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  • You only live once

    You only live once

    This entry is part 4 of 4 in the series The fallacies of scenario analysis

    You only live once, but if you do it right, once is enough.
    — Mae West

    Let’s say that you are considering new investment opportunities for your company and that the sales department has guesstimated that the market for one of your products will most likely grow by a little less than 5 % per year. You then observe that the product already has a substantial market and that this in fifteen years’ time nearly will be doubled:

    Building a new plant to accommodate this market growth will be a large investment so you find that more information about the probability distribution for the products future sales is needed. Your sales department then “estimates” the market yearly growth to have a mean close to zero and a lower quartile of minus 5 % and an upper quartile of plus 7 %.

    Even with no market growth the investment is a tempting one since the market already is substantial and there is always a probability of increased market shares.

    As quartiles are given, you rightly calculate that there will be a 25 % probability that the growth will be above 7 %, but also that there will be a 25 % probability that it can be below minus 5 %. At the face of it, and with you being not too risk averse, this looks as a gamble worth taking.

    Then you are informed that the distribution will be heavily left skewed – opening for considerable downside risk. In fact it turns out that it looks like this:

    A little alarmed you order the sales department to come up with a Monte Carlo simulation giving a better view of the future possible paths of the market development.

    The return with the graph below giving the paths for the first ten runs in the simulation with the blue line giving average value and the green and red the 90 % and 10 % limits of the one thousand simulated outcomes:

    The blue line is the yearly ensemble  averages ((A set of multiple predictions that is all valid at the same time. The term “ensemble” is often used in physics and physics-influenced literature. In probability theory literature the term probability space is more prevalent.

    An ensemble provides reliable information on forecast uncertainties (e.g., probabilities) from the spread (diversity) amongst ensemble members.

    Also see: Ensemble forecasting; a numerical prediction method that is used to attempt to generate a representative sample of the possible future states of dynamic systems. Ensemble forecasting is a form of Monte Carlo analysis: multiple numerical predictions are conducted using slightly different initial conditions that are all plausible given the past and current set of observations. Often used in weather forecasting.));  that is the time series of average of outcomes. The series shows a small decline in market size but not at an alarming rate. The sales department’s advice is to go for the investment and try to conquer market shares.

    You then note that the ensemble average implies that you are able jump from path to path and since each is a different realization of the future that will not be possible – you only live once!

    You again call the sales department asking them to calculate each paths average growth rate (over time) – using their geometric mean – and report the average of these averages to you. When you plot both the ensemble and the time averages you find quite a large difference between them:

    The time average shows a much larger market decline than the ensemble average.

    It can be shown that the ensemble average always will overestimate (Peters, 2010) the growth and thus can falsely lead to wrong conclusions about the market development.

    If we look at the distribution of path end values we find that the lower quartile is 64 and the upper quartile is 118 with a median of 89:

    It thus turns out that the process behind the market development is non-ergodic ((The term ergodic is used to describe dynamical systems which have the same behavior averaged over time as averaged over space.))  or non-stationary ((Stationarity is a necessary, but not sufficient, condition for ergodicity. )). In the ergodic case both the ensemble and time averages would have been equal and the problem above would not have appeared.

    The investment decision that at first glance looked a simple one is now more complicated and can (should) not be decided based on market development alone.

    Since uncertainty increases the further we look into the future, we should never assume that we have ergodic situations. The implication is that in valuation or M&A analysis we should never use an “ensemble average” in the calculations, but always do a full simulation following each time path!

    References

    Peters, O. (2010). Optimal leverage from non-ergodicity. Quantitative Finance, doi:10.1080/14697688.2010.513338

    Endnotes

  • The probability distribution of the bioethanol crush margin

    The probability distribution of the bioethanol crush margin

    This entry is part 1 of 2 in the series The Bio-ethanol crush margin

    A chain is no stronger than its weakest link.

    Introduction

    Producing bioethanol is a high risk endeavor with adverse price development and crumbling margins.

    In the following we will illustrate some of the risks the bioethanol producer is facing using corn  as feedstock. However, these risks will persist regardless of the feedstock and production process chosen. The elements in the discussion below can therefore be applied to any and all types of bioethanol production:

    1.    What average yield (kg ethanol per kg feedstock) can we expect?  And  what is the shape of the yield distribution?
    2.    What will the future price ratio of feedstock to ethanol be? And what volatility can we expect?

    The crush margin ((The relationship between prices in the cash market is commonly referred to as the Gross Production Margin.))  measures the difference between the sales proceeds of finished bioethanol and its feedstock ((It can also be considered as the productions throughput; the rate at which the system converts raw materials to money. Throughput is net sales less variable cost, generally the cost of the most important raw materials. (see: Throughput Accounting)).

    With current technology, one bushel of corn can be converted into approx. 2.75 gallons of corn and 17 pounds of DDG (distillers’ dried grains). The crush margin (or gross processing margin) is then:

    1. Crush margin = 0.0085 x DDG price + 2.8 x ethanol price – corn price

    Since from 65 % to 75 % of the variable cost in bioethanol production is cost of corn, the crush margin is an important metric especially since the margin in addition shall cover all other expenses like energy, electricity, interest, transportation, labor etc. and – in the long term the facility’s fixed costs.

    The following graph taken from the CME report: Trading the corn for ethanol crush, (CME, 2010) gives the margin development in 2009 and the first months of 2010:

    This graph gives a good picture of the uncertainties that faces the bioethanol producers, and can be a helpful tool when hedging purchases of corn and sale of the products ((The historical chart going back to APR 2005 is available at the CBOT web site)).

    The Crush Spread, Crush Profit Margin and Crush Ratio

    There are a number of other ways to formulate the crush risk (CME, July 11. 2011):

    The CBOT defines the “Crush Spread” as the Estimated Gross Margin per Bushel of Corn. It is calculated as follows:

    2. Crush Spread = (Ethanol price per gallon X 2.8) – Corn price per bushel, or as

    3. Crush Profit margin = Ethanol price – (Corn price/2.8).

    Understanding these relationships is invaluable in trading ethanol stocks ((We will return to this in a later post.)).

    By rearranging the crush spread equation, we can express the spread as its ratio to the product price (simplifying by keeping bi-products like DDG etc. out of the equation):

    4. Crush ratio = Crush spread/Ethanol price = y – p,

    Where: y = EtOH Yield (gal)/ bushel corn and p = Corn price/Ethanol price.

    We will in the following look at the stochastic nature of y and p and thus the uncertainty in forecasting the crush ratio.

    The crush spread and thus the crush ratio is calculated using data from the same period. They therefore give the result of an unhedged operation. Even if the production period is short – two to three days – it will be possible to hedge both the corn and ethanol prices. But to do that in a consistent and effective way we have to look into the inherent volatility in the operations.

    Ethanol yield

    The ethanol yield is usually set to 2.682 gal/bushel corn, assuming 15.5 % humidity. The yield is however a stochastic variable contributing to the uncertainty in the crush ratio forecasts. As only starch in corn can be converted to ethanol we need to know the content of extractable starch in a standard bushel of corn – corrected for normal loss and moisture.  In the following we will lean heavily on the article: “A Statistical Analysis of the Theoretical Yield of Ethanol from Corn Starch”, by Tad W. Patzek (Patzek, 2006) which fits our purpose perfectly. All relevant references can be found in the article.

    The aim of his article was to establish the mean extractable starch in hybrid corn and the mean highest possible yield of ethanol from starch. We however are also interested in the probability distributions for these variables – since no production company will ever experience the mean values (ensembles) and since the average return over time always will be less than the return using ensemble means ((We will return to this in a later post))  (Peters, 2010).

    The purpose of this exercise is after all to establish a model that can be used as support for decision making in regard to investment and hedging in the bioethanol industry over time.

    From (Patzek, 2006) we have that the extractable starch (%) can be described as approx. having a normal distribution with mean 66.18 % and standard deviation of 1.13:

    The nominal grain loss due to dirt etc. can also be described as approx. having a normal distribution with mean 3 % and a standard deviation of 0.7:

    The probability distribution for the theoretical ethanol yield (kg/kg corn) can then be found by Monte Carlo simulation ((See formula #3 in (Patzek, 2006))  as:

    – having an approx. normal distribution with mean 0.364 kg EtHO/kg of dry grain and standard deviation of 0.007. On average we will need 2.75 kg of clean dry grain to produce one kilo or 1.74 liter of ethanol ((With a specific density of 0.787 kg/l)).

    Since we now have a distribution for ethanol yield (y) as kilo of ethanol per kilo of corn we will in the following use price per kilo both for ethanol and corn, adjusting for the moisture (natural logarithm of moisture in %) in corn:

    We can also use this to find the EtHO yield starting with wet corn and using gal/bushel corn as unit (Patzek, 2006):

    giving as theoretical value a mean of 2.64 gal/wet bushel with a standard deviation of 0.05 – which is significantly lower than the “official” figure of 2.8 gal/wet bushel used in the CBOT calculations. More important to us however is the fact that we easily can get yields much lower than expected and thus a real risk of lower earnings than expected. Have in mind that to get a yield above 2.64 gallons of ethanol per bushel of corn all steps in the process must continuously be at or close to their maximum efficiency – which with high probability never will happen.

    Corn and ethanol prices

    Looking at the price developments since 2005 it is obvious that both the corn and ethanol prices have a large variability ($/kg and dry corn):

    The long term trends show a disturbing development with decreasing ethanol price, increasing corn prices  and thus an increasing price ratio:

    “Risk is like fire: If controlled, it will help you; if uncontrolled, it will rise up and destroy you.”

    Theodore Roosevelt

    The unhedged crush ratio

    Since the crush ratio on average is:

    Crush ratio = 0.364 – p, where:
    0.364 = Average EtOH Yield (kg EtHO/kg of dry grain) and
    p = Corn price/Ethanol price

    The price ratio (p) has to be less than 0.364 for the crush ratio in the outset to be positive. As of January 2011 the price ratios has overstepped that threshold and have for the first months of 2011 stayed above that.

    To get a picture of the risk an unhedged bioethanol producer faces only from normal variation in yield and forecasted variation in the price ratio we will make a simple forecast for April 2011 using the historic time series information on trend and seasonal factors:

    The forecasted probability distribution for the April price ratio is given in the frequency graph below:

    This represents the price risk the producer will face. We find that the mean value for the price ratio will be 0.323 with a standard deviation of 0.043. By using this and the distribution for ethanol yield we can by Monte Carlo simulation forecast the April distribution for the crush ratio:

    As we see, will negative values for the crush ratio be well inside the field of possible outcomes:

    The actual value of the average price ratio for April turned out to be 0.376 with a daily maximum of 0.384 and minimum of 0.363. This implies that the April crush ratio with 90 % probability would have been between -0.005 and -0.199, with only the income from DDGs to cover the deficit and all other costs.

    Hedging the crush ratio

    The distribution for the price ratio forecast above clearly points out the necessity of price ratio hedging (Johnson, 1960) and (Stein, 1961).
    The time series chart above shows both a negative trend development and seasonal variations in the price ratio. In the short run there is nothing much to do about the trend development, but in the longer run will probably other feedstock and better processes change the trend development (Shapouri et al., 2002).

    However, what immediately stand out are the possibilities to exploit the seasonal fluctuations in both markets:

    Ideally, raw material is purchased in the months seasonal factors are low and ethanol sold the months seasonal factor are high. In practice, this is not possible, restrictions on manufacturing; warehousing, market presence, liquidity, working capital and costs set limits to the producer’s degrees of freedom (Dalgran, 2009).

    Fortunately, there are a number of tools in both the physical and financial markets available to manage price risks; forwards and futures contracts, options, swaps, cash-forward, and index and basis contracts. All are available for the producers who understand financial hedging instruments and are willing to participate in this market. See: (Duffie, 1989), (Hull, 2003) and (Bjørk, 2009).

    The objective is to change the margin distributions shape (red) from having a large part of its left tail on the negative part of the margin axis to one resembling the green curve below where the negative part have been removed, but most of the upside (right tail) has been preserved, that is to: eliminate negative margins, reduce variability, maintain the upside potential and thus reduce the probability of operating at a net loss:

    Even if the ideal solution does not exist, large number of solutions through combinations of instruments can provide satisfactory results. In principle, it does not matter where these instruments exist, since both the commodity and financial markets are interconnected to each other. From a strategic standpoint, the purpose is to exploit fluctuations in the market to capture opportunities while mitigating unwanted risks (Mallory, et al., 2010).

    Strategic Risk Management

    To manage price risk in commodity markets is a complex topic. There are many strategic, economic and technical factors that must be understood before a hedging program can be implemented.

    Since all the hedging instruments have a cost and since only future outcomes ranges and not exact prices, can be forecasted in the individual markets, costs and effectiveness is uncertain.

    In addition, the degrees of desired protection have to be determined. Are we seeking to ensure only a positive margin, or a positive EBITDA, or a positive EBIT? With what probability and to what cost?

    A systematic risk management process is required to tailor an integrated risk management program for each individual bioethanol plant:

    The choice of instruments will define different strategies that will affect company liquidity and working capital and ultimately company value. Since the effect of each of these strategies will be of stochastic nature it will only be possible to distinguish between them using the concept of stochastic dominance. (selecting strategy)

    Models that can describe the business operations and underlying risk can be a starting point, to such an understanding. Linked to balance simulation they will provide invaluable support to decisions on the scope and timing of hedging programs.

    It is only when the various hedging strategies are simulated through the balance so that the effect on equity value can be considered that the best strategy with respect to costs and security level can be determined – and it is with this that S@R can help.

    References

    Bjørk, T.,(2009). Arbitrage Theory in Continuous Time. Oxford University Press, Oxford.

    CME Group., (2010).Trading the corn for ethanol crush,
    http://www.cmegroup.com/trading/agricultural/corn-for-ethanol-crush.html

    CME Group., (July 11. 2011). Ethanol Outlook Report, , http://cmegroup.barchart.com/ethanol/

    Dalgran, R.,A., (2009) Inventory and Transformation Hedging Effectiveness in Corn Crushing. Journal of Agricultural and Resource Economics 34 (1): 154-171.

    Duffie, D., (1989). Futures Markets. Prentice Hall, Englewood Cliffs, NJ.

    Hull, J. (2003). Options, Futures, and Other Derivatives (5th edn). Prentice Hall, Englewood Cliffs, N.J.

    Johnson, L., L., (1960). The Theory of Hedging and Speculation in Commodity Futures, Review of Economic Studies , XXVII, pp. 139-151.

    Mallory, M., L., Hayes, D., J., & Irwin, S., H. (2010). How Market Efficiency and the Theory of Storage Link Corn and Ethanol Markets. Center for Agricultural and Rural Development Iowa State University Working Paper 10-WP 517.

    Patzek, T., W., (2004). Sustainability of the Corn-Ethanol Biofuel Cycle, Department of Civil and Environmental Engineering, U.C. Berkeley, Berkeley, CA.

    Patzek, T., W., (2006). A Statistical Analysis of the Theoretical Yield of Ethanol from Corn Starch, Natural Resources Research, Vol. 15, No. 3.

    Peters, O. (2010). Optimal leverage from non-ergodicity. Quantitative Finance, doi:10.1080/14697688.2010.513338.

    Shapouri,H., Duffield,J.,A., & Wang, M., (2002). The Energy Balance of Corn Ethanol: An Update. U.S. Department of Agriculture, Office of the Chief Economist, Office of Energy Policy and New Uses. Agricultural Economic Report No. 814.

    Stein, J.L. (1961). The Simultaneous Determination of Spot and Futures Prices. American Economic Review, vol. 51, p.p. 1012-1025.

    Footnotes

  • Moddeling World 2011

    Moddeling World 2011

     

     

    S&R participated as a keynote speaker at the Modelling World conference held in London June 16. The theme was forecasting and decision making inn an uncertain world. The event was organized by Local Transport Today Ltd. and Modelling World 2011 © Local Transport Today and covered a broad range of issues in transport modeling (Conference programme as Pdf-file).

    The presentation can be found as a Pdf-file here.

     

     

  • The tool that would improve everybody’s toolkit

    The tool that would improve everybody’s toolkit

    Edge, which every year ((http://www.edge.org/questioncenter.html))   invites scientists, philosophers, writers, thinkers and artists to opine on a major question of the moment, asked this year: “What scientific concept would improve everybody’s cognitive toolkit?”

    The questions are designed to provoke fascinating, yet inspiring answers, and are typically open-ended, such as:  “What will change everything” (2008), “What are you optimistic about?” (2007), and “How is the internet changing the way you think?” (Last’s years question). Often these questions ((Since 1998))  are turned into paperback books.

    This year many of the 151 contributors pointed to Risk and Uncertainty in their answers. In the following we bring excerpt from some of the answers. We will however advice the interested reader to look up the complete answers:

    A Probability Distribution

    The notion of a probability distribution would, I think, be a most useful addition to the intellectual toolkit of most people.

    Most quantities of interest, most projections, most numerical assessments are not point estimates. Rather they are rough distributions — not always normal, sometimes bi-modal, sometimes exponential, sometimes something else.

    Related ideas of mean, median, and variance are also important, of course, but the simple notion of a distribution implicitly suggests these and weans people from the illusion that certainty and precise numerical answers are always attainable.

    JOHN ALLEN PAULOS, Professor of Mathematics, Temple University, Philadelphia.

    Randomness

    The First Law of Randomness: There is such a thing as randomness.
    The Second Law of Randomness: Some events are impossible to predict.
    The Third Law of Randomness: Random events behave predictably in aggregate even if they’re not predictable individually

    CHARLES SEIFE, Professor of Journalism, New York University; formerly journalist, Science magazine; Author, Proofiness: The Dark Arts of Mathematical Deception.

    The Uselessness of Certainty

    Every knowledge, even the most solid, carries a margin of uncertainty. (I am very sure about my own name … but what if I just hit my head and got momentarily confused?) Knowledge itself is probabilistic in nature, a notion emphasized by some currents of philosophical pragmatism. Better understanding of the meaning of probability, and especially realizing that we never have, nor need, ‘scientifically proven’ facts, but only a sufficiently high degree of probability, in order to take decisions and act, would improve everybody’ conceptual toolkit.

    CARLO ROVELLI, Physicist, University of Aix-Marseille, France; Author, The First Scientist: Anaximander and the Nature of Science.

    Uncertainty

    Until we can quantify the uncertainty in our statements and our predictions, we have little idea of their power or significance. So too in the public sphere. Public policy performed in the absence of understanding quantitative uncertainties, or even understanding the difficulty of obtaining reliable estimates of uncertainties usually means bad public policy.

    LAWRENCE KRAUSS, Physicist, Foundation Professor & Director, Origins Project, Arizona State University; Author, A Universe from Nothing; Quantum Man: Richard Feynman’s Life in Science.

    Risk Literacy

    Literacy — the ability to read and write — is the precondition for an informed citizenship in a participatory democracy. But knowing how to read and write is no longer enough. The breakneck speed of technological innovation has made risk literacy as indispensable in the 21st century as reading and writing were in the 20th century. Risk literacy is the ability to deal with uncertainties in an informed way.

    GERD GIGERENZER, Psychologist; Director of the Center for Adaptive Behavior and Cognition at the Max Planck Institute for Human Development in Berlin; Author, Gut Feelings.

    Living is fatal

    The ability to reason clearly in the face of uncertainty. If everybody could learn to deal better with the unknown, then it would improve not only their individual cognitive toolkit (to be placed in a slot right next to the ability to operate a remote control, perhaps), but the chances for humanity as a whole.

    SETH LLOYD, Quantum Mechanical Engineer, MIT; Author, Programming the Universe.

    Uncalculated Risk

    We humans are terrible at dealing with probability. We are not merely bad at it, but seem hardwired to be incompetent, in spite of the fact that we encounter innumerable circumstances every day which depend on accurate probabilistic calculations for our wellbeing. This incompetence is reflected in our language, in which the common words used to convey likelihood are “probably” and “usually” — vaguely implying a 50% to 100% chance. Going beyond crude expression requires awkwardly geeky phrasing, such as “with 70% certainty,” likely only to raise the eyebrow of a casual listener bemused by the unexpected precision. This blind spot in our collective consciousness — the inability to deal with probability — may seem insignificant, but it has dire practical consequences. We are afraid of the wrong things, and we are making bad decisions.

    GARRETT LISI, Independent Theoretical Physicist

    And there is more … much more at the Edge site

  • Plans based on average assumptions ……

    Plans based on average assumptions ……

    This entry is part 3 of 4 in the series The fallacies of scenario analysis

     

    The Flaw of Averages states that: Plans based on the assumption that average conditions will occur are usually wrong. (Savage, 2002)

    Many economists use what they believe to be most likely ((Most likely estimates are often made in-house based on experience and knowledge about their operations.)) or average values ((Forecasts for many types of variable can be bought from suppliers of ‘consensus forecasts’.))  (Timmermann, 2006) (Gavin & Pande, 2008) as input for the exogenous variables in their spreadsheet calculations.

    We know however that:

    1. the probability for any variable to have outcomes equal to any of these values is close to zero,
    1. and that the probability of having outcomes for all the (exogenous) variables in the spreadsheet model equal to their average is virtually zero.

    So why do they do it? They obviously lack the necessary tools to calculate with uncertainty!

    But if a small deviation from the most likely value is admissible, how often will the use of a single estimate like the most probable value be ‘correct’?

    We can try to answer that by looking at some probability distributions that may represent the ‘mechanism’ generating some of these variables.

    Let’s assume that we are entering into a market with a new product, we know of course the maximum upper and lower limit of our future possible market share, but not the actual number so we guess it to be the average value = 0,5. Since we have no prior knowledge we have to assume that the market share is uniformly distributed between zero and one:

    If we then plan sales and production for a market share between 0, 4 and 0, 5 – we would out of a hundred trials only have guessed the market share correctly 13 times. In fact we would have overestimated the market share 31 times and underestimated it 56 times.

    Let’s assume a production process where the acceptable deviation from some fixed measurement is 0,5 mm and where the actual deviation have a normal distribution with expected deviation equal to zero, but with a standard deviation of one:

    Using the average deviation to calculate the expected error rate will falsely lead to us to believe it to be zero, while it in fact in the long run will be 64 %.

    Let’s assume that we have a contract for drilling a tunnel, and that the cost will depend on the hardness of the rock to be drilled. The contract states that we will have to pay a minimum of $ 0.5M and a maximum of $ 2M, with the most likely cost being $ 1M. The contract and our imperfect knowledge of the geology make us assume the cost distribution to be triangular:

    Using the average ((The bin containing the average in the histogram.)) as an estimate for expected cost will give a correct answer in only 14 out of a 100 trials, with cost being lower in 45 and higher in 41.

    Now, let’s assume that we are performing deep sea drilling for oil and that we have a single estimate for the cost to be $ 500M. However we expect the cost deviation to be distributed as in the figure below, with a typical small negative cost deviation and on average a small positive deviation:

    So, for all practical purposes this is considered as a low economic risk operation. What they have failed to do is to look at the tails of the cost deviation distribution that turns out to be Cauchy distributed with long tails, including the possibility of catastrophic events:

    The event far out on the right tail might be considered a Black Swan (Taleb, 2007), but as we now know they happen from time to time.

    So even more important than the fact that using a single estimate will prove you wrong most of the times it will also obscure what you do not know – the risk of being wrong.

    Don’t worry about the average, worry about how large the variations are, how frequent they occur and why they exists. (Fung, 2010)

    Rather than “Give me a number for my report,” what every executive should be saying is “Give me a distribution for my simulation.”(Savage, 2002)

    References

    Gavin,W.,T. & Pande,G.(2008), FOMC Consensus Forecasts, Federal Reserve Bank of St. Louis Review, May/June 2008, 90(3, Part 1), pp. 149-63.

    Fung, K., (2010). Numbers Rule Your World. New York: McGraw-Hill.

    Savage, L., S.,(2002). The Flaw of Averages. Harvard Business Review, (November), 20-21.

    Savage, L., S., & Danziger, J. (2009). The Flaw of Averages. New York: Wiley.

    Taleb, N., (2007). The Black Swan. New York: Random House.

    Timmermann, A.,(2006).  An Evaluation of the World Economic Outlook Forecasts, IMF Working Paper WP/06/59, www.imf.org/external/pubs/ft/wp/2006/wp0659.pdf

    Endnotes

  • Planning under Uncertainty

    Planning under Uncertainty

    This entry is part 3 of 6 in the series Balance simulation

     

    ‘Would you tell me, please, which way I ought to go from here?’ (asked Alice)
    ‘That depends a good deal on where you want to get to,’ said the Cat.
    ‘I don’t much care where—‘said Alice.
    ‘Then it doesn’t matter which way you go,’ said the Cat.
    –    Lewis Carroll, Alice’s Adventures in Wonderland

    Let’s say that the board have sketched a future desired state (value of equity) of the company and that you are left to find if it is possible to get there and if so – the road to take. The first part implies to find out if the desired state belongs to a set of feasible future states to your company. If it does you will need a road map to get there, if it does not you will have to find out what additional means you will need to get there and if it is possible to acquire those.

    The current state (equity value of) your company is in itself uncertain since it depends on future sales, costs and profit – variable that usually are highly uncertain. The desired future state is even more so since you need to find strategies (roads) that can take you there and of those the one best suited to the situation. The ‘best strategies’ will be those that with highest probability and lowest costs will give you the desired state that is, that has the desired state or a better one as a very probable outcome:

    Each of the ‘best strategies’ will have many different combinations of values for the variables –that describe the company – that can give the desired state(s). Using Monte Carlo simulations this means that a few, some or many of the thousands of runs – or realizations of future states-will give equity value outcomes that fulfill the required state. What we need then is to find how each of these has come about – the transition – and select the most promising ones.

    The S@R balance simulation model has the ability to make intermediate stops when the desired state(s) has been reached giving the opportunity to take out complete reports describing the state(s) and how it was reached and by what path of transitional states.

    The flip side of this is that we can use the same model and the same assumptions to take out similar reports on how undesirable states were reached – and their path of transitional states. This set of reports will clearly describe the risks underlying the strategy and how and when they might occur.

    The dominant strategy will then be the one that has the desired state or a better one as a very probable outcome and that have at the same time the least probability of highly undesirable outcomes (the stochastic dominant strategy):

    Mulling over possible target- or scenario analysis; calculating backwards the value of each variable required to meet the target is a waste of time since both the environment is stochastic and a number of different paths (time-lines) can lead to the desired state:

    And even if you could do the calculations, what would the probabilities be?

    Carroll, L., (2010). Alice‘s Adventures in Wonderland -Original Version. City: Cosimo Classics.