Decision Trees

Decision trees help lay out the sequence of decisions that can be made and present a tabular or graphical comparison resembling the branches of a tree, which highlights the differences between investment choices. In Table 13-6, we examine a retailer considering two choices: (a) opening additional physical stores in a new geographic region but using a format that has already proven successful elsewhere, or (b) developing a new online-only retail venture. The cost of both projects is the same, $60 million (column 4), but the net present value (NPV) and risk are different. If the firm expands its physical store count (Project A), it has a high likelihood of a modest positive rate of return. This market has some uncertainty, but long-run success seems to be likely. If the firm launches a new online store, it faces stiff competition from many established firms. It stands to lose more money if expected sales are lower than it would under option A, but it will make more if sales are high. Even though Project B has a higher expected NPV than Project A (last column in Table 13-6), its extra risk does not make for an easy choice. More analysis would have to be done before management made the final decision between these two projects. Nevertheless, the decision tree provides an important analytical process.

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Figure 13-7 Simulation flow chart

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Table 13-6 Decision trees

The Portfolio Effect

Up to this point, we have been primarily concerned with the risk inherent in an individual investment proposal. While this approach is useful, we also need to consider the impact of a given investment on the overall risk of the firm—the portfolio effect. For example, we might undertake an investment in the building products industry that appears to carry a high degree of risk—but if our primary business is the manufacture of electronic components for industrial use, we may diminish the overall risk exposure of the firm. Why? Because electronic component sales expand when the economy does well and falter in a recession. The building products industry reacts in the opposite fashion—performing poorly in boom periods and generally reacting well in recessionary periods. By investing in the building products industry, an electronic components manufacturer could smooth the cyclical fluctuations inherent in its business and reduce overall risk exposure, as indicated in Figure 13-8.

The risk reduction phenomenon is demonstrated by a less dispersed probability distribution in panel C. We say the standard deviation for the entire company (the portfolio of investments) has been reduced.

Portfolio Risk

Whether or not a given investment will change the overall risk of the firm depends on its relationships to other investments. If one airline purchases another, there is very little risk reduction. Highly correlated investments—that is, projects that move in the same direction in good times as well as bad—do little or nothing to diversify away risk. Projects moving in opposite directions (building products and electronic components) are referred to as being negatively correlated and provide a high degree of risk reduction.

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Figure 13-8 Portfolio considerations in evaluating risk

Finally, projects that are totally uncorrelated provide some overall reduction in portfolio risk—though not as much as negatively correlated investments. For example, if a beer manufacturer purchases a textile firm, the projects are neither positively nor negatively correlated; but the purchase will reduce the overall risk of the firm simply through the “law of large numbers.” If you have enough unrelated projects going on at one time, good and bad events will probably even out.

The extent of correlation among projects is represented by a new term called the coefficient of correlation—a measure that may take on values anywhere from −1 to +1.6 Examples are presented in Table 13-7.

In the real world, few investment combinations take on values as extreme as −1 or +1, or for that matter exactly 0. The more likely case is a point somewhere between, such as −0.2 negative correlation or +0.3 positive correlation, as indicated along the continuum in Figure 13-9.

The fact that risk can be reduced by combining risky assets with low or negatively correlated assets can be seen in the example of Conglomerate Inc. in Table 13-8. Conglomerate has fairly average returns and standard deviations of returns. The company is considering the purchase of one of two separate but large companies with sales and assets equal to its own. Management is struggling with the decision since both companies have a 14 percent rate of return, which is 2 percentage points higher than that of Conglomerate, and they have the same standard deviation of returns as that of Conglomerate, at 2.82 percent. This information is presented in the first three columns of Table 13-8.