An alternative or choice that becomes available with a business investment opportunity. Real options can include opportunities to expand and cease projects if certain conditions arise, amongst other options. They are referred to as "real" because they usually pertain to tangible assets such as capital equipment, rather than financial instruments. Taking into account real options can greatly affect the valuation of potential investments. Oftentimes, however, valuation methods, such as NPV, do not include the benefits that real options provide.
Note that this kind of option is not a derivative instrument, but an actual option (in the sense of "choice") that a business may gain by undertaking certain endeavors. For example, by investing in a particular project, a company may have the real option of expanding, downsizing or
abandoning other projects in the future. Other examples of real options may be opportunities for R&D, M&A and licensing.
Real Options Valuation (ROV) is revolutionizing corporate strategy and bridging the gap between finance and strategic planning. Just as an option gives its owner the right - but not the obligation - to take a particular course of action at some time in the future, flexibility embedded in capital investment projects and company strategies allows managers to take a staged approach to corporate strategy and react to changes in the business environment, so they can limit
downside losses while fully capitalizing on upside potential opportunities. Real Options - Some Examples
• Defer - Investing now eliminates the option to defer (learning) • Expand - An option to defer part of the scale of investment • Contract - The flexibility to reduce the rate of output • Abandon - Stop investing, and liquidate existing assets
• Staging - Substitute a series of small investments for one large • Switching - Re-deploy resources or change inputs
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Techniques for Reasoning Through Decision Trees 1. Focus on the most important decisions.
2. Reason forward to construct the tree.
3. Track certainties and uncertainties at each decision point. 4. Calculate backward to evaluate choices.
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Decision Tree Example – Assumptions
Consider an investment project where there is uncertainty about the state of the world. Suppose it can be either good or bad and it's as likely to be one as the other. The market research provides us the following data that:
• Demand may be high (30%), medium (50%), low (20%). • Cost of large restaurant is $750,000.
• Cost of small restaurant is $600,000.
• Entrepreneur will invest $400,000, outside investor provides the rest. • Investor requires 1% of equity for each $10,000 invested.
• If demand is high - PV large is $1,500,000, PV small is $800,000. • If demand is medium - PV large is $800,000, PV small is $800,000. • If demand is low - PV large is $300,000, PV small is $400,000.
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Accept/reject Decision to Invest in Restaurant Business
Evaluation of Accept/Reject Alternatives • Large-scale entry:
NPV conditional on high demand = $575,000 NPV conditional on intermediate demand = $120,000 NPV conditional on low demand = ($205,000) NPV = .3 x $575,000 + .5 x $120,000 – .2 x $205,000 = $191,500
2 0 1 2 - 1 3 • Small-scale entry:
NPV conditional on high demand = $240,000 NPV conditional on intermediate demand = $240,000 NPV conditional on low demand = ($ 80,000) NPV = .3 x $240,000 + .5 x $240,000 - .2 x $80,000 = $176,000
• Do not enter: NPV = $0
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Evaluation of Option to Delay
• Large-scale entry strategy: NPV = $191,500 • Delay until uncertainty is resolved:
– High demand
• Build large restaurant
• NPV conditional on high demand = $445,000 – Intermediate demand
• Build small restaurant
• NPV conditional on intermediate demand = $160,000 – Low demand
• Do not enter
• NPV conditional on low demand = $0 • NPV of delay strategy:
– = .3 x $445,000 + .5 x $160,000 + .2 x $0 – = $213,500
• Value of Option to Delay = $213,500 - 191,500 – = $22,000
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Restaurant Business Investment with an Option to Expand Initial Investment
Evaluation of Option to Expand
• Large-scale entry strategy: NPV = $191,500
• Delay until uncertainty is resolved: NPV = $213,500 • Build small, with Option to Expand:
– Conditional on High demand:
• NPV if Expand = $580,000 • NPV if Remain Small = $240,000 • Conclusion: Expand if demand is high
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– Conditional on Intermediate demand:
• NPV of Remaining Small = $240,000 – Conditional on Low demand:
• NPV of Remaining Small = ($80,000)
• NPV of Small-scale entry with Option to Expand – = .3 x $580,000 + .5 x $240,000 - .2 x $80,000 – = $278,000
• Value of Expansion Option = $86,500
• Incremental value over Delay Option = $64,500 – The Options are Mutually Exclusive
Evaluation of Option to Abandon
• Large-scale entry strategy: NPV = $191,500 • Large-scale entry with Abandonment option:
– Convert to office with $600,000 value
– NPV of converting for entrepreneur = ($10,000) – NPV with Abandonment Option:
• = .3 x $575,000 + .5 x $120,000 - .2 x $10,000 = $230,500 – Would pay up to $39,000 extra for location that is convertible • Small-scale entry with Expansion and Abandonment Options:
– Convert to office with $300,000 value
– NPV of converting for entrepreneur = ($160,000) – NPV with Abandonment Option:
• = .3 x $580,000 + .5 x $240,000 - .2 x $160,000 = $262,000 – Abandonment has negative value for the small restaurant
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– A result of discreteness of the analysis • Conclusion: Build small with Expansion Option
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Value-at-Risk
History of Value-at-RiskVaR was pioneered by major U.S. banks in the ’80s, as the derivative markets developed. The birth of derivatives represented a new challenge for risk management because traditional measures of exposure were clearly inadequate. For example, two derivative contracts with the same notional value could have very different risks. With VaR, banks had developed a general measure of economic loss that could equate risk across products and aggregate risk on a port- folio basis.
The value of a portfolio of financial assets is subject to many risks: credit risks, market risks, etc. Value at Risk, VaR, is a statistical estimate of the market risk of a portfolio. VaR attempts to answer the following question. Given a certain confidence level and a specified time horizon, what is the maximum potential loss of the portfolio?
Definition of VaR
The value at risk (VaR) indicates the maximum percentage value of our multiple trading systems portfolio that could be lost during a fixed period (e.g. one day) within a certain confidence level (e.g. 95%).
VaR is defined as the predicted worst-case loss at a specific confidence level (e.g., 95%) over a certain period of time (e.g., 1 day).
For example, every afternoon, J.P. Morgan takes a snapshot of its global trading positions to estimate its Daily-Earnings-at-Risk (DEaR), which is a VaR measure that Morgan defines as the 95% confidence worst-case loss over the next 24 hours due to adverse market movements. One the major advantage of VaR Method is that it works across different asset classes such as bonds and stocks. The elegance of the VaR solution is that it works on multiple levels, from the position-specific micro level to the portfolio-based macro level. VaR has become a common language for communication about aggregate risk taking, both within an organization and outside (e.g., with analysts, regulators, rating agencies, and shareholders).
Virtually all major financial institutions have adopted VaR as a cornerstone of day-to-day risk measurement. Now with the VaR method it is possible to measure the aggregated risk on a portfolio level. But there are some limitations of VaR model that is it can only be achieved under normal market condition. Three approaches for VaR calculation:
• Risk Metrics
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• Monte Carlo simulation Risk Metrics
The RiskMetrics variance model (also known as exponential smoother) was first established in 1989, when Sir Dennis Weather stone’s, the new chairman of J.P. Morgan, asked for a daily report measuring and explaining the risks of his firm. Nearly four years later in 1992, J.P. Morgan launched the RiskMetrics methodology to the marketplace, making the substantive research and analysis that satisfied Sir Dennis Weather stone’s request freely available to all market participants.
Risk metrics by definition is a set of financial models used by investors to determine portfolio risk.
Risk measurement process
Portfolio risk measurement can be broken down into steps. The first is modeling the market that drives changes in the portfolio's value. The market model must be sufficiently specified so that the portfolio can be revalued using information from the market model. The risk measurements are then extracted from the probability distribution of the changes in portfolio value. The change in value of the portfolio is typically referred to by portfolio managers as profit and loss, or P&L. Market models
RiskMetrics describes two models for modeling the risk factors that define financial markets. Historical Simulation
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HS involves using past data as a guide to what will happen in the future
Suppose we want to calculate VaR for a portfolio using 1-day horizon, a 99% confidence level, and 500 days of data. Collect data on the daily movements in the given market variables.Conduct 500 trials assuming as if todays prices will change at a past rate of change in each of the 500 days
0 This way forecasted value for tomorrow will be:
Where Vn is today’s value of the variable Vi is the variable value in past days
Vi-1 is the variable value one-day before the vi value
After that, calculate the value of portfolio based on the trial values of each variable and find the difference between the forecasted values and today’s value of the portfolio in all 500 trials. Find the given percentile of these differences, and that will be the VaR estimate.
The 1st percentile in 500 observations means the 5th worst loss in all 500 observations
In Excel, we do this by: =percentile (range, .01) if it is for 1st percentile. 1 − i i n v v v
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Monte Carlo simulation
Risk analysis is part of every decision we make. We are constantly faced with uncertainty, ambiguity, and variability. And even though we have unprecedented access to information, we can’t accurately predict the future. Monte Carlo simulation (also known as the Monte Carlo Method) lets you see all the possible outcomes of your decisions and assess the impact of risk, allowing for better decision making under uncertainty.
Monte Carlo simulation furnishes the decision-maker with a range of possible outcomes and the probabilities they will occur for any choice of action. It shows the extreme possibilities—the outcomes of going for out of business and for the most conservative decision—along with all possible consequences for middle-of-the-road decisions.
Monte Carlo simulation is a computerized mathematical technique that allows people to account for risk in quantitative analysis and decision making.
How Monte Carlo simulation works:
Monte Carlo simulation performs risk analysis by building models of possible results by substituting a range of values—a probability distribution—for any factor that has inherent uncertainty. It then calculates results over and over, each time using a different set of random values from the probability functions. Depending upon the number of uncertainties and the ranges specified for them, a Monte Carlo simulation could involve thousands or tens of
thousands of recalculations before it is complete. Monte Carlo simulation produces distributions of possible outcome values.
During a Monte Carlo simulation, values are sampled at random from the input probability distributions. Each set of samples is called iteration, and the resulting outcome from that sample is recorded. Monte Carlo simulation does this hundreds or thousands of times, and the result is a probability distribution of possible outcomes. In this way, Monte Carlo simulation provides a much more comprehensive view of what may happen. It tells you not only what could happen, but how likely it is to happen.
Advantages
Monte Carlo simulation provides a number of advantages over “single-point estimate” analysis:
• Probabilistic Results. Results show not only what could happen, but how likely each outcome is.
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• Graphical Results. Because of the data a Monte Carlo simulation generates, it’s easy to create graphs of different outcomes and their chances of occurrence. This is important for communicating findings to other stakeholders.
• Sensitivity Analysis. With just a few cases, deterministic analysis makes it difficult to see which variables impact the outcome the most. In Monte Carlo simulation, it’s easy to see which inputs had the biggest effect on bottom-line results.
• Scenario Analysis: In deterministic models, it’s very difficult to model different
combinations of values for different inputs to see the effects of truly different scenarios. Using Monte Carlo simulation, analysts can see exactly which inputs had which values together when certain outcomes occurred. This is very useful for pursuing further analysis.
Who uses Monte Carlo simulation?
Many companies use Monte Carlo simulation as an important tool for decision-making. Here are some examples.
General Motors, Procter and Gamble, and Eli Lilly use simulation to estimate both the average return and the riskiness of new products. At GM, this information is used by CEO Rick
Waggoner to determine the products that come to market.
GM uses simulation for activities such as forecasting net income for the corporation, predicting structural costs and purchasing costs, determining its susceptibility to different kinds of risk (such as interest rate changes and exchange rate fluctuations).
Lilly uses simulation to determine the optimal plant capacity that should be built for each drug. Wall Street firms use simulation to price complex financial derivatives and determine the Value at RISK (VAR) of their investment portfolios.
Procter and Gamble uses simulation to model and optimally hedge foreign exchange risk.
Sears uses simulation to determine how many units of each product line should be ordered from suppliers — for example, how many pairs of Dockers should be ordered this year.