Department of Management Science & Engineering

Number 9/Fall 2001

Investment Science Newsletter

By Professor David G. Luenberger

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Investment Science is becoming better known every month, and the range of possible applications seems to still be expanding. Many interesting and important problems can be fruitfully addressed with the power and clarity of Investment Science. For example, the technical discussion in this issue of the Newsletter addresses the very important topic of infrastructure projects.

Investment Science is of course much broader than the sub-field of real options, but real options has attracted a lot of attention. Many people first discover the potential of modern financial methods through real options considerations. In accord with this, we have coined the phrase "Real Options and Beyond" as one characteriz- ation of Investment Science. Investment Science includes real options, but goes beyond-considering portfolio problems, pricing problems, business models, and more. This is proving to be a good way for people to understand the essence of Investment Science.

The New Website

There is a new website devoted to the academic activities of Investment Science at Stanford University. The website is appropriately titled "Real Options and Beyond". It can be found at ~luen/RealOptions. The other site is still of great importance for general and applied aspects of investment science. You will find copies of past issues of this Newsletter at both sites. Your comments on these sites are welcome.

Short Course News

Investment Science for Industry was given at Stanford last April. Several recent participants were referred to the course by past members. It is heartening to see the chain build in this way.

Infrastructure Projects

Enormous investment levels are associated with most infrastructure projects-projects such as the building of dams, gas or oil pipelines, power plants, semiconductor fabs, petrochemical plants, bridges, highways, or tracks for fast trains. These projects are also extremely complex, and subject to special risks, often including a large degree of political risk. The success of such projects can hinge on the careful crafting and analysis of a financially-driven management and planning process. Investment Science provides a rich and rigorous framework for the development of such processes.

Standard financial methods (especially traditional discounted cash flow methods) have three major shortcomings when applied to infrastructure problems. The first is that ordinary discounting does not properly value projects that have embedded options, limits, or timing variations; and most infrastructure projects do have these characteristics. The second difficulty is that risks associated with infrastructure problems are long-term risks, for which there are usually no direct markets. The ultimate financial return of an oil pipeline project, for example, depends on the price of oil over a span of a few decades and current oil futures markets do not extend nearly that far.

The third shortcoming of discounting methods is that the large scale of infrastructure projects often takes them out of the realm of "small to medium" projects for the investing party. A typical project is so large that its private risk (the risk that cannot be hedged through market action) is not diversified within a larger portfolio of projects. Hence, investors want to employ risk-averse criteria for purposes of valuation and decision making. Again, this cannot be properly achieved by standard discounting within a complex project consisting of several stages and containing options and other on-going decisions.

Fortunately, Investment Science principles can overcome all three difficulties in ways that are easy to understand and implement.

The first difficulty, that of treating options and other decisions, can be addressed in exactly the same way as for other projects; specifically, by laying out possibilities and decisions in a tree structure. Proper evaluation and decision making can then be carried out either by simulation or by a backward moving evaluation.

The second difficulty, namely the lack of long-term futures markets can be overcome by generating artificial (or proxy) markets based on the observed behavior of large firms in the field. For example, large oil companies make capital investment decisions on the basis of a view of long-term oil prices, these decisions together with spot price characteristics can be used to generate a synthetic futures market for purposes of evaluation and hedging of oil infrastructure projects such as pipelines. How this is done is a possible topic for a future newsletter.

We shall concentrate here on the third difficulty, namely, the large size of typical infrastructure problems. This large size, itself, invalidates normal discounting methods, which are inherently linear. Consider a bet on the flip of a coin. Heads you win X one year from now, tails you get nothing (as shown in the diagram). How much is that worth? That is, how much would you pay to take those chances of payoff?

Simple Project

The expected value of the bet is X/2. However, the value to an investor is less than that for two reasons: the time delay and the risk of the payoff. In terms of time delay the value is reduced to [X/2]/Rf , where Rf is the risk free return (say Rf = 1.06). If X is small, like a few dollars, most people would be happy to pay close to V = [X/2]/ Rf. However, if X is large compared to a person's net worth, that person would most likely not be willing to gamble nearly X/2 for a 50-50 chance to win X. He or she would discount the value quite heavily. In fact, the degree of discount will increase with X. This means that there can be no one, fixed, discount rate that works for all X's. But given a specific X, an investor would settle on a rate characterized by a return R1, so that the coin flip was worth V = [X/2 ]/R1.

For instance, if X were $10 billion, investors might set a value (the amount they are willing to invest) at $2 billion rather than the expected value of $5 billion. This would amount to setting R1 = 5/2= 2.5 which is equivalent to discounting at a rate of 150%.

Things gets more complex in a project that has structure. For example, consider the situation below, on the left.

Complex Project - Two Year tree with each branch being taken with a probability of 1/2

This is a two-year tree with each branch being taken with a probability of 1/2. Notice that if we were to reach point A, we have the same coin flip situation as before. Hence, from above, we know the value from there is [X/2]/ R1. The same applies to point B, and the value is the same as at A. Hence, the first year appears to be completely risk-free, for the project will go to A or to B and the value is the same at each of these. Hence we should discount the first year at the risk-free rate. This means that, overall, V = [X/2 ]/(R1R f ).

The graph on the left is actually equivalent to the one on the right, when the two years are considered together. In two years there is a 50-50 chance of getting X or 0. This is the original coin flip but delayed two years instead of one. If we were to use a constant discount rate of R1 each year, we would value this as [X/2]/(R1 R1) which is much more severe discounting than we obtained by considering the situation on the left. The method on the left is actually the correct one, if we are to be consistent with the simple coin flip. Notice that in the correct method the discount factor varies in different parts of the project, and this is typical of proper valuation.

For the numbers we used for the coin flip, the two valuation methods produce values of $2 billion and $800 million, respectively, for this more complex example. This is an enormous difference, entirely due to the difference in discounting.

Contradictions such as this arise frequently in complex projects, but there is a methodology for getting everything right. Technically, the method is that of "certainty equivalence" which means that we keep track of how much each portion of the project is worth.

Proper valuation is important, not simply because we want a realistic assessment of a project. It is also essential for proper design and on-going decision making. If valuation is too conservative (because high discount rates are used throughout) then decisions will be too conservative. Conversely, if discount rates are too low, unwarranted risks will be taken. In practical terms for an oil pipeline, decisions made regarding materials, routing, timing, maintenance plans, and so forth may be not be consistent with the risks involved. Decisions based on proper valuation methods can account for a significant fraction (often 30% or more) of the total value of the project. Indeed, infrastructure projects are projects where Investment Science has tremendous potential, for it can save the equivalent of billions of dollars in a single large project.