IntroToRealOptions

Real Options Approach to Valuation : Real Options Approach to Valuation Eduardo S. Schwartz Anderson Graduate School of Management at UCLA


What are Real Options? : What are Real Options? The Real Options approach is an extension of financial options theory to options on real (non financial) assets Options are contingent decisions Give the opportunity to make a decision after you see how events unfold Payoff is not linear Real Option valuations are aligned with financial market valuations Use financial market input and concepts


Examples of Real Options : Examples of Real Options Waiting to invest: Option to postpone investment: Project may have a positive NPV now, but it might not be optimal to exercise the option to invest now, but wait until we have more information in the future (valuation of mines). Tradeoff between the increase in revenues from immediate investment and the losses avoided by waiting to resolve uncertainty


Examples of Real Options : Examples of Real Options Growth options: Option to expand a project Initial investment leads to future opportunities (e.g., investment in IT infrastructure) Invest in a negative NPV project which gives the option to develop a new project


Examples of Real Options : Exit Options: Option to abandon a project Projects are analyzed with a fixed life, but we always have the option to abandon it if we are loosing money. Abandon a project whose expected development cost is substantially higher than the initial estimates Examples of Real Options


Examples of Real Options : Examples of Real Options Mothballing Option: Option to temporarily suspend production Close facility when unit prices of output go down and reopen when prices come up again taking into account closing and opening costs (mines)


Examples of Real Options : Examples of Real Options Flexibility options Option to switch production between two small plants (versus economies of scale of a large plant) Option to switch inputs (natural gas or fuel oil) to a power plant (versus a more efficient single input plant)


Problems with Traditional Tools : Problems with Traditional Tools Require forecasts A single expected value of future cash flows is generally used Difficulty for finding an appropriate discount rate when options (e.g., exit option) are present Future decisions are fixed at the outset no flexibility for taking decisions during the course of the investment project


Using Options : Using Options Uncertainty and the firm’s ability to respond to it are the source of value of an option When not to use options: When there are no options at all When there is little uncertainty When consequences of uncertainty can be ignored Most projects are subject to options valuation


Fundamental Result in Finance : Fundamental Result in Finance It can be shown that the absence of arbitrage opportunities in the economy imply the existence of a probability distribution such that securities are priced at their discounted expected cash flows under this risk neutral or risk adjusted probabilities, where the discount rate is the risk free rate. Adjustment for risk is in probability distribution of cash flows instead of the discount rate (Certainty Equivalent Approach).


Risk Neutral Probabilities : Risk Neutral Probabilities If markets are complete (all risks can be hedged) these probabilities are unique. If markets are not complete they are not necessarily unique (any of them will determine the same market value). Futures prices, when they exist, are the expected future spot prices under this risk neutral distribution. This applies when the interest rate is also uncertain.


Real Options Valuation : Real Options Valuation Risk neutral distribution is known BS world (gold mine?) Risk neutral distribution can be obtained for futures prices or other traded assets Copper mine, oil deposits (Interest rate derivatives) Need an equilibrium model (CAPM) to obtain risk neutral distribution Internet companies R&D projects


RO Approach: Solution Methods : RO Approach: Solution Methods Dynamic Programming approach lays out possible future outcomes and folds back the value of the optimal future strategy binomial method widely used of pricing simple options good for pricing American type options not so good when there are many state variables or there are path dependencies


RO Approach: Solution Methods : RO Approach: Solution Methods Partial differential equation (PDE) has closed form solution in very few cases BS equation for European calls generally solved by numerical methods very flexible good for American options for path dependencies need to add variables not good for problems with more than three factors technically more sophisticated


RO Approach: Solution Methods : RO Approach: Solution Methods Simulation approach averages the value of the optimal strategy at the decision date for thousands of possible outcomes very powerful approach easily applied to multi-factor models directly applicable to path dependent problems can be used with general stochastic processes intuitive, transparent, flexible and easily implemented ideally suited for parallel computing


Slide16 : Simulation Approach But it is forward looking, whereas optimal exercise of American options has features of dynamic programming Valuing American Options by Simulation: A simple least-squares approach (Longstaff and Schwartz, RFS 2001) key idea is that the conditional expected value of continuation can be estimated from the cross-sectional information from the simulation by least squares comparing the immediate exercise value with the conditional expected value of continuation gives a complete specification of optimal exercise strategy at each exercise date along each path


My Research on Real Options Valuation : My Research on Real Options Valuation Mines and Oil Deposits Forestry Resources Stochastic Behavior of Commodity Prices Internet Companies Information Technology Research and Development


Conclusion : Conclusion For many projects, flexibility can be an important component of value The option pricing framework gives us a powerful tool to analyze those flexibilities The real options approach to valuation is starting to be applied in practice The approach is being extended to take into account competitive interactions (impact of competition on exercise strategies)