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Real Options Approach
Risk Management in
Investment Decisions
Asen Kolaksazov
Kolaksazov, Asen: Risk Management in Investment Decisions: Real Options Approach,
Hamburg, Anchor Academic Publishing 2015
PDF-eBook-ISBN: 978-3-95489-874-9
Druck/Herstellung: Anchor Academic Publishing, Hamburg, 2015
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i
Abstract
Numerous managers associate uncertainty with a bad outcome which should be
averted. This thesis' aim is to provide the opposite view. This dissertation will
reveal the strategic potential hidden in each investment. If one firm is on the
right track, it could obtain profit from the uncertainty. Uncertainty could generate
value and capture a market share. Real option approach will present the way
how this key aspect could be evaluated.
The roots of the real option approach are derived from the emblematic formula
for the finance world of Fischer Black, Robert Merton and Myron Scholes. The
revolutionary in their work is that complex contracts could be evaluated. The op-
tion-pricing theory take unalterable place not only in financial but also in the real
investments. In addition to this, the real option approach becomes a very pow-
erful tool for managing the real assets. This approach could be used in a wide
spectrum of managing action. For all the managers who associate uncertainty
and risk with a bad aftermath, the real option approach offers a solution for their
worries and could advise them with an appropriate way to operate an invest-
ment (Amram, 1999, p. vii).
In this work would be made practical as well as theoretical overarching from fi-
nancial to real options. Chapter 6 is very constructive and useful for future re-
search purposes, because it is suitable contribution to risk management analy-
sis, and it uses a combination of volatility with option pricing, which can calcu-
late more precisely the project risk.
ii
Acknowledgment
I would like to thank those who made this possible. First and foremost thanks to
my family for the enormous support. I thank all those form whom I was lectured
und especially thanks to my supervisor Dr Arief Daynes.
iii
Table of Content
Abstract ... i
Acknowledgment ... ii
Table of Content ... iii
Register of Illustrations ... v
List of Tables ... vi
1. Introduction ... 1
1.1. Introductory example ... 1
1.2. Statement of the problem ... 2
2. Research Methods ... 3
3. Frame of Reference and Literature Study ... 7
3.1. Traditional investment appraisal ... 7
3.1.1. Static methods ... 7
3.1.2. Dynamic methods ... 8
3.2. Options ... 11
3.2.1. Introductions ... 11
3.2.2. Fundamentals and Options' concept ... 12
3.3. Real Options ... 14
3.3.1. Decision-Tree Analysis ... 17
3.3.2. Contingent-Claims-Analysis (CCA) ... 17
3.4. Option Pricing Models ... 18
3.4.1. The Black-Sholes Model ... 19
3.4.2. The Binomial Model ... 20
3.5. Monte Carlo Simulation ... 22
iv
4. Finding ... 24
4.1. DTA ... 24
4.2. CCA ... 30
4.3. Option Pricing Model ... 32
5. Analysis ... 38
6. Case Study ... 44
6.1. The Real Property Project ... 45
6.1.1. Planning of Project Cost ... 46
6.1.2.
Planning of Project Revenue ... 46
6.2. The Project Valuation ... 48
6.2.1. Valuation with the Net Present Value Approach ... 48
7. Conclusion ... 57
8. Recommendation ... 58
List of Literature ... 59
Appendix ... 63
v
Register of Illustrations
Figure 1: Outline of the research's steps ... 3
Figure 2: Road Map of Real Options' Application ... 4
Figure 3: Net Cash Flows Discounting by the capital value method ... 9
Figure 4: Options structure ... 13
Figure 5: Coin Toss Bet and Hypothetical Yield Curve Strategy ... 16
Figure 6: Multiplicative binomial lattice ... 18
Figure 7: Performance of the replication portfolio and the call option ... 21
Figure 8: Quarter Unit Circle ... 23
Figure 9: Probability curve ... 24
Figure 10: A platform investment in R&D in a Decision Tree Analysis ... 25
Figure 11: A platform investment in R&D with a put option... 29
Figure 12: One-period Binomial Model ... 32
Figure 13: Portfolio solving system ... 33
Figure 14: Black & Scholes Formula ... 35
Figure 15: B&S price development ... 35
Figure 16: B&S Price Development ... 36
Figure 17: Black & Scholes Model vs. Binomial Pricing Model ... 36
Figure 18: Convergence in Option Pricing Models ... 37
Figure 19: Scope of action with and without flexibility ... 38
Figure 20: Probability distribution with and without flexibility ... 39
Figure 21: Option's value and strike price calculation ... 54
vi
List of Tables
Table 1: Option values at different stock prices ... 21
Table 2: Variant I of the Model - Scenario Analyse ... 41
Table 3: Normal Probability Distribution of the Revenues ... 41
Table 4: Variant II of the Model - LogNormal Distribution ... 42
Table 5: LogNormal Probability Distribution of the Revenues ... 42
Table 6: Simulations Results ... 43
Table 7: Breakdown of project development costs ... 46
Table 8: Price scenarios for the project ... 47
Table 9: Calculating the net present value of the project ... 48
Table 10: Determination of the evaluation parameters of the abandon option... 50
Table 11: Calculating of the underlying asset in case of abandon option ... 51
Table 12: Calculating of the strike price in case of abandon option ... 51
Table 13: Presentation of project value ... 55
1
1. Introduction
The main aim of this master thesis is to demonstrate a new approach which
could estimate the values of management activities better than the methods
used so far. A key word for this approach is the flexibility. In this study, the moti-
vation behind the real options' approach is emphasized. The research question
of this dissertation - "How `real options' could support management's decisions?
1.1. Introductory example
During the 90s, one paradox caused great confusion in the science circles in
the United States. A paradox is an announcement which seems to contradict it-
self at first appearance, but on closer inspection is, nevertheless, true (Olin,
2003, p.6). The assumption of the Real Options Approach is affected mostly by
this problematic nature. This paradox is better known in the mathematic and
statistic world as the "Monty Hall Problem". The name comes from the American
television show "Let's make a Deal" and is labelled with the name by the pre-
senter of this show. This problematic is known as well as the "the car and the
goats' problem". The participant is faced with three doors. Behind one of them is
hidden a brand-new sport car, but one does not know behind which of these
three doors. At the back of the remaining two doors are placed literary two
goats. The game rules follow as it is a turn now for the participant to make a
choice and select one of the three doors. Whereupon the presenter opens an-
other door different from the one that has already been chosen. One of the
goats appears. The participant is given the opportunity to make a new choice.
Should he select another door, or he should stay with his initial choice? This
problem separated the mathematicians around the world. What should the par-
ticipant do in order to maximize the chance of winning the brand-new sport car?
Marilyn von Savant, who has the highest IQ at that time, answered that the right
decision is to make a new choice. Upon her opinion, the participant has the
possibility of winning equals 2/3, in contradiction to the ignition chose, which is
equal to 1/3 (Gill, 2011, pp. 59-61).
2
That statement triggered a torrent of reactions and protests because many
mathematicians believed this is a wrong strategy (Gill, 2011, p.62; Olin, 2003,
pp. 1-3). As a matter of fact, she was right. For more detailed background of
this problem see the Appendix of this work.
1.2. Statement of the problem
In the U.S. literature for investment analysis and its applications, e.g. in the
company valuation, since the 90s exists an accusation that the most used ap-
proach Net Present Value (NPV) is incapable of evaluating properly the busi-
ness value of the investment and management decisions. In particular, it disre-
gards the value of management flexibility. To take this into account, it is rec-
ommended to be made an analogy between financial options and management
decisions. For implementation of this idea, the management's activities are con-
templated as an option on real assets. Designation "Real Options" was estab-
lished to be distinguished from financial option. However, this is a clear indicator
that the "real" value of future decisions could not be distinguished from the
methods used in the moment in the praxis; also they do not support the man-
agement accurately. The main reason for this enormous disadvantage is that a
management's decision's change could not be calculated (Trigeorgis, 2000, pp.
1-32; Copeland, 2003, pp. 1-10).
However, the traditional methods of corporate and investment calculation are no
longer appropriate for accomplishing of future investments
.
The reason for this
miscalculation is simple; they do not take into accounts the arising opportunities
and flexibilities. So far, risky or unusual investment opportunities are being clas-
sified by the traditional capital budgeting as a non-profitable. However, these in-
vestments possess enormous market potential. Such investment opportunities
could be calculated much better with the real options' approach, which consid-
ers the strategically aspect as well. Moreover, the value of risk-based assess-
ment has been recognized by the investors. For this reason, the real options'
approach is increasingly being used for evaluation.
3
2. Research Methods
According to Bryman et al. inductive approach is an approach in which exists a
tight interconnection between theory and praxis (Bryman & Bell, 2011, p. 714).
Inductive researches use the available data to generate a theory (Bryman &
Bell, 2011, p. 13). As a next step many methodologists make additional distinc-
tion between quantitative and qualitative research (Bryman & Bell, 2011, p. 26).
Qualitative research focuses on operation describing as quantitative research
aims to collect data and analyses it after that. Both methods are used in induc-
tive data collection (Bryman & Bell, 2011, p. 717). The dissertation would use
an inductive approach as the data gathering would be accomplished with quan-
titative research. For more effectiveness of the method, data would be gathered
from different sources to get a triangulation. Even the generated results of simu-
lations would be produced once again with different programs. The progress of
the dissertation would follow as in the diagram taken by Bryman et al. (Bryman
& Bell, 2011, p. 391).
1. General research question
2. Collection of relevant data
3. Interpretation of data
4. Conceptual and theoretical
framework
5. Writing up findings/
conclusion
4b. Collection of further data
4a. Tighter specificaton of
the research queastion
Figure 1: Outline of the research's steps
4
The next overview of the four-step model is the solution how the real option ap-
plication would be implemented. This should be also a road map for new users
(Amram & Kulatilaka, 1999, p. 89)
Step 1 Frame the Application
Step 4 Redesign?
Step 2 Implement the Real Option Model
Step 3 Review the Results
Figure 2: Road Map of Real Options' Application
Step 1: Frame the Application
Robert Jarrow is an academic who works on Wall Street. He says: "The more
realistic the model, the more time-consuming it is to compute and estimate, and
to understand and to use intelligently. People tend to want to use the simplest
model for the product and application at hand intuition can play a part. If the
models become too complex, you lose a lot of the intuition" (Amram &
Kulatilaka, 1999, p. 90). For that reason, the created model will be always in ac-
cordance with the situation.
5
Step 2: Implement the Option Valuation Model
This is the most important part on the model. The implementation itself is noting
to get excited about. It is vital for this project that the particular element be pre-
cisely calculated. The major difficulties come with the volatility determination.
Many solutions for this problem will be presented as well.
Step 3: Review the Results
Once the option evaluator has been installed, many solutions might be generat-
ed. The generated date will be evaluated and classified. After all, it will be taken
a decision if the generated data could be used. The follow points will be taken
into consideration.
Valuation results
Critical values for strategic decision making
The strategy space
Investment risk profile
Step 4: Redesign If Necessary
If the generated results seem implausible, the whole process should be im-
proved and repeated. It is not necessary that all elements have to be changed.
May be just one single part need more adjusting? As already mentioned, the
failure point is almost the volatility determination.
The master thesis will try to collect previous research in the Real Options area
and to present the reader a quintessence of it. It will consist of theoretical and
practical part. For the theoretical part, this assessment will go back to the foun-
dations of the Real Option's idea. A reveal during the years shows systematic
updates of this awareness. The practical part consists of variety of simulations
(Bryman & Bell, 2011, p. 45). One of these approaches is the Monte Carlo Ap-
proach which is used the most, but it is still full of mystery for most of the partic-
6
ipants and newcomers. Especially in this part of the dissertation it will be fo-
cused on the Monte Carlo simulation to be given the opportunity for every ex-
ternal reader to comprehend the idea and the outcomes. This means that a
relatively large percentage of the theoretical part will be spent on simulation and
outcome interpretations. On the question: Why exactly Monte Carlo Simulation
will be used? It could be answered quite simple. Monte Carlo simulations have
a large practical application. Every single bank has to make periodically "Stress
Test" and provide Risk Management (Braithwaite & Alloway, 2012). All these
activities are based on the random walk idea which could be simulated perfectly
with Monte Carlo programs. The program which is going to be used is "@ Risk".
The next question: Why it should be exactly this program but not anyone else?
could be answered also quite simple. This program is chosen because it is rela-
tively simple and at the same time powerful. When decisions have to be made
under uncertainty, it is used a method called discrete time modules (Buckley,
Casson, & Gulamhussen, 2005, p. 8).
On one hand, the scenario analysis and decision tree are techniques that con-
tribute to the visualization of the risk, on the other hand, they are not enough
meaningful. In this case, the simulations provide support for deeper risk man-
agement analysis. For the simulation to be closer to the reality, each of them
has to generate hundreds of possible outcomes. In this way, it provides an ad-
vance illustration of the situation before important decisions are taken
(Damodaran, 2008, p. 164). When a lot of results are generated, it exists the
risk of generating all in the wrong direction. This statement was made by the
well-known mathematician, Thomas Bayes, in 1756: Not that the errors arising
from the imperfection of the instrument and the organs of sense should be thus
reduced to nothing or next to nothing only by multiplying the number of observa-
tion seems to me extremely incredible. On the contrary the more observations
you make with an imperfect instrument the more it seems to be that the error in
your conclusion will be proportional to the imperfection of the instrument made
use of... (Young & Coleman, 2009, p. 105).
7
To be assured that the model is properly working, it is required to be made a
validation method though back testing or stress testing. Back testing works as
follows, historical data are inserted into this method. On this way, it could be
checked if they match the reality. The stress testing functions on the same
method as historical data are used to be avoided eventual complications
(Young & Coleman, 2009, p. 127).
3. Frame of Reference and Literature Study
3.1. Traditional investment appraisal
3.1.1. Static methods
The economically advantageous of investments' selection is conveniently based
on an appropriate investment appraisal (Götze, Northcott, & Schuster, 2010, p.
6). In the literature, the methods of statistical investment analysis are also called
"practical proceeding". They are applied willingly because of their convenient
handling. They do not require complicated mathematical challenges and in the
same time, operational costs are relatively low. The term "static" comes from
the non-consideration of the time factor differences in the occurrence of cash
outflow and -inflow during the investment. The follow techniques are part of the
static methods (Perridon, Steiner, & Rathgeber, 2009, pp. 33-48):
Cost Comparison Calculation,
Profit Comparison Calculation,
Average Rate of Return Calculation,
Static Payback Period Calculation.
Some textbooks do not introduce the static methods anymore, but rather com-
mencing directly with the dynamical methods (Rolfes, 2003, p. 9). Reasons for
this reluctance lie in the serious disadvantages of the static capital budgeting
process. As already outlined above, serious disadvantages could be mentioned,
as the failure in the temporal cash flows structure and the short-term perspec-
tive of the investment project (Kruschwitz, 2007, p. 42). For this reason, the
static methods would be no further treated in the thesis.
8
However,
dynamic methods eliminate these drawbacks, by taking into account
all cash inflows and outflows, which arise during the investment project term
(Perridon, Steiner, & Rathgeber, 2009, p. 49; Kruschwitz, 2007, p. 44;
Kruschwitz, 2007, p. 51). The main distinguish between the dynamic and statis-
tic method is the time value of money (Kruschwitz, 2007, p. 51).
3.1.2. Dynamic methods
There some methods of the classical investment design without exclude the un-
certainty calculation (Götze, Northcott, & Schuster, 2010, pp. 51-83; Perridon,
Steiner, & Rathgeber, 2009, p. 49):
Net Present Value Method,
Annuity
Method,
Internal Rate of Return Method,
Dynamic Payback Period Method.
That may be true, these methods do not regard risk, because of the fact, that all
future payments are for sure and there is non-payment (Perridon, Steiner, &
Rathgeber, 2009, p. 49). At this, a discount rate plays a decisive role. Rather
than one common interest rate, they could be utilized two different interest
rates, one for a debit interest and one for a credit interest. On the one side, the
determination of these rates is of fundamental importance for the results of the
dynamic investment calculations; on another side, the determination of these
represents one of the biggest problems of these methods (Perridon, Steiner, &
Rathgeber, 2009, pp. 55-60). With the ever-changing interest rates, however, it
should be used: either separate discounting interest rate for each period, or
compounding factors, again for every period.
(Götze, Northcott, & Schuster,
2010, p. 52).
The Net Present Value Method is undisputed the most important method for as-
sessing of investment's profitability. The capital value of an investment project
provides information about the capital appreciation to the investors. This meth-
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