Choosing the Right Model

The most realistic options

But there are, it seems, at least as many customers who are dissatisfied with this tool.

"Real Options" Underlie Agile Practices

The reasons for this high defection rate seem just as sensible as the reasons for using the tool and are usually based on technical grounds. As many executives point out, options embedded in management decisions are far more complex and ambiguous than financial options.

Their concern is that it would be dangerous to try to reduce those complexities into standard option models, such as the Black-Scholes-Merton model, which have only five or six variables. Yet the technical difficulties of real options are easy to address: There are valuation methodologies that effectively capture the complexities and the iterative nature of managerial decisions, and the Black-Scholes-Merton model is not the only, or even the most appropriate, way to value real options.

CFOs tell us that real options overestimate the value of uncertain projects, encouraging companies to overinvest in them. These concerns are legitimate, but we believe that abandoning real options as a valuation model is just as bad. How can managers escape this dilemma?

The valuation model we present here is a binomial model, so called because in each time period the value can only go up to one particular value or down to another. It captures the contingencies of real options and addresses nearly how to make money per month for a student of the most commonly voiced criticisms of using option theory to manage those contingencies.

We do not maintain, however, that simply switching to a binomial model will put everything right, for the biggest problem with real options though it is seldom voiced is more managerial than technical. In calculating real-option values, most managers, academics, and consultants assume that option holders will always make optimal exercise decisions—timely choices based on rational analyses of all the available information.

But if an option holder fails to make exercise decisions optimally, the the most realistic options become far less valuable. If you buy auto insurance, the most realistic options example, but do not file a claim when you have an accident, you will have overpaid for the insurance. In the same way, if you purchase a call option on a stock that appreciates wildly, but exercise it at the wrong time, you will have overpaid for the option.

There is a long-standing and mounting body of evidence showing that even financial options are exercised suboptimally. At times, holders are the most realistic options, exercising too soon; at other times, they fall asleep at the switch. What can managers do about the danger that real options will be exercised at the wrong time? They could give up on real options, throwing away a tool that ideally captures the contingencies in managing growth opportunities.

Real Option

Or they could adjust the model by assuming that their behavior will be suboptimal. That would give a more accurate value for the options—but at the expense of institutionalizing and perhaps perpetuating inferior decision making. Our preferred solution is to change the processes of corporate planning and budgeting to help improve the timeliness of managerial decisions; after all, good management is as much about making decisions at the right time as about making the right decisions.

Choosing the Right Model Critics of options-based approaches to valuing and managing growth opportunities often point out that there is a world of difference between relatively simple financial options and highly complex real options.

These differences, they argue, make it practically impossible to apply financial-option models to real-option decisions. They are right about the differences but wrong to assume that they are insurmountable. Valuation models can accurately capture even the most complex real options.

There are two main differences between financial the most realistic options real options. First, the most realistic options information necessary to value financial options and make decisions about exercising them is typically much more readily available than for real options. In some cases, the values of the assets underlying real options are similarly observable.

But in most cases, the value of the underlying asset is not so clear. For instance, the value of an unmade movie sequel or an untested drug cannot be read off a Bloomberg screen. Sometimes the value of comparable assets can be observed—or guessed at. For instance, it might be possible to estimate the evolving value of a new drug based on the past performance of other drugs that treat the same disease.

Some critics of the real-options tool feel that these kinds of assumptions render option-based valuation models useless. Option models are not alone in requiring assumptions, however. Net-present-value analysis of expected cash flows—the main alternative to real-options analysis and the method most firms use to value investment projects—requires making simplifying assumptions that are at least as heroic as any made in an options-based calculation.

For example, people applying cash-flow valuation models implicitly assume that all future investments are precommitted—in other words, that the company has already decided to make those investments. That, of course, is never the case.

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Companies can always choose not best dealing center reviews make investments in a project. It is surely no less acceptable to make educated assumptions about the value of the asset underlying a real option. The truth is, all models are simplified representations of reality, and all involve assumptions.

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The right to exercise financial options is unambiguous. But it is often unclear what the holder of a real option has the right to buy or how long that right will last. Even if it is relatively clear what the underlying asset is—a new plant, for instance—the maturity of an option can be indeterminate: Does the most realistic options opportunity to expand a business last forever or until a competitor takes away the opportunity by expanding first?

And whereas the owner of a financial option typically has exclusive rights—for those shares of IBM, say—the same may not be true for a the most realistic options option: Your company might have the option of building a plant in Brazil, but so do many others.

Many of the problems with real-options analysis stem from the use of a valuation model that demands more simplicity and clarity than the real-options world presents.

A Real-World Way to Manage Real Options

The elegant, Nobel Prize—winning Black-Scholes-Merton model, published inwas the most realistic options to value an option that was exercisable only at the end of its life and whose underlying share paid no dividends.

It was a breakthrough in economics, because it represented the first complete formula for pricing so-called European-style options. But it was never intended for use with more complicated derivatives, such as compound options, and attempts to use it for real-option valuation are misguided and inappropriate. In particular, work by John Cox, Steve Ross, and Mark Rubinstein has led to the creation of binomial, or lattice, models that are built around decision trees and are ideally suited to real-option valuation.

Making Real Options Really Work

What distinguishes binomial models is that they use algebra. The math, in other words, is much less formidable, although there may be more of it. Binomial models can also be more easily customized to reflect changing volatility, early decision points, and multiple decisions. It is true that building a customized binomial model for each real option involves more work than plugging numbers into a Black-Scholes-Merton box, but most managers evaluating major projects using NPV analysis prefer to create their own spreadsheets anyway rather than rely on generic models.

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Another advantage is that because the models are the most realistic options transparent and can be spreadsheet based, even managers whose math skills are long forgotten can understand and thus provide insight into the assumptions. Using the binomial model to value this work on a binary option project as a compound option is a two-step process. These second-step calculations provide you with numbers for all the possible future values of the option at the various points where a decision is needed on whether to continue with the project.

Modeling the Value of the Underlying Asset. The first step in drawing a tree for Copano is estimating what the value of the plant would be if it existed today, a figure that may be derived from traditional nonoption valuation techniques, such as discounted cash flow.

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The second step is estimating how much this value is likely to move up or down during the period in question. If we assume that the distribution of possible plant values is fairly standard what statisticians refer to as lognormalthe factor to apply for an up movement is given by the formula e the most realistic options the power of sigma multiplied by the square root of the time elapsedwhere e is the base of the natural logarithm 2.

Other formulas can be used in cases where the distribution of the possible underlying asset values is not lognormal. The challenge, clearly, is to calculate sigma. For a commodity chemical company like Copano, plant value is often driven by changes in a single key variable, such as the spread between the price of the output commodity chemical polyethylene terephthalic acid, or PTA, for example and the cost of a key input commodity chemical p-xylene, say.

The volatility of such a spread can be easily estimated.

This means that about two-thirds of the time over the course of the next year, the value would be expected to go up or down by less than With a sigma of The next step is to put a value on each of those intermediate real options, as well as on the total compound option of which they are a part, so that you will know whether to hold the most realistic options to the option or abandon it.

You can easily make it more complicated by, for example, breaking it down into smaller time periods, thereby capturing more of the intermediate values. The most realistic options Events Should they commit to investing the full amount needed? Keep the project alive by spending a lesser amount? Or simply pull the plug? To build that decision tree, they calculate how much the plant would be worth if it existed today and what its value could be at points in the future.

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That involves creating another type of tree, called an event tree. The values the plant could have a year hence, two years hence, and three years hence are as shown They worked backward from the end of year three, using the values from the event tree, and they relied on the replicating portfolio technique, which is explained in the sidebar with that title.

See steps 1 through 4 above the decision tree.

Real options valuation

The figures in black boxes are derived using the replicating portfolio technique. Valuing Your Options. To calculate the possible values of the project as an option at each stage in the decision tree, you have to begin from the end, the point furthest in the future.

If you abandon the project, its value is zero. Otherwise, the value at the end of year three is the difference between the value of the plant at the end of year three and the cost of building it. If it decides to defer building the plant, however, the company still has a valuable option. Unfortunately, we cannot determine, a priori, what that discount rate should be, because the risk of the option on the project is different from the risk of the project itself.

In this case, that number is greater than the value of exercising the option by building the plant. Note that in this the most realistic options model, the numbers show that delaying exercise of the option until maturity is always optimal.

In more complex situations, early exercise may sometimes be better, and the model would bring that out very clearly.

The Replicating Portfolio Technique As MBA graduates may remember from their finance courses, any option on a share can be expressed as a portfolio consisting of a certain number of the most realistic options and a certain number of bonds. For instance, a call option more or less amounts to the same thing as selling a number of risk-free par-value bonds and buying shares with the proceeds. We have, of course, two unknowns—the proportion of plant value and the number of bonds in the portfolio—but since we also have two equations, we can solve for both unknowns.

To determine the value of that right to invest, we simply work backward from the possible values at the end of year two that we have already calculated using the replicating portfolio technique, just as we worked back from year three to get the potential values at the end of year two.

Obviously, to build the tree, managers must make some fairly bold assumptions—about the value of the plant today supposing it were immediately operational and how that value might change over time. Using our real-option model would force them to do this, and by looking at how the values of their previous chemical plants—and those of competitors—have evolved in the past, they can construct plausible scenarios for binary options on the internet different possible futures.

The Problem of Poor Exercise Using the right valuation model will make real-options-based management work a lot better. These critics are correct to suspect that some kind of valuation error is occurring, but we believe that they are wrong in ascribing the problem to the options approach itself.

This is not by any means a new problem, and it is one that financial-option holders suffer from, too. American-style call options give holders the right to buy the stock at any time through the maturity date, and sometimes it is best to exercise an option early rather than sell it to someone else.

Early financial magazines carried articles advising investors to be alert to impending splits. While current-day options are protected against stock splits—the exercise prices and number of options are adjusted in response to splits—investors still have to vigilantly keep track of the most realistic options dividends, because most options are not dividend protected.

Their exercise prices are not adjusted downward when the stock goes ex dividend. It is therefore sometimes best to exercise call options just before the stock loses its right to the dividend.

The real power of real options

Recent the most realistic options shows that individual holders of traded options sometimes exercise their options far too early. A study by Allen M. A study by Chip Heath, Steven Huddart, and Mark Lang revealed that corporate officers who hold executive stock options also have a tendency to exercise their options too early if there has been a recent run-up in the stock price.

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Professional investors are much savvier—the former study showed that proprietary traders never exercise early.