Real Options Tutorial. Gordon Sick Haskayne School of Business University of Calgary and Mark Cassano, PhD, Yale

Transcription

1 Real Options Tutorial Gordon Sick Haskayne School of Business University of Calgary and Mark Cassano, PhD, Yale 1

2 Real Options as a Normative Science Normative disciplines describe how agents should do things. Positive disciplines describe how we would expect to observe people, economic interactions, markets. 2

3 Normative We generally teach normative science to business-school students. We teach them to manage firms, portfolios, risk. 3

4 Positive We can take normative models of preference and get positive models. Asset pricing theory, microstructure, behavioural finance Positive models are often empirically testable. 4

5 Finance journals generally prefer positive models. Working on what is right for your students is hazardous to your publishing career. 5

6 Positive models are built on normative models. CAPM is built on Markowitz risk-return assessment. Consumption CAPM So, we will start with the normative models 6

7 Real Options Real Assets Risk Leverage Flexibility 7

8 Financial options are valued as if they are redundant assets in a payoff-replication and arbitrage approach. The absence of arbitrage gives a M-M result As a first approximation, financial options do not create or destroy value. Hedging with financial options neither creates nor destroys value 8

9 Modigliani Miller M-M say dividends are irrelevant because any corporate change in payout policy can be replicated or undone by investor transactions in financial markets homemade dividends from selling shares dividend reinvestment plan buying shares Financial market transactions are efficient 9

10 Capital structure policy can be undone or replicated by financial market transactions Investors borrow to replicate leverage Investors buy bonds and shares to unlever Financial markets are efficient, so the transaction neither creates nor destroys value 10

11 Real Assets Shareholders can t replicate or undo the firm s capital budgeting decisions These involve proprietary assets Real asset markets can be inefficient and incomplete Bad capital budgeting can destroy enormous corporate value 11

12 Risk Arrival of information over time allows decisions to be made Most real options are American They can be exercised early Decisions depend on information 12

13 Leverage Real options involve a claim on the value arising from a future decision Development option involves a future capital expenditure This gives significant operating leverage 13

14 Operating leverage ratio increases as underlying asset value falls and increases as it rises, for a development option This makes the cost of capital of a levered asset a random number If the underlying asset or cash flow follows GBM, the option doesn t 14

15 This means that we have to use certaintyequivalent techniques (risk-neutral probabilities) to value options This problem arises from the leverage, not just the optionality Indeed, you can t discount flows to equity at cost of equity & get same answers as discounting unlevered (EBIT) flows at weighted average cost of capital 15

16 Option beta is the underlying beta times the elasticity of the option price with respect to the underlying, so it is a random number. Elasticity equals leverage ratio times hedge ratio. 16

17 Flexibility Real options are about decision making Use the arriving information to make decisions Works only if there is flexibility Beware of those who would use Black- Scholes european formulas to value real options with early development decisions 17

18 Risk Management Flexible decisions adapt to the arrival of information. Allows upside potential to flow to the firm. It mitigates downside risk. Unlike the popular financial risk management tools, this adds corporate value. 18

19 Risk-neutral Probability If the underlying asset is traded and has an observable dividend yield, then is the risk-neutral growth rate of the underlying asset. For example, in a lattice model the riskneutral probability is 19

20 Unobservable Dividend If we can t observe dividends on the underlying, but we can model the futures price for delivery at the time step in the future, then we can replace 20

21 Risk-Neutral Growth We can use the CAPM to get a risk-neutral growth rate. 21

22 Diffusion and PDE 22

23 Modeling Growth Allows a variety of models of growth For example, multi-factor mean reversion allows high-frequency and low-frequency shocks to deviate from long run mean Long run mean can have a trend and follow GBM 23

24 Estimate this with a Kalman filter model on the corresponding term structure of futures prices. It is log-gaussian. Cortazar, G. and Naranjo, L. (2006). An n-factor gaussian model of oil futures prices. Journal of Futures Markets, 26(3):

25 Futures prices are log-linear in the state variables : 25

26 Kalman Filter Estimation 1. Start with initial parameter estimates. a) Start with initial shock and long-run mean estimate for starting date b) This gives forward price estimate for next date. The actual forward price differs by a forecast error. 26

27 c. The next-period state variable estimates are linear in previous state variables and previous state variable estimates error learning model d. Iterate forward to get time series of estimated forward prices, state variables and actual forward prices 27

28 2. After this run through the time series, form a likelihood function from the measurement errors between forecast and actual futures prices, as well as the update shocks of the state variables. 3. Revise the parameter estimates (and initial state variable) to maximize the likelihood function. Likelihood function is not too sensitive to initial estimates 28

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31 The Curse of Dimensionality The multi-factor futures model has a highdimensional PDE to solve for real option Similar problems if we model price and quantity or prices of inputs and prices of outputs Try Least Squares Monte Carlo (LSMC) 31

32 Least Squares Monte Carlo started with Brodie and Glaserman and was applied by Longstaff and Schwartz to real options. A discussion appears in Sick-Gamba References Broadie, M. and Glasserman, P. (1997). Pricing american-style securities using simulation. Journal of Economic Dynamics and Control, 21(8-9): Longstaff, F. A. and Schwartz, E. S. (2001). Valuing american options by simulation: a simple least-squares approach. The Review of Financial Studies, 14(1): Sick, G. and Gamba, A. (Forthcoming). Some important issues involving real options: An overview. Multinational Finance Journal. Accepted April 18, 2007, Multinational Finance Journal Issue on Real Options. 32

33 LSMC Intuition The common lattice approach estimates the next-period continuation (unexercised) value of the real option from the value in up- and down-states and risk-neutral probability. It forms an estimate of next period continuation value, conditional on the current-period information. 33

34 Thus, we can replace the conditional expectation on the lattice by a conditional expectation from a leastsquares projection. Run the MC simulation to get all possible paths that go through the current state and time, evaluating all possible values. Project or regress these future values on information about the current state and time, including polynomials of these variables. 34

35 Save the coefficients for the projection at each date and state of the world (multidimensional) Now, use these to form conditional expected values to decide whether or not to develop (exercise) or continue to keep the option alive. This gives a set of decisions for each date and state of nature. 35

36 Given the set of decisions, run through the simulation again to estimate the true value the development policy. 36

37 Least-squares Monte Carlo is just an algorithm to perform this computation. The objective is to be computationally efficient with the multiple runs through the simulation data. But, care must be take that the expectations are only based on prior state variables and not future state variables. 37

38 Positive Real Options Models Do managers actually do what we suggest they do? Do your children do what you suggest they do? Do your students do what you suggest they do? Thought I d ask! 38

39 Managerial Incentives Unfortunately, managers usually have poor incentives to maximize real options value. Management incentive compensation is based on Measurable Performance Indicators (MPIs). An undeveloped real option is not measurable. 39

40 Activity-based MPIs Thus, we would expect managers to exercise their real options too early. Consider the classic resource case problem. 40

41 Petroleum Development The oil price shock of 1974 took fields that were profitable with $1.50 oil and gave them $6 oil. The oil price shock of 1979 took fields that were profitable at $ $6.00 and gave them $15 oil. The NPV models said: Develop 41

42 Early 1980s Oil Price Forecasts The standard headline forecast was a rise from $15 in 1980 to $100 in 2000, a 10% per year gain. Don t worry about the forecast error If there was no risk, oil company should leave oil in ground and defer development cost. 42

43 Introduce Risk Now, add price risk to this scenario. The oil producer initially says that it is good to resolve price risk early and develop in But, real options models say to delay and learn whether the oil price rises or not. Bad to develop if the price doesn t rise! 43

44 What Happened? The early 1980s saw a oil development boom. Fueled by the free cash flow that the oil companies had from windfall profits. In the mid-80s, oil prices collapsed. They stayed under $20 for the most part until

45 The oil companies lost their real options discipline, if they ever had it. Getting a consulting job telling oil companies about real options was almost impossible. The oil companies wanted to bury their mistakes. 45

46 Sometimes government policy actually helped them make the right decisions, but they complained. Gas pipelines from the Arctic to the lower 48 states were fortuitously held up by native land claims and environmental concerns. Gas prices collapsed even without the supply. 46

47 Are Assets Priced as if they Include Real Options? There is an empirical literature in petroleum markets. It provides modest support for the price premia predicted by real option values, compared to DCF values. References Paddock, J. L., Siegel, D. R., and Smith, J. L. (1988). Option valuation of claims on real assets: The case of offshore petroleum leases. The Quarterly Journal of Economics, 103(3):

48 Real Estate Markets Capozza and Schwann found a weak positive relationship between real estate value and volatility, but did not separate systematic from unsystematic risk. Quigg found evidence of option-development-premia in real estate values. References Capozza, D. R. and Schwann, G. M. (1989). The asset approach to pricing urban land: Empirical evidence. Journal of the American Real Estate & Urban Economics Association, 17(2): Quigg, L. (1993). Empirical testing of real option-pricing models. Journal of Finance, 2(48):

49 Empirical Leverage Effects in Real Options Recall that the presence of a real option provides operating leverage. This makes the beta of the firm owning the option vary as the underlying asset value varies. 49

50 Thus, we should expect to see empirical pricing anomalies for firms richly endowed with real options relative to firms not so endowed. If the study treats the beta of a firm as being constant, other variables can proxy for the changing beta and appear to be priced. Size, book to market and debt ratio! 50

51 This can explain Fama-French CAPM anomalies References Aguerrevere, F. (2005). Real options, product market competition, and asset returns. Real Options Conference Berk, J. B., Green, R. C., and Naik, V. (1999). Optimal investment, growth options, and security returns. Journal of Finance, 54(5): Berk, J. B., Green, R. C., and Naik, V. (2004). Valuation and return dynamics of new ventures. Rev. Financ. Stud., 17(1):1 35. Carlson, M., Fisher, A., and Giammarino, R. (2004). Corporate investment and asset price dynamics: Implications for the cross-section of returns. Journal of Finance, 59(6):