4th
Annual Real Options
Conference
2000 University of Cambridge
Judge Institute of Managment Studies
Valuing Natural Resource Investments
| International Investment Flexibility | Keynote Address | Organizational
Adoption and Implications | Practitioner
Perspective from Consulting Firms | Empirical
Evidence | Competition and Strategy | Theoretical Issues in Real Option Valuation | Academic Perspectives on Future Developments
Valuing Natural
Resource Investments
Chairperson: Gordon
Sick (U. Calgary)
Gonzalo Cortazar (Catholic U. of Chile), Eduardo Schwartz (UCLA), and F. Riera (Catholic U. of Chile), Market-based Forecasts of Commodity Prices
Using Futures
Commodity prices are very volatile, with
typical annual variations from 20 to 40%. This price uncertainty has a major
impact on asset valuation and risk management issues and typically may be
dealt with in several ways. For valuation purposes, for example, market
prices that have already taken into account this risk may be used. Futures
contracts markets provide these risk-free estimates. There is now a wide
consensus that for valuing commodity contingent cash flows it is better to
compute them using futures prices instead of expected spot prices. The virtue
of this approach is twofold. First actual market prices can be used instead
of private predictions that are subject to all sort
of biases depending on who performs the prediction. Second, risk free
interest rates can be used for discounting cash flows instead of having to
add a risk premium, subject to great estimation error. One remaining
implementation problem remains when the time-horizon of the commodity
contingent cash flows exceeds the futures longest maturity that is traded in
the market. In this case it is necessary to make an estimate of which would
have been the current price for a futures
contract with a matching maturity, should there be one.
For risk management purposes futures
markets may be used to hedge risk. Once the optimal exposure is defined, the
hedging strategy must be designed in a way that it not only considers current
futures prices but also their process. It is well known that hedging ratios
critically
depend on volatility and factor correlation estimates. Thus a good model for
explaining the stochastic movement of futures prices becomes critical for
risk management purposes.
Sometimes expected cash flows (not only
their present value) are relevant. Most
of the academic literature and industry practice forecast commodity spot
prices using econometric models that estimate short, medium and long-term
equilibrium prices using expected demand and supply functions. Another common
method is to use time series estimates
and base the forecast on past behavior of prices. We build on a different
approach which models the stochastic behavior of prices for purposes of
explaining futures prices, and use this stochastic process to obtain
market-based forecasts of expected spot prices. We consider that expected
spot prices should be the addition of a risk premium to the known (or
estimated) futures price. Even though we recognize that we have rather noisy
estimates of the risk premium, we think that by using futures prices to help
predict expected prices is at the least a good additional source of
information that should be taken into account when making expected price
forecasts.
In this article we present two new models
of the stochastic behavior of commodity prices, both of which accommodate
mean reversion, use parameters which we believe are easier to interpret than
those of most of the existing models, and do not require to
specify the interest rate.
The first model has two factors, the spot
price and the deviations from long term expected returns. Our second model
introduces as its third risk factor a stochastic long-term drift on the
logarithm of the spotprice. We estimate the models
by implementing a simple procedure using the well-known Excel program. We
apply this procedure to estimate the same model (and database) in Schwartz
(97) and obtain similar results without resorting to the Kalman
filter approach described there. Then, we estimate our new models on an
updated data base that includes copper and oil futures prices traded at NYMEX
until 1998, and compare futures
price estimates with those obtained by previous studies. Finally we use our
futures price estimates to obtain market-based forecasts of expected spot
prices for both commodities.
Contingent claims analysis is currently
being used extensively in the energy industry. For example, energy traders
often use models suggested by Black (1976), Brennan and Schwartz (1985),
Schwartz (1997) and others for risk management as well as for valuing financial
contracts and real investments. These applications, which typical calibrate
the models' parameters using some combination of historical prices and
observed forward and option prices, have proven to be successful in valuing
and hedging relatively short-term financial contracts.
There is, however, an inherent
inconsistency in the application of these models that is likely to create a
problem when the models are applied to value and hedge longer horizon
investments. Specifically, although the models assume the parameters in the
price process are constant, the calibration procedures that are used in
practice typically provide for a more flexible specification by allowing the
parameters to change with time. Although these procedures generally provide reasonably
good approximations when the models are used to interpolate among prices in
liquid markets, as we will show, they can generate biases when the
methodology is used to extrapolate from observed derivative prices to value
long term real
investments like the pipelines and other infrastructure needed to exploit oil
and gas reserves.
To explore these issues in more detail we
develop a general equilibrium model of an extractable resource market where
both the prices and extraction choices are determined endogenously. As we
show, with plausible parameters the model generates prices that are roughly
consistent with observed forward and option prices as well as with the price
processes that were calibrated in Schwartz (1997). However, the subtle
differences between the endogenous price process determined within our
general equilibrium model and the exogenous processes considered in earlier
papers can generate significant differences in both financial and real option
values.
Our model extends existing general equilibrium
models that have appeared in both the finance and economics literature. The
model is particularly close in spirit to the Pindyck
(1980) model, which adds uncertainty to the seminal Hotelling
(1931) model that describes how the price of exhaustible
resources evolve through time. It is also related to the more
recent work of Litzenberger and Rabinowitz
(1995), who argue that because the option to wait has value in an uncertain
environment, resources will be extracted more slowly and prices will appreciate
less rapidly than they would in the Hotelling
certainty model. In contrast to the Pindyck (1980)
and Litzenberger and Rabinowitz
(1995) models, the endogenous price process that arises in our model exhibits
mean reversion, which is consistent with the empirical data discussed by
Schwartz (1997) and others. Moreover, our model is consistent with the
observation that discounted futures prices may be both above and below the
current spot price (i.e. futures curves can be in weak contango
or backwardation). These results are not simply due to the stochastic nature
of the exogenous state variables but arise endogenously from the assumed
frictions associated with the supply responses.
Our model generates insights about the
evolution of natural resource prices that can potentially have important
implications on the valuation and hedging of long dated financial or real
options. In particular, although the endogenous price process generated by
our model is qualitatively similar to the price process assumed by Schwartz
(1997), the functional form
of the drift is, in general, non-linear and generates equilibrium price paths
with less extreme realizations than would be generated by Schwartz's model.
As a result, options, whose payoffs are especially sensitive to these extreme
realizations, are generally less valuable in our general equilibrium setting
where the extreme realizations are observed less frequently.
Gonzalo Cortazar, Paulina Acosta and
Manuel Osorio (Catholic U. of Chile),
Monte Carlo Evaluation of Natural Resource Investments
This paper presents valuation models of
natural resource investments solved by a Montecarlo
simulation approach. We solve two real options models: the investment of an
undeveloped oil field as modeled by Cortazar and Schwartz (1998) and the
production schedule of a copper mine as modeled by Brennan and Schwartz
(1985). We analyze alternative Montecarlo
simulation implementations and discuss their results.
Since Boyle (1977) proposed Montecarlo simulation for valuing financial European
options, this approach has become increasingly attractive because of its easy
handling of path-dependent cash flows and complex uncertainty models.
However, standard Montecarlo simulation models,
with their forward induction approach, have traditionally been considered
inappropriate for valuing American-type options.
In the last decade there have been several
efforts to extend Monte
Carlo simulation
techniques for solving American-type options. These methods attempt to
combine the simplicity of forward induction with the ability of determining
the optimal option exercise of backward induction. One of the simulation
methods, proposed by Barraquand and Martineau (1995), show that it is possible to discretize and to reduce the dimensionality of the
valuation problem, and still get reasonably good approximations. For example,
if we assume a multi-factorial process for a state variable S, the procedure
calls for making several thousand
Monte Carlo simulations on S and grouping the obtained values into a fixed
set of "bins". Then, by making successive simulation runs it is
possible to empirically determine the transition probabilities between
successive bins and finally to solve backwards the valuation process using
each bin as a decision unit.
One of the main issues in this methodology
is the selection of the one-dimensional state variable that will represent
all state variables in the problem. As Broadie and Glasserman (1997b) point out, this procedure does not
ensure convergence when, for example, there are
disjoint optimal exercise sectors. In this case, further increases in the
number of one-dimensional bins are not able to determine the optimal exercise
policy. To reduce this problem, Raymar and Zwecher (1997) recommend adding a second dimension to the
bin grouping process, so the state of the economy can be represented by more
than one dimension. In one recent implementation of the Barraquand
and Martineau (1995) method to solving a real
option problem, Cortazar and Schwartz (1998) determine the optimal timing of
an undeveloped oil field. They argue that given that there is no disjoint
exercise region in the valuation of an undeveloped oil field, there probably
is no need to implement this valuation model using a two-dimensional Raymar and Zwecher (1997)
method, but it suffices to make a one dimensional implementation of the Barraquand and Martineau (1995)
method.
In Cortazar and Schwartz (1998), the Barraquand and Martineau (1995)
method is used to obtain the optimal timing of an undeveloped oil field.
Uncertainty is described using a two-factor model for oil spot prices and convenience yield (Schwartz (1997). Instead of using two
state variables (in addition to time) the problem is reduced to a one
dimensional model using the value of the developed oil field (for the
optimization stage) as the only state variable for deciding when it is
optimal to invest. By reducing the problem dimensionality the implementation
of this method is argued to remain simple yet to obtain reasonably accurate
value estimates.
In Section 2 of this paper we solve the
same undeveloped oil field considered in Cortazar and Schwartz (1998) but
using the two-dimensional Raymar and Zwecher (1997) method and compare it with the Barraquand and Martineau (1995)
approach used earlier.
In Section 3 we analyze alternative
solutions to Brennan and Schwartz (1985) classic mine model using both
simulation methods. Section 4 concludes.
Robert Elliott (U. of Alberta), Gordon Sick (U. of Calgary) and Michael Stein (U. of Oregon),
Pricing Electricity
Calls
In this paper we develop a general model
of spot electricity price that encom- passes the
stylized features of many of the emerging deregulated electricity pools
around the world. We incorporate seasonality on an annual basis and a daily
basis around a mean-reverting de-seasonalized
intrinsic price. A unique feature of this paper is the
treatment of jumps in the spot price as arising from supply shocks as large
generators in the system come off-line and go on-line in a partially
predictable manner. We model the number of large generators on line as a
discrete Markov process. This feature is motivated by the Alberta electricity pool,which has 14 large base-load generators and very
little excess capacity. We show how to estimate the diffusion process with a Kalman filter technique and the discrete Markov model
with maximum likelihood model. The motivation for pricing calls on this price
process is two-fold.First many electricity
customers purchase call options to manage their risk.Sec-
ond,generators are called
into the system or turned on, according to whether their marginal price is
less than or greater than the system marginal price (spot price).The revenue
stream to a company that builds a new generator that is not part of base load
will be a strip of call options.Thus,this is a real
option valuation model.
International
Investment Flexibility
Chairperson: Blake Johnson (Stanford U.)
Arun S.Muralidhar (J.P.
Morgan),
Valuing the Financial Flexibility of a Multinational Enterprise
Paper,
Slides
This chapter argues that when corporate
tax obligations are variable, a multinational firm has financial flexibility
(the option to shift profits to favorable tax regions in every period and
lower the global tax liability), and that traditional NPV analyses of foreign
projects may not capture the value of this flexibility. It introduces an
options pricing model to value the flexibility that internalizing tax
management provides, and offers an adjusted NPV calculation that incorporates
this portfolio of options into the investment decision. While national firms
may find certain projects unattractive, a multinational firm is shown to
acquire projects once they value the flexibility. Corporate tax rate data are
used to compare potential projects in different countries for a U.S.-based
MNE. The chapter concludes by discussing the implications of these results
for MNEs and governments.
This paper considers the role of
production technology in export oriented, irreversible investments made in a
regime of volatile exchange rates. In this relatively simple model,
technologies are characterized by their flexibility. More specialized
technologies incur larger sunk costs in return for a cost advantage at the
expected level of output. By reducing sunk costs and offering the firm a
broader array of responses to changes in the exchange rate, flexibility
reduces the cost of regret incurred by an investment. Accordingly, more
flexible technologies enter the foreign markets at less favorable exchange
rates and with higher scale. Where the firm has a choice of technology,
increases in volatility lead to the selection of less specialized
technologies, the sacrifice of cost advantages for flexibility.
Hiroshi Yamaguchi, Nobuya
Takezawa, Ushio Sumita
and Ted Azami (International University of Japan),
The Real Option Premium
in Japanese Land Prices
The present paper examines the empirical
implications of the real option pricing model developed in Quigg (1993). The present value of cash flows generated
from developed property less the development costs gives us the value of the
vacant plot of land. The owner of vacant plot of land, however, has the right
to exercise the option of developing the property or can simply defer
development. It is this real option to wait to develop vacant plots of land
that we empirically investigate.
The study focuses on a sample of 754
transactions in the residential areas of Nerima-ward of Tokyo. We estimate the option premium during the late
1980's to be at 18.04% and the premium during our early 1990's sample at
18.52%. This is substantially larger than the premiums documented for
residential areas in Seattle (Quigg).
The empirical approach taken in this paper
involves estimating a hedonic regression so that we can obtain forecasted
values of developed property. Our regression specification takes into account
features of importance in the Japanese real estate market.
Our findings are also consistent with the
notion of a building cycle where the property prices in a given area are
highly correlated. When it is profitable to exercise the option to develop a
plot of land in one area, it should be profitable to develop property in
adjacent areas as well. This then leads to a construction booms such as that
witnessed in Tokyo during the second half of the 1980's.
Keynote Luncheon
Address
Risk and Options
Dr. Myron S. Scholes
Stanford University
Professor Scholes
is the Frank E. Buck Professor of Finance Emeritus at Stanford University´s Graduate School of Business and a partner in
Oak Hill Capital Management. Prior to that he taught at MIT and the University of Chicago, and has been a Senior Research Fellow at the Hoover Institution. He
received a Ph.D. in 1969 from the University of Chicago. Professor Scholes is a member of the
Econometric Society and was President of the American Finance Association.
Professor Scholes
is widely known for his seminal work in options pricing, capital markets, tax
policies and the financial services industry. He is co-originator of the
Black-Scholes options pricing model and
risk-neutral valuation, which are the basis of the pricing and
risk-management technology that is used to value and manage the risk of
derivative instruments around the world and for much of real options
valuation. For this work, he was awarded the Nobel Prize in Economic Sciences
in 1997.
On the practitioner side, Dr. Scholes has been a principal and Limited Partner at
Long-Term Capital Management from 1993-1998. Between 1991 1993, he was a
Managing Director at Salomon Brothers, a member of Salomon's risk management
committee and Co-Head of its Fixed Income Derivatives Sales and Trading
Department.
Organizational
Adoption & Implications
Chairperson: Soussan Faiz
(Texaco Inc.)
Andrew Stark (Manchester Business School),
Successfully Integrating the Real Options Approach into your Corporate
Decision Making
Diversified corporations competing in
industries characterized by uncertain and rapidly changing structures can
enhance their competitiveness by increasing their level of strategic
flexibility, i.e., their ability to reconfigure divisional relationships to
exploit shifting industry-level complementarities.
The value of this kind of strategic
flexibility can be understood using a real options framework. Specifically,
part of the value of a diversified portfolio of operating assets is a
function of the present value of future synergies between currently unrelated
businesses that are subject to market convergence. By diversifying and
acquiring assets in industries subject to increasing complementarity,
firms acquire the right, but not the obligation, to pursue interdivisional
synergies when and as appropriate. In other words, under particular
circumstances, diversification creates real options on the integration of
currently separate operating units.
This paper investigates the administrative
implications of attempting to create and exercise real options on future
synergies through diversification. For whereas an investor can acquire and
exercise a financial option simply by issuing the appropriate ìbuyî orders, creating and exercising a real option on
future synergies has potentially significant organizational ramifications.
Using a case study methodology, this paper examines the implications of a
real options approach to diversification on the nature and quality of
corporate-divisional and
interdivisional relationships and proposes an administrative theory of real
options diversification.
Panel Discussion:
Current Status and Future Prospects I
(Practitioner Perspectives from Consulting Firms)
Moderator: Gregg Bell (Charles
River Associates)
Panelists include:
Remy Schosmann (Ernst & Young)
Mike Kaye (Andersen Consulting)
Yann Bonduelle (Pricewaterhouse Coopers)
Gunnar Pritsch (McKinsey
& Co.)
Ravi Bulchandani (Morgan
Stanley Dean Witter)
Laura Martin (Credit Suisse First Boston)
Alberto Micalizzi (Real Options Group)
Empirical Evidence
Chairperson: Bhagwan Choundhry
(UCLA)
Han Smit (Erasmus U.
Rotterdam, Netherlands),
Option Characteristics of Growth Stocks
A. Al-Horani (Manchester Business School), Peter Pope (Lancaster University) and Andrew Stark (Manchester Business School),
Research and Development Expenditures, Real Options and the Book-to-Market
Effect on Expected Returns
Antonio Bernardo
(UCLA), Bhagwan Chowdhry
(UCLA), Darius Palia (Columbia U.), and Elena Sernova.
Real Options and the Diversification
Discount
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