From option, to real option to an analytical theory of investment

1. From option, to real option to an analytical theory of investment

2. When Black-Scholes theory was initially developed, it was thought as an arcane academic theory that only applies to narrow technical areas. Soon its application became broader and broader. At the beginning of the classes, we explained that most of the financial activities can be beneficially thought as options. Today, we will discuss problems in broader horizons.

3. Marriage as an option • Marriage is a right, and not an obligation. Therefore, marriage is an option. But does labeling marriage as an option enhance our understanding about marriage? • An option to wait is more valuable when the market is more uncertain. Hence marriage, as an option, is more valuable when the future is more uncertain. This explains why people generally delay their marriage in a society, such as ours, when future is more uncertain.

4. Limited liability company as an option • As a limited liability company, upward profit is unlimited while downward loss is limited to company’s capital. Therefore it is an call option on its asset. This makes a LLP more prone to risky businesses, especially when a company’s capital comes from other people’s money.

5. Examples • S&L scandals • Banking regulation and competition from foreign countries, e.g. CitiBank in Argentina • Traders’ pay, such as Nick Leeson from Barings • industries that are promoted by governments • Subprime lending: Good time, big money; Bad time, retirement

6. Why LLP become legal entities? • In the history of human evolution, we cannot store large amount of wealth or food. Unlimited upward potential is not very useful for us. On the other hand, without food for several days may lead to starvation. Therefore, people are risk averse. LLP makes people less risk averse. • Why LLP generally occur in highly developed societies? • It is because more resourceful systems can afford more try and error.

7. The problem with using NPV to value project investment • It ignores the irreversibility, ongoing uncertainty, timing in investment and the context within a firm. • Real option theory address these issues. • However, most articles on this subject either use stylized numerical examples or adopt a purely conceptual approach to describing how option pricing can be used in capital budgeting. Not clear about the source of advantage.

8. An analytical theory of project investment • Directly investigate the relation among fixed cost, variable cost, duration of project and uncertainty.

9. The evolution of commodity prices • Lognormal process can represent commodity prices change • Variable cost, as a function of commodity price, satisfy the following equation, when the discount rate is r

10. The initial condition • When the duration of a project is infinitesimal small, it has only enough time to produce one piece of product. In this situation, if the fixed cost is lower than the value of the product, the variable cost should be the difference between the value of the product and the fixed cost to avoid arbitrage opportunity. If the fixed cost is higher than the value of the product, there should be no extra variable cost needed for this product.

11. The initial condition (continued)

12. Solution

13. Similarity and difference between option theory and capital investment • Both the evolution of share prices and value of economic commodities are represented by lognormal processes. For a financial option, the strike price at the end of the contract is known. The problem in option theory is to estimate the option price when the strike price, as well as several other parameters, is given. For a business project, irreversible fixed investment is determined at the beginning of a project. The problem in project investment is to estimate variable cost when fixed cost, as well as other factors, is given. Mathematically speaking, option theory is a backward problem while the problem in project investment is a forward problem.

14. Properties of this analytical theory • First, when the fixed cost investment, K, is higher, the variable cost, C, is lower. • Second, for the same amount of fixed investment, when the duration of a project, T, is longer, the variable cost is higher. • Third, when uncertainty, , increases, the variable cost increases.

15. Properties of this analytical theory (Continued) • Fourth, when the fixed cost approaches zero, the variable cost will approach to the value of the product. • Fifth, when the value of the product approaches zero, the variable cost will approach zero as well. • All these properties are consistent with our intuitive understanding of production processes.

16. Uncertainty and variable cost • The variable cost of a production mode is an increasing function of uncertainty. As fixed costs are increased, variable costs, calculated from (6), decrease rapidly in a low uncertainty environment and decreases slowly in a high uncertainty environment.

17. Uncertainty and variable cost (Figure)

18. Rate of return from investment • Then the total value of the products and the total cost of production are • respectively. The return that this producer earns is

19. Output and return with different levels of fixed costs • higher fixed cost investments, which have lower variable costs in production, need higher output volume to breakeven.

20. Output and return with different levels of fixed costs (Figure)

21. The fundamental tradeoff • The efficiency of high fixed cost systems and the flexibility of low fixed cost systems • Market size and level of uncertainty

22. Implication on capital budgeting • Microsoft, with high existing assets, can demand high rate of return. At the same time, it is very cautious to avoid projects with high uncertainty.

23. Capital Budgeting • Fixed cost • Variable cost • Diffusion rate • Market size • Duration of project

24. Uncertainty and duration • The amount of uncertainty accumulated over a project is • Higher uncertainty situation benefit from shorter duration

25. Fixed cost and duration of the project

26. It explains why individual life does not go on forever. Instead, it is more efficient for animals to produce offspring. This also determines most businesses fail in the end • Question: Currently, there are a lot of medical research on longevity. How these researches affect the society?

27. Fixed cost and discount rate

28. Question: Who will benefit more from low interest rates? What will happen to housing pricing in a low interest rate environment?

29. Explaining real options • Option to abandon: Lower fixed cost, less costly to abandon • Option to switch: Shorter duration of projects, easy to switch. • Option to delay: Shorter duration and lower fixed cost, easy to delay • Option to grow, invested fixed assets and variable assets offer new foundation to grow.

30. Exercise A product can be manufactured with two different technologies. The first technology needs ten million dollars of fixed investment while the second technology needs fifty millions of fixed investment. Suppose the unit price of the product is 1 million. A production facility based on either technology will last for twenty years. The diffusion rate is 60% per annum. The expected rate of change of the price of the product is 5% per annum. What is the variable cost for each technology? What technology you will recommend to your CEO if she estimates market size to be 100 and 300 respectively? Please support your recommendation with calculated rates of return.

31. Original motivation • Biological entities need to extract low entropy from the environment to compensate continuous diffusion. This can be modeled as

32. Universality • Since this theory is based on the most fundamental properties of life, we would expect it offers a universal understanding of human activities.

33. Applications • Projects and firms • Capital structure • Software development: Standard and agile • Product life cycle • Biological evolution • Resource, fertility, economy and stock market return • Dynamics of merger and acquisition

34. Biological evolution

35. Biological evolution (Continued) • Carbon is the element of organic compounds. Except the inert gas Ne, C is at the center of the period. “Carbon is a particularly mediocre element, easygoing in the liaisons it forms. … In chemistry as in life, this unpretentiousness has rewards, and in its mediocre way carbon has established itself as king of the Periodic Kingdom.”

36. From carbon to silicon • Carbon’s principle products, living organisms, have struggled over a few billion years to establish mechanisms for the accumulation and dispersal of information (an austere distillation and definition of what we mean by “life”), and silicon has lain in wait. The recent alliance of two regions, in which carbon-based organisms have developed the use of silicon-based artifacts for information technology, has resulted the enslavement of silicon. However, such is the precocity of carbon’s organisms that they are steadily developing silicon’s latent powers, and one day silicon may well overturn the suzerainty of its northern neighbor and assume the dominant role. It certainly has long term potential, for its metabolism and replication need not be as messy as carbon’s. Here we may see one of the most subtle interplays of alliances anywhere in the kingdom, for silicon will not realize its potential without the burden of development being carried out by carbon.

37. From sulfur to oxygen • Nature discovered that in some respects hydrogen sulfide (H2S), the analog of water (H2O), can be used by organisms in much the same way as water is used in the process of photosynthesis --- as a source of hydrogen. The great difference to note is that when hydrogen is removed from a water molecule by a green plant, the excrement is gaseous oxygen, which then mingles with the globally distributed atmosphere. However, when hydrogen is removed from hydrogen sulfide in the interior of a bacterium, the excrement is sulfur. Sulfur, being a solid, does not waft away, so the colony of organisms has to develop a mode of survival based on a gradually accumulating mound of its own sewage.

38. The reward and pollution in economic development • The transition from sulfur to oxygen was a major pollution event in biological history, which destroyed most living systems at that time. This example shows the importance of dumping high entropy waste in ecological systems. Those who are able to dump the excrement of themselves effectively will prosper, often at a cost to others. This is the same to human beings in economic development. Many industrial facilities are built by rivers or near seaside so wastes can be diffused quickly. While the gains from the industrial output are more concentrated and harvested by the owners of the industrial facilities, the wastes are diffused and shared by many others.

39. K and r strategies • The pattern of biological evolution is very similar to the pattern of the product life cycle. Biological species are sometimes classified, according to the relative level of fixed and variable costs, into two categories, the r-strategists and the K-strategists. The fixed costs are low for the r-strategists. They are usually of small size, produce abundant offspring and invest very little in each one. They are the species that prosper in a volatile environment for low fixed costs make them flexible. But they cannot compete well with other species in a stable environment for their marginal costs are high.

40. K and r strategies • In contrast, the fixed costs are high for the K-strategists. They are usually large in size, produce fewer offspring but invest much more in each one. They are the conservative species that are able to out-compete the r-strategists in stable environments, for their marginal costs are low. But they cannot adjust quickly when the environment changes. Between the extreme r-strategists such as bacteria and the extreme K-strategists such as elephants, there lies the r and K continuum