Identification and Quantification of Incremental Market Risk

1. Identification and Quantification of Incremental Market Risk BySy Sarkarat Ph. D.* * Dr. Sarkarat is professor of economics at WVU-Parkersburg, his research interest is in real asset appraisals and valuation and economic impact studies.

2. Presentation Objectives • Introduction • Background • Methods • Results • Conclusion

3. Introduction Prominent Techniques For Asset Valuation • Discounted Cash Flow Analysis (DCF) n NPV = ∑CF/(1+ r´)n - Io 1 • Option Valuation (Black/Scholes 1973).

4. + Current value of Reserve + Variance of rate of return of developed reserve - Development cost + Relinquishment requirement + Risk free rate of return + Stock price (S) + Variance of rate return on stock - Exercise value (E) + Time to expiration (T) + Risk-free interest rate Comparison for Pricing ModelsStock Call Options and Undeveloped Reserves

5. Problems • Discounted Cash Flow (DCF) analysis is “static analysis” that account only imperfectly with uncertainty and does not recognize the possibility of changing operations in reaction to changing future economic conditions. • The Option Pricing Method (OPM) provides more flexibility for management in investment and operation decision making. However OPM could overvalue the worth of a given project if the output price is highly volatile. • Where: DCF = Discounted Cash Flow, OPM = Option Pricing Method

6. Reasons for Alternative Evaluation Method • DCF analysis - undervalues the project by assuming higher discount rate to adjust for risk, and • OPM - overvalue a project with a high volatile output price. • Absent of operational flexibility.

7. Expert Systems • Expert systems (Es) are computer programs that mimic human logic and solve problems much as a human expert would. • The expert system is written to obey the rules in decision making. • Advantage of expert system in investment decision making include the opportunities to: • explore the alternatives; • recommend strategies; • determine the value of a project for given strategy; and • explain the expert system’s reasoning process.

8. The Architecture of the Expert System For The Project Expert User Spreadsheet Decision Rules .KBS Data Base Work Sheet .WKS VP-Expert .VPX Domain Knowledge Base

9. SignificanceThe result of this study will: • Establish an empirical decision support system that mimics the actual decision process for investment and operation strategies; and • Provide an alternative valuation method for investment and operation decision making.

10. Significance… Contd. • Compare the performance of the Expert Systems with other methods using simulation. • Perform Sensitivity Analysis • Using the results of the above comparison, identify the incremental market risk. • Establish the statistical significance of the results using Hypothesis testing.

11. Context of the Present Research: Valuation of Gold Mine Project • An investment simulation was developed using a gold mine project with stochastic output price. • Time series data for 1973 to 84 (gold price). • To test the behavior of the simulation for 1985 to 1994. • The simulation was based on Decision Rule and NPV.

12. Max. NPV = ∑ (1-δ)-t [(pt qt) – Cv,t qt] – Io Which Investment Model Maximizes Project’s Value? n 1 Subject to Rt = qt , Investment method Given Ro, qt≥ 0 Where: NPV = expected net present value, Pt = exogenous gold price qt = gold output per year, Cv = extraction cost Io = initial capital expenditure, Ro = original stock of ore δ = discount rate

13. Model Specification The life of this project is assumed to be 10 years (ℓ = 10) and there are 10 individual project cycles Pcj, j = 1 to 10. Net present value of each project cycle is determine as:

14. Model Specification…….Contd Net Present Value ℓ • Pcj = Io -∑ [(Pi – Vi) Qi / (1+δ)t ], j = 1 to 10. 1 where 1(1+δ)t discount factor (r and ŕ), t = 1, 2,….T ℓ = the life of gold mine project, (ℓ = 10). Pcj, j = 1 to10 (number of individual project cycles, i.e. jth project cycle). n = life of each individual project cycle (PCj ), and for j = 1 to 6, n is 5, and for j = 7 to 10, n is 11 - j, (ℓ = 10). Io Capital outlay 10 NPV =∑ [(CF1+ CF2 +…..+ CF0)/ (1+δ)t ]

15. Process of project valuationAn Example • Using u & σ on historical gold price • Price forecast for n iterations • Data period 1973 to 84, add a year for PCt +1 • Ex post simulation 1985 - 94 Pc1 1 2 3 4 5 6 7 8 9 ˝ ˝ ˝ ˝ ˝ ˝ ˝ 10 ℓ = 10 CFDcf, 1 to 10. μ NPVDcf CFDcf NPV Dcf For 10 Pcj with n price Iterations, n = 50 CFEs, 1 to 10. ’ CFEs μ NPVEs NPV Es for n = 50 10 NPV =∑ [(CF1+ CF2 +…..+ CF10)/ (1+δ)t ] 1

16. Example

17. Example

18. Cash Flows

19. Value of Project with Alternative Valuation Methods 16 14 12 10 8 In million of $ 6 4 2 0 ? NPVc, n = ? NPVe, n = ? NPVc, n = ? NPVe, n = ? NPVc, n ? NPVe, n = 30 30 40 40 =50 50 Convergence test for the expected NPVs. Methods Values % Change μ NPVc, n = 307.70 μ Nave, n = 3012.2 μ NPVc, n = 409.10 0.14 μ Nave, n = 4013.5 0.10 μ NPVc, n =509.30 0.01 μ Nave, n = 5013.9 0 02 r =9% r’ = 14% ==========================

20. Hypothesis Testing:Test of Difference in means μ NPV State hypothesis Ho μ NPVEs - μ NPV Dcf = 0 H1 μ NPVEs -μ NPV Dcf # 0 @ α =0.05 (+ & - 1.96 ) The test of significant rejects the null hypothesis and accepts the alternative hypothesis μ Es = 13.97 & σEs = 6.00, μ Dcf = 9.26 & σDcf = 5.53, n = 50

21. The Results

22. Risk of Project With Each Evaluation Method The probability project will yield negative return ( μ < 0 ) = 0.00 Where: μ Es = 13.97 & σE = 6.00, P (μ Es < 0) = 0 μ Dcf = 9.26 & σDcf = 5.53, P (μ Dcf < 0) = 5%

23. Sensitivity Analysis • As r , μ Es • ρ (u < 0) = 0.00, invest. & operations are postponed.

24. n = 30 μ Dcf 7.96 μ Es 12.24 OPM 22.30 n = 40 μ Dcf 9.10 μ Es 13.50 OPM 22.30 n = 50 μ Dcf 9.30 μ Es 13.90 OPM 22.30 Alternative Value OF The Project

25. Identification Of Incremental Market Risk Captured By Expert System • Find μ Dcf @ r’ =14% (risk adjusted discount rate), which amounted to $9.30 million; • Find μ Es @ r = 9% (risk free rate of return), which amounted to $13.97 million; • Find that discount rate (r*) which equates μDcf to μ Es at risk-free @ r = 9% (risk free rate of return), which is 10.6%; and • Find the differences in discount rates used in step 3. This difference is the values of incremental market risk (r m = r* - r) that is removed through operational flexibility using expert system technology in project evaluation.

26. (r m = r* - r) = 10.60% - 9% = 1.60% Where: ŕ = r + r m + r a r m = market risk increment r a = market risk increment due to other risk elements r = risk free discount rate ŕ = risk adjusted discount rate Identification Of Incremental Market Risk Captured By Expert System

27. 10.60% - 9% = 1.60% 9% 14%

28. Expert system Vs. DCF Conduct sensitivity analysis (responsiveness to change in disct. rate?) Ability of Es to quantify and capture the incremental market risk through O.F. Analysis of Result

29. Analysis contd…… • Expert System valuation resulted in lower relative risk in project’s expected NPV; • Expert System diversified a portion of market risk by recognizing the value of operational flexibility; • Expert System quantified the increment of market risk captured through operational flexibility; and • Expert System recognized the effects active management may have on the value of a project.

30. Analysis contd….. • Te ρ (μ NPV < 0 ) exist with DCF valuation, but not with Es. • Value (μ NPV ) obtained by DCF analysis is more volatile than value obtained with Es. • Thus supporting the notion that Es diversify increment of market risk through operational flexibility.

31. Thank you

32. Questions

33. Risk Adjusted Discount Rate ŕ = r + ßi (r m – r) = 9% + 1 (14% – 9%) ŕ = 14% (rate of return on gold investment, 1974- 84), r =9% (interest return on short-term U.S. Securities for early 80s) and ß = 1, historical volatility of rate of return on gold for Newmont mining co.