Department of Management Science & Engineering

Number 1/Autumn 1997

Investment Science Newsletter

By Professor David G. Luenberger

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Forward Pricing

Current Pricing

General Pricing

This is the first of several planned newsletters describing events in the Investment Science program at Stanford. In each issue we plan to report on the nature of research and projects underway. There will also be a short article of substance related to Investment Science concepts (See Pricing the Future in this issue.) A primary goal of the newsletter is to continue to build a network for exchanging ideas. We welcome comments and examples.

For detailed information about Investment Science for Industry Course

Investment Science Published

The text, Investment Science, was published by Oxford University Press in early June this year. This is good news to the students who in the past have had to put up with preliminary versions. The book can be purchased through the web at or through many bookstores.

Order Investment Science from Here

Short Course News

The course, Investment Science for Industry, presents the concepts of Investment Science to practioners in industry and to industry leaders who wish to learn how modern concepts can b applied to business problems. the course also is an important window to the business world, bringing us in contact with those who deal with real problems. The interchange is always very lively.

November and April
Last May

Investment Science for Industry will be offered at Stanford November 13-14, 1997 and April 30-May1, 1998.

Investment Science for Industry will be taught in Taiwan, hosted by Yuan-Ze University, on September 19-20, 1997.

The course was taught last May 15-16 at Stanford. There was a very good group of people from a wide range of backgrounds and industries. We learned a great deal from each other and several new relationships were formed.


Several projects with industry sponsorship are underway:

ENRON has sponsored general research in the department, which this year focused on evalution of foreign investments subject to specific country risk as well as other technological and market risks. This reearch is being carried out by Kian Esteghamat.

CHEVRON is sponsoring research on real options theory which is being carried out by Marius Holtan.

NATIONAL SEMICONDUCTOR sponsored a student project team (directed by Professor Blake Johnson) on licensing arrangements. National also held a one-day conference on valuation. Several people from our departmen were on the program.

HEWLETT-PACKARD has worked with us on an exciting project that applies the concepts of valuation to commodity contract design.

Student interest in Investment Science continues to be very strong, and support from industry as well as industry interaction is greatly valued.

Recent Graduates

This June three students in Investment Science received Ph.D degrees.

Lucie Tepla's dissertation title is "Constrained Optimal Portfolio Insurance." Her research solves the problem of determining an optimal portfolio of stocks when the portfolio is constrained to hold certain assets. This is an important problem for owners of firms who are restricted from selling their shares after an IPO, for owners of inherited stock who for varius reasons cannot sell their stock, and for owners of ill-liquid assets.

Lauren Wang's dissertation title is "The Valuation of Assets with Non-Traded Risks." Her research develops an innovative way of determining the value of a future cash flow associated with a commodity sale or purchase. Her method relates that cash flow to the operations of companies that deal with that commodity. The method is based on the assumption that the company is operated to maximize its long term growth rate. From this assumption, the implied forward price of the underlying commodity can be inferred. An example treated in the dissertation is to determine the foward price (10 years out) of oil.

Marius Holtan's dissertation title is "Evaluation and Portfolio Optimization in Incomplete Markets." Marius develops a complete systematic theory of pricing that can be applied in either continuous or discrete time, which covers complete, incomplete, or partially complete markets, and which accounts for investor preferences and asset holding. He also developed efficient numerical procedures for finding prices and optimal portfolios.

Pricing the Future

The fundamental problem of financial valuation is that of assigning a current value (or price) to a cash flow that will occur in the future. If this cash flow is deterministic (that is, known with certainty) then the proper way to assign a current value is to use its present value. For a cash flow x that occur in one year, the present value is defined as PV=x/(1+r) where r is the riskfree rate of interest. Hence, in this simple case, there is a simple answer to the question of valuation. Typically, however, the magnitude of the future cash flow is uncertain -- but nevertheless a current value must be assigned to complete a useful analysis.

There are a number of methods that can be used to find an appropriate value, depending on the relation of the cash flow to existing markets. In this article we discuss some of the simplest methods, which apply when suitable markets are present.

Forward Pricing

Consider the cash flow generated by the harvest of 1000 pineapples that will occur in one year. The cash flow is uncertain because it depends on the price of pineapples one year from now. At first it may seem difficult to assign an equivalent value to this cash flow. However, if there is a forward market for pineapples with a price of, say, F per 1000 pineapples, then the value, today, of the harvest that will take place in a year is exactly F/(1+r) where again r is the riskfree rate of interest. The reason, of course, is that we can duplicate the harvest by currently placing F/(1+r) in a bank and entering a foward contract to buy 1000 pineapples. In one year our deposit will have grown to F, which we can use to satisfy our side of the contract, buying the pineapples at the previously agreed upon price. At that time we will have 1000 pineapples, just like we would if we had harvested them.

In general, if a foward market exists for a commodity whose price is perfectly tied to the cash flow we wish to value, we can assign value unambiguously without further analysis -- the proper value is the foward price discounted to the present. This is the easy case. The foward market solves our valuation problem.

Current Pricing

Now consider a project that will in one year general a cash flow equal to the value of a share of IBM stock at that time. The magnitude of this cash flow is uncertain, and there is no forward market for shares of IBM stock. How can we assign value in this case? Must we attempt to predict the value of IBM? Must we search for a suitable discount rate? The answer is again simple. The value of the project cash flow is exactly equal to the current value of a share of IBM stock (we are assumming for simplicity that no dividends are to be paid during the year). The reason that this is the value is, again, that we can duplicate the project cash flow with a marketed asset. In this case th cash flow can be duplicated by buying a share of IBM; it will have the same value as the project in one year. Hence, the market for current IBM stock acts almost like the forward market for pineapples in the previous example. However, in the case of IBM stock it is not necessary to apply a discount factor because the price is already in current terms. This example works because there is no cost for sotring IBM stock and it can be sold short. Hence, purchase (or short sale) of the stock now gives exactly the same effect as initiating (or selling short) the project cash flow now. the general principle is that if we can find an asset, such as a commodity or security, that duplicates the cash flow, the value of this asset provides the proper value of the cash flow.

There are sometimes complications. If the duplicating asset has associated storage costs, the relationship must be slightly modified. If the duplicating asset cannot b sold short (at the negative of the purchasing price), the simple relationship may destroyed.

As a general rule, if the duplicating asset is widely held by investors (such as is the case for stock, gold, silver, and some collectibles) a simple relation of the type abov can be used. If, on the other hand, people do not hold the commodity for investment purposes (such as is the case for soy beans, crude oil, DRAM, and electricity) the simple relation breaks down. Other methods must be used.

General Pricing

In most situations future cash flows are not as closely related to marketed assets as in the above examples. However, the basic methods discussed here often form the starting point for better approaches. Many of the research topics carried out in the Investment Science program are directed at finding suitable methods of valuation in complex situations.