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February 2008 – Strategy @ Risk

Month: February 2008

  • Risk and Monte Carlo simulation

    Risk and Monte Carlo simulation

    This entry is part 1 of 6 in the series Monte Carlo Simulation

     

    Risk, when does it occur? Whenever the outcome of a situation is not perfectly certain you have uncertainty or risk. Investment decisions taken under these circumstances involve a probability for an outcome that will differ from your estimated target. Decisions taken under uncertainty are a reality and a constraint manager’s face. In order to reduce the risk (probability of gain/loss) you have basically two ways of doing it, reduce the exposure or try to reduce the uncertainty by gathering more information.

    Risk – randomness with knowable probabilities.

    Uncertainty – randomness with unknowable probabilities.

    The problem with information is very often the lack of it due to cost and time factors. A major point in this context is that uncertainty can be reduced but risk can be calculated.

    We will illustrate this by describing a typical investment decision and look into the decisions and how they can be enhanced by taking advantage of calculating the risk by using Monte Carlo Simulation. This is a method especially developed to handle situations with uncertainty and to calculate the risk involved. The logic is fairly simple and the applications are numerous.

    Most business concepts involve various proportions of income, costs and investments. We will in the following use the philosophy that every decisions shall be taken in order to maximize shareholder value, corporate competitiveness and customer satisfaction.

    We have here split the decision process into various steps in order illustrate actually how easy it is to do it. By clicking on each theme you will see how we have given a flavor on how the problem can be solved.

  • Risk, price and value

    Risk, price and value

    This entry is part 3 of 4 in the series A short presentation of S@R

     

    Having arrived at the probability distribution for the value of equity (see full story) we are able to calculate expected gain, loss and their probability when investing in a company where the capitalized value (price) is known. (see “The Probability of Gain and Loss”)

    In the figure below we have illustrated the investment and speculative area. The investment area comprice the part of the cumulative probability distribution below 50%.

     

    investment_figure.jpg

    The speculative area is the area above 50%. The expected value is given at the 50% probability point (stapled line). The literature advices, and successful investors insists, on having a safety margin (discount) of at least 20% between expected value (intrinsic value) and the market price, as shown by the yellow area in the figure below. Graham and Dodd in Security Analysis introduced the concept of a margin of safety in 1934.

    In a stochastic framework as ours it is better to set the safety margin at one of the percentiles or quartiles giving directly the value of the safety margin. A fixed percentage safety margin will always give a different probability for gain (loss), depending on the shape of the cumulative probability distribution.

    An investor having a portfolio of stocks should thus use percentiles as a margin – having the same probability for gain (loss) throughout the portfolio. In the case below a 20% safety margin coincide with the first quartile, – giving a 25% probability for loss and 75% probability for gain. The expected value of the company is 1.452 the first quartile is 1.160 giving an exepcted gain of 292 or more with 75% probability (dotted lines).

    We know that the total risk of any individual asset is the sum of the systematic and unsystematic risk. When computing the figure above we have used the company’s appropriate beta to account for the systematic risk (in calculating WACC). The unsystematic risk is given by the variance in the figure above.

    In a well-diversified portfolio the expected value of the unsystematic return is assumed to be zero. When investing in a single asset we should be looking for assets with a high unsystematic return. In our context companies with a capitalized value below the percentile set as limit of the safety margin.

    References

    1. Security Analysis: The Classic 1934 Edition by Benjamin Graham, David L. Dodd. October 1, 1996, McGraw-Hill Professional Publishing; ISBN: 0070244960
    2. and an interesting webiste The Graham-Buffett Teaching Endowment
  • Real options

    Real options

    In real life both for investment decisions and in valuation of companies there are managerial flexibility in the sense that at future points of time there is flexibility in choosing among alternatives.

    When investing, the simplest example is the choice between to invest after a feasibility study or walk away. In valuation the choice can be at a future point of time to continue operation or disinvest.

    These alternatives are real options available for the decision maker. Recognizing these real options will usually increase (reduce loss) the value of the investment or the company under valuation.

    It is well known that most standard valuation techniques of risk-adjusted discounted cash flow (DCF) analysis fails to capture all sources of value associated with this type of investment, in that it assumes that the decision to invest is irreversible and inflexible, i.e., the investment cash flows are committed and fixed for the life of the project.

    A main contribution of real options analysis is to incorporate managerial flexibility inherent in the project in its valuation. Added flexibility value, overlooked in DCF analysis, comes from managerial decisions that can take advantage of price movements: operating flexibility and investment timing flexibility.

    Strategy @ Risk has the ability to incorporate a client’s specific decision alternative in the simulation model. Thus combining Monte Carlo simulation with decision tree analysis. The four-step process of the real option decision analysis is shown below.

    roaprocess

    Production Plant Case

    The board faces the following situation: The company has a choice between building a plant with production capacity of 150 000 metric tons at a most likely cost of $450 mill. or a smaller plant with a capacity of 85 000 metric tons at a most likely cost of $300 mill..

    The demand for the product is over 100 000 metric tons and rising. The decision between a small and large plant will be taken in year 1 and full production starts in year 2.

    If the decision has been to build the smaller plant (at a higher cost per unit produced) the capacity can be increased by 65 000 metric tons at most likely cost of $275 mill. (Normal distributed with variance of ±25%). The decision to increase capacity will be taken in year 2 if the demand exceeds 110 000 metric tons. It is assumed that the demand is normally distributed with a most likely demand of 100 000 metric tons, and demand varies ±20% (upper and lower 5% limit). The demand later periods is assumed to have an increasing variance and a 30% autocorrelation

    In year 3 and 4 it is considered that there is a 40% chance that if sales has been good (over 110 000 metric tons) a competitor will have entered the market reducing sales by 30 000 metric tons. If the demand falls below 70 000 metric tons the company will disinvest.

    The decisions will be made on the value of the discounted cash flows (20% discount rate).
    The above problem can be presented as a decision tree.

    real-options-web

    The boxes represent the “decision point”. The circles represent chance events. The chance events may be continuous, as is the case with demand forecasts, or discrete, as is the case of a competitor entering the market or not.

    Net Present Value of the Alternatives

    The analysis using both the decision tree and Monte Carlo simulation gives us the net present value of the different alternatives. As shown in the figures to the right, the best alternative is to build a large plant immediately giving a net present value of $679 mill.
    A small plant will give a lower net present value (NPV $626 mill.) even if we increase the capacity at a later stage (NPV $637 mill.).

    plant-alternatives

    In this case it will never be profitable to disinvest at any point of time. This will always give a lower value.In some cases it is difficult to distinguish the best strategy from its alternatives. We will in a later post come back to selection strategies using stochastic dominance.