With his coauthors he has won best paper awards at ASEE, ASEM, ASCE, & IIE conferences, and the 2009 Grant award for the best article in The Engineering Economist. He earned his B.S. from Purdue in 1971, his doctorate in industrial engineering from Stanford University in 1975, and his masters in civil engineering from UAA in 1999.

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Neal A Lewis University of Bridgeport

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Neal Lewis received his Ph.D. in engineering management in 2004 and B.S. in chemical engineering in 1974 from the University of Missouri – Rolla (now the Missouri University of Science and Technology), and his MBA in 2000 from the University of New Haven. He is an associate professor in the School of Engineering at the University of Bridgeport. He has over 25 years of industrial experience, having worked at Procter & Gamble and Bayer. Prior to UB, he has taught at UMR, UNH, and Marshall University. Neal is a member of ASEE, ASEM, and IIE.

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Teaching Students about the Value of Diversification— A Retirement Portfolio’s Efficient FrontierFirms and individuals diversify their investments in order to achieve better combinations of riskand return. This can easily be modeled for stocks, and the lessons learned can be qualitativelyextended to the selection of engineering projects. In teaching this material, it is common to startwith a simple example of two stocks. Stock A has an expected return of 8% with a standarddeviation of 15%, and Stock B has an expected return of 12% with a standard deviation of 20%.The correlation of returns on the two stocks is 35%. Graph the return and risk for all portfolios ofthe two stocks ranging from 100% of Stock A to 100% Stock B. In introductory classes therequired equation would typically be supplied, while in more advanced classes it might bederived. Note that because we prefer larger expected returns and smaller standard deviations,neither choice is dominant.Because this simple example has only two stocks, it is possible to graph all possibilities. Studentsquickly see that while a 100% Stock B portfolio might be attractive; the 100% Stock A portfoliois not. Mixing mostly Stock A with some Stock B can both increase return and reduce risk. Thecurve suggests that an intermediate mix will be better than either extreme. This is enough todemonstrate the value of diversification. It can also be the foundation for explaining efficientfrontiers, defining a minimum variance portfolio, and demonstrating that the less positivelycorrelated the stocks are; the more diversification value there is. It can also be used to show thatif the stocks were perfectly negatively correlated, then a risk-free portfolio could be constructed.We present results from replacing Stock A with long-term data from 10-year government bondsand stock B with values from a long-term S&P 500 index. This supports all of the previouspossibilities, and the reality increases student interest. By adding matching inflation data we canalso discuss realistic returns on savings and investments to buy a home, pay for a future collegeeducation, or retire. In addition, we explain how a low-cost stock or bond index fund alreadyrepresents a widely diversified portfolio of stocks or bonds. Since this generation of students isgoing to be impacted by the ever increasing shift to defined contribution pension plans, wesuggest that engineering economy courses should include at least some coverage of saving forretirement.For those who want a more sophisticated coverage of saving for retirement, T-bills can be addedto the previous graph. The efficient frontier that is then formed shows how a “near-cash”investment can be used to build lower risk portfolios with a specific weighted mix of bonds andstocks. This can also be contrasted with some of the conventional guidelines, such as the % ofbonds in an individual’s investment portfolio should match the individual’s age. We find that theincreased reality of this approach dramatically increases student interest, and we feel that we arehelping them better prepare for life.

Eschenbach, T., & Lewis, N. A. (2015, June), Teaching Students About the Value of Diversification – A Retirement Portfolio's Efficient Frontier Paper presented at 2015 ASEE Annual Conference & Exposition, Seattle, Washington. 10.18260/p.24828

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