Real Option Analysis of a Technology Portfolio

Transcription

1 Real Option Analysis of a Technology Portfolio Petri Hilli Maarit Kallio Markku Kallio Helsinki School of Economics The Finnish Forest Research Institute Real Option Analysis of a Technology Portfolio p.1

2 Outline ➀ problem definition production technology uncertainty ➁ valuation methods stochastic optimization ➂ numerical results Real Option Analysis of a Technology Portfolio p.2

3 Valuation problem A multi-product forest industry firm is considering an investment in new production capacity. The problem is to find the maximum price the firm is willing to pay for the new capacity. Real Option Analysis of a Technology Portfolio p.3

4 Technology data Techno- Mill unit Inputs (per t,m ) Fixed logy Capacity Cost Spruce Pine Log Other Cost mill.t,m /a mill.euro m m m euro euro/t,m Pulp News News News SC SC LWC LWC LWC Fine.U Fine.C Kraft Flut Sawn Real Option Analysis 21of a Technology 30Portfolio p.4 /a

5 Industry inputs spruce pulpwood pine pulpwood saw logs other (assumed deterministic) energy labor recycled fiber chemicals etc. Real Option Analysis of a Technology Portfolio p.5

6 Input prices Spruce Pine Log Jan-98 Jul-98 Jan-99 Jul-99 Jan-00 Jul-00 Real Option Analysis of a Technology Portfolio p.6 Jul-97 Jan-97 Jul-96 Jan-96 Jul-95 Jan-95 Jul-94 Jan-94 Euro / m3 Jan-89 Jul-89 Jan-90 Jul-90 Jan-91 Jul-91 Jan-92 Jul-92 Jan-93 Jul-93

7 Industry outputs bleached softwood pulp (Pulp) newsprint (News) uncoated magazine paper (SC) coated magazine paper (LWC) uncoated fine paper (Fine.U) coated fine paper (Fine.C) kraftliner (Kraft) fluting (Flut) sawn wood (Sawn) Real Option Analysis of a Technology Portfolio p.7

8 Jan-98 Jul-98 Jan-99 Jul-99 Jan-00 Jul-00 Jul-97 Jan-97 Jul-96 Jan-96 Jul-95 Jan-95 Output prices Euro / m Pulp News SC LWC Fine.U Fine.C Kraft Flut Sawn Real Option Analysis of a Technology Portfolio p.8 Jan-89 Jul-89 Jan-90 Jul-90 Jan-91 Jul-91 Jan-92 Jul-92 Jan-93 Jul-93 Jan-94 Jul-94

9 Valuation methods net present value (NPV) doesn t take into account uncertainty explicitly arbitrage pricing single-valued price requires perfect and complete markets valuation via stochastic programming takes into account uncertainty and yields single-valued price in imperfect and incomplete markets Real Option Analysis of a Technology Portfolio p.9

10 Stochastic programming Randomness poses a serious challenge for solving many optimization problems. The solutions obtained are optimal for specific problem but may not be optimal for the situation that actually occurs. Stochastic programming is concerned with decision making in the presence of uncertainty. Real Option Analysis of a Technology Portfolio p.10

11 Stochastic programming In stochastic programming, the distribution of the stochastic factors is approximated in the form of a scenario tree. Scenario tree approach makes possible to adjust activities according to market conditions take into account of nonanticipativity of future graphical representation. Real Option Analysis of a Technology Portfolio p.11

12 Scenario tree time Scenario tree, representing = 6 different market scenarios during the next two time periods ( corresponding probabilities ( ). ) and Real Option Analysis of a Technology Portfolio p.12

13 Scenario tree, In decision node 1 (the present day) we make a decision knowing that we will can adjust our decision next stage, depending on which node (2,3,4) we will end up and market conditions and market expectations in that node. Real Option Analysis of a Technology Portfolio p.13

14 Scenario tree, In decision node 2 we observe new market conditions and make new decisions based on decisions we have made so far (in node 1) and knowing that we can adjust our decision at next stage, depending on which node we will end up (5,6) 3 we observe new market conditions and make new decisions based on decisions we have made so far (in node 1) and knowing that we can adjust our decision at next stage, depending on which node we will end up (7,8) etc. for all nodes occurring time period. Real Option Analysis of a Technology Portfolio p.14

15 Scenario tree, In decision node 5 we observe new market conditions and make new decisions based on decisions we have made so far (in nodes 1 and 2) 6 we observe new market conditions and make new decisions based on decisions we have made so far (in nodes 1 and 2) 7 we observe new market conditions and make new decisions based on decisions we have made so far (in nodes 1 and 3) 8 we observe new market conditions and make new decisions based on decisions we have made so far (in nodes 1 and 3) etc. for all nodes occurring time period. Real Option Analysis of a Technology Portfolio p.15

16 Scenario tree Future prospects, i.e. scenario realizations and probabilities, can be based, for example, on quantitative methods subjective views both quantitative methods and subjective views. We assume that input and output prices will behave like in the past and estimate VEqM-model a from history data above. a Engle & Granger, Cointegration and Error-Correction: Representation, Estimation and Testing. Econometrica 55 pp Real Option Analysis of a Technology Portfolio p.16

17 0,- / % " ,- / % 6 * > Time series model The montly price development is described with a VEqC model: & * %. '&)( '&)( "! "$# % where 5 :8 78 6! 3 % is a vector of intercepts, matrices define how the prices depend on preceding prices movements in short run, long run equilibrium prices, = < ; : 8( 78 %. & ( defines responds to deviations from the long-run equilibrium and is a vector of residuals with a multivariate normal distribution of zero mean and covariance matrix. :8 78 Real Option Analysis of a Technology Portfolio p.17

18 Example: Monte Carlo simulated prices for pulp and news Pulp 400 News Euro / m Jan-89 Jan-90 Jan-91 Jan-92 Jan-93 Jan-94 Jan-95 Jan-96 Jan-97 Jan-98 Jan-99 Jan-00 Jan-01 Jan-02 Jan-03 Jan-04 Jan-05 Jan-06 Jan-07 Jan-08 Jan-09 Jan-10 Jan-11 Jan-12 Jan-13 Jan-14 Jan-15 Jan-16 Jan-17 Jan-18 Jan-19 Jan-20 Jan-21 Jan-22 Real Option Analysis of a Technology Portfolio p.18

19 Example: Monte Carlo simulated prices for pulp, sc and lwc Pulp 500 SC LWC Euro / m Jan-89 Jan-90 Jan-91 Jan-92 Jan-93 Jan-94 Jan-95 Jan-96 Jan-97 Jan-98 Jan-99 Jan-00 Jan-01 Jan-02 Jan-03 Jan-04 Jan-05 Jan-06 Jan-07 Jan-08 Jan-09 Jan-10 Jan-11 Jan-12 Jan-13 Jan-14 Jan-15 Jan-16 Jan-17 Jan-18 Jan-19 Jan-20 Jan-21 Jan-22 Real Option Analysis of a Technology Portfolio p.19

20 Example: Monte Carlo simulated prices for pulp, fine.u and fine.c Pulp 600 Fine.U Fine.C Euro / m Jan-89 Jan-90 Jan-91 Jan-92 Jan-93 Jan-94 Jan-95 Jan-96 Jan-97 Jan-98 Jan-99 Jan-00 Jan-01 Jan-02 Jan-03 Jan-04 Jan-05 Jan-06 Jan-07 Jan-08 Jan-09 Jan-10 Jan-11 Jan-12 Jan-13 Jan-14 Jan-15 Jan-16 Jan-17 Jan-18 Jan-19 Jan-20 Jan-21 Jan-22 Real Option Analysis of a Technology Portfolio p.20

21 Example: Monte Carlo simulated prices for pulp, kraft and flut Pulp 400 Kraft Flut Euro / m Jan-89 Jan-90 Jan-91 Jan-92 Jan-93 Jan-94 Jan-95 Jan-96 Jan-97 Jan-98 Jan-99 Jan-00 Jan-01 Jan-02 Jan-03 Jan-04 Jan-05 Jan-06 Jan-07 Jan-08 Jan-09 Jan-10 Jan-11 Jan-12 Jan-13 Jan-14 Jan-15 Jan-16 Jan-17 Jan-18 Jan-19 Jan-20 Jan-21 Jan-22 Real Option Analysis of a Technology Portfolio p.21

22 Example: Monte Carlo simulated prices for pulp and sawn Pulp 400 Sawn Euro / m Jan-89 Jan-90 Jan-91 Jan-92 Jan-93 Jan-94 Jan-95 Jan-96 Jan-97 Jan-98 Jan-99 Jan-00 Jan-01 Jan-02 Jan-03 Jan-04 Jan-05 Jan-06 Jan-07 Jan-08 Jan-09 Jan-10 Jan-11 Jan-12 Jan-13 Jan-14 Jan-15 Jan-16 Jan-17 Jan-18 Jan-19 Jan-20 Jan-21 Real Option Analysis of a Technology Portfolio p.22

23 Valuation problem no investment maximize wealth with current capacity investment maximize wealth with current and new capacity bought at price The problem is to find price equally attractive at the moment. that makes both choices Real Option Analysis of a Technology Portfolio p.23

24 Mathematical formulation Assuming risk averse behavior, if all decision variables are continous, stochastic programming model is a convex optimization problem standard theory and methods of convex optimization apply standard optimization software is sufficient for analysis and available integers, stochastic programming model is an integer optimization problem standard theory and methods of integer optimization apply standard optimization software is maybe sufficient for analysis and available. Real Option Analysis of a Technology Portfolio p.24

25 Numerical results investment budget is 1.23 bill euro firm can also invest in index fund and risk free asset Real Option Analysis of a Technology Portfolio p.25

26 A Numerical results I Decision variables are continuos, i.e. we can buy any amount of each capacity. Employing the estimated VEqM-model and Monte Carlo-simulation in scenario tree generation, optimal technology portfolio is sawmill capacity mill. m newsprint (News.1) mill. t. Maximum value of the optimal technology portfolio is 3.26 bill. euro which is more than investment expenditure. Therefore, the investment is attractive. Real Option Analysis of a Technology Portfolio p.26

27 B Numerical results II Some of decision variables are integers, i.e. we can buy only optimal capacity units in this case the stochastic programming model above is very difficult to solve. Employing the estimated VEqM-model, double binary tree and dynamic programming recursion, optimal technology portfolio is sawmill capacity (1 unit) mill. m newsprint (News.1) (2 units) mill. t. coated fine paper (Fine.C) (1 unit) mill. t. Maximum value of the optimal technology portfolio is 3.09 bill. euro and the investment attractive. Real Option Analysis of a Technology Portfolio p.27

28 Conclusions valuation of real options by indifference consistency with arbitrage theory unique value justified easy to explain optimization software available Real Option Analysis of a Technology Portfolio p.28