Risk Management in Investment Decisions. Real Options Approach

Master's Thesis, 2012

71 Pages, Grade: Merit


Table of Contents



Register of Illustrations

List of Tables

1. Introduction
1.1. Introductory example
1.2. Statement of the problem

2. Research Methods

3. Frame of Reference and Literature Study
3.1. Traditional investment appraisal
3.1.1. Static methods
3.1.2. Dynamic methods
3.2. Options
3.2.1. Introductions
3.2.2. Fundamentals and Options’ concept
3.3. Real Options
3.3.1. Decision-Tree Analysis
3.3.2. Contingent-Claims-Analysis (CCA)
3.4. Option Pricing Models
3.4.1. The Black-Sholes Model
3.4.2. The Binomial Model
3.5. Monte Carlo Simulation

4. Finding
4.1. DTA
4.2. CCA
4.3. Option Pricing Model

5. Analysis

6. Case Study
6.1. The Real Property Project
6.1.1. Planning of Project Cost
6.1.2. Planning of Project Revenue
6.2. The Project Valuation
6.2.1. Valuation with the Net Present Value Approach
6.2.2. Valuation with the Real Option Approach

7. Conclusion

8. Recommendation

List of Literature



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 option-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 powerful 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 investment (Amram, 1999, p. vii).

In this work would be made practical as well as theoretical overarching from financial to real options. Chapter 6 is very constructive and useful for future research purposes, because it is suitable contribution to risk management analysis, and it uses a combination of volatility with option pricing, which can calculate more precisely the project risk.


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.

Register of Illustrations

Figure 1: Outline of the research’s steps

Figure 2: Road Map of Real Options’ Application

Figure 3: Net Cash Flows Discounting by the capital value method

Figure 4: Options structure

Figure 5: Coin Toss Bet and Hypothetical Yield Curve Strategy

Figure 6: Multiplicative binomial lattice

Figure 7: Performance of the replication portfolio and the call option

Figure 8: Quarter Unit Circle

Figure 9: Probability curve

Figure 10: A platform investment in R&D in a Decision Tree Analysis

Figure 11: A platform investment in R&D with a put option

Figure 12: One-period Binomial Model

Figure 13: Portfolio solving system

Figure 14: Black & Scholes Formula

Figure 15: B&S price development

Figure 16: B&S Price Development

Figure 17: Black & Scholes Model vs. Binomial Pricing Model

Figure 18: Convergence in Option Pricing Models

Figure 19: Scope of action with and without flexibility

Figure 20: Probability distribution with and without flexibility

Figure 21: Option's value and strike price calculation

List of Tables

Table 1: Option values at different stock prices

Table 2: Variant I of the Model - Scenario Analyse

Table 3: Normal Probability Distribution of the Revenues

Table 4: Variant II of the Model - LogNormal Distribution

Table 5: LogNormal Probability Distribution of the Revenues

Table 6: Simulations Results

Table 7: Breakdown of project development costs

Table 8: Price scenarios for the project

Table 9: Calculating the net present value of the project

Table 10: Determination of the evaluation parameters of the abandon option

Table 11: Calculating of the underlying asset in case of abandon option

Table 12: Calculating of the strike price in case of abandon option

Table 13: Presentation of project value

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 motivation 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 itself 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 presenter 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 another 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 participant 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).

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 approach Net Present Value (NPV) is incapable of evaluating properly the business value of the investment and management decisions. In particular, it disregards the value of management flexibility. To take this into account, it is recommended to be made an analogy between financial options and management decisions. For implementation of this idea, the management’s activities are contemplated as an option on real assets. Designation “Real Options” was established 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 management 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 classified by the traditional capital budgeting as a non-profitable. However, these investments possess enormous market potential. Such investment opportunities could be calculated much better with the real options’ approach, which considers the strategically aspect as well. Moreover, the value of risk-based assessment has been recognized by the investors. For this reason, the real options' approach is increasingly being used for evaluation.

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 distinction 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 inductive data collection (Bryman & Bell, 2011, p. 717). The dissertation would use an inductive approach as the data gathering would be accomplished with quantitative research. For more effectiveness of the method, data would be gathered from different sources to get a triangulation. Even the generated results of simulations 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).

illustration not visible in this excerpt

Figure 1: Outline of the research’s steps

The next overview of the four-step model is the solution how the real option application would be implemented. This should be also a road map for new users (Amram & Kulatilaka, 1999, p. 89)

illustration not visible in this excerpt

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 accordance with the situation.

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 precisely 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 generated. 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 improved 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 foundations 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 Approach which is used the most, but it is still full of mystery for most of the participants and newcomers. Especially in this part of the dissertation it will be focused on the Monte Carlo simulation to be given the opportunity for every external 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 relatively 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 contribute 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 management 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 advance 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 observation 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).

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 commencing 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 perspective of the investment project (Kruschwitz, 2007, p. 42). For this reason, the static methods would be no further treated in the thesis.

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 statistic 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 uncertainty 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 assessing of investment’s profitability. The capital value of an investment project provides information about the capital appreciation to the investors. This method contains information about the return of the utilized capital. Because of this fact, this approach will be introduced and analysed.

Discounted Cash Flow Approach

A common approach in practice lies in the different variants of the net present value method. For calculation of the net present value, the future net cash flows are estimated and in the second step, they are discounted to the present. The investment interest rate is used for discounting.

The NPV method works as follow: every prospective cash flow being discounted to point t = 0, see the figure below. Figure 3 illustrates the process of discounting on the time t ="<"/span> 0 using a time line on which the individual periods are enumerated. By the period length, once take usually one year. The incoming and outgoing payments are combined to one and are called net payment (Net Cash Flow). These payments and the time in which they arise are illustrated in the next figure (Götze, Northcott, & Schuster, 2010, p. 54).

illustration not visible in this excerpt

Figure 3: Net Cash Flows Discounting by the capital value method

The net present value is thus calculated as follows (Perridon, Steiner, & Rathgeber, 2009, p. 72). The same formula could be found in many English books, for instance, in Demodaran (2008, p. 100).


illustration not visible in this excerpt

As already mentioned, the most-used method as in theory as in practice is the NPV method. This is accomplished by the point that data collection and implementation are easier to operate with. As an advantage of this method is the fact that it is not required to perform some huge calculations but just regular mathematical skills. However, it also has its disadvantage when a longer period has to be forecasted (Götze, Northcott, & Schuster, 2010, p. 62).

Very important aspect for successful design, as already stated, is the interest rate, which is applied for cash flow discounting. If ones want to take an appropriate interest rate, the interest rate of the similar project and equivalent risk has to be taken into consideration (Teisberg, 1995, p. 36). For much more precise calculation, different cash flows have to be discounted with a different interest rate, because the corresponding risk for every cash flow is also different (Teisberg, 1995, pp. 36-37). One very useful model which could be used for calculation of interest rate in different projects is a capital asset pricing model. An interesting fact is that this method takes into account the project risk and that interest rate varies towards the risk involved in the project. With the usage of risk adjusted interest rate it makes the project more developed than the DCF approach. Hull (2012, pp. 696-698) also supports this idea in his book saying that when an analysis of an investment is made, the risk has to be adopted into the interest rate of investment. For more details about the project risk acording to CAPM is given the next formula which is suggested by Thram et al. (2004, p. 27).

illustration not visible in this excerpt

According to Hull (2012, p. 78) systematic risk is a risk which is always based on return on the market and cannot be scrutinised separately. Despite of this it could be implemented in an investment related to the market.


Excerpt out of 71 pages


Risk Management in Investment Decisions. Real Options Approach
University of Portsmouth  (Business School)
Masterarbeit - Risk Management
Catalog Number
ISBN (eBook)
ISBN (Book)
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Risk Management, uncertainty, Real Option, option-pricing theory, Investment, real assets, NPV, DCF, investment calculations, CAPM, Options, flexibility, risk-adjusted, R&D, Decision-Tree Analysis, Contingent-Claims-Analysis, binomial lattice, random walk, replicating portfolio, arbitrage, Black-Sholes Model, Binomial Model, Monte Carlo Simulation, twin security trading, @Risk, Case Study, Planning of Project Cost, Planning of Project Revenue, Project Valuation, WACC
Quote paper
Asen Kolaksazov (Author), 2012, Risk Management in Investment Decisions. Real Options Approach, Munich, GRIN Verlag, https://www.grin.com/document/299087


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