Identification and Quantification of Incremental Market Risk By Sy 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.

Presentation Objectives Introduction Background Methods Results Conclusion

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

Comparison for Pricing Models Stock Call Options and Undeveloped Reserves +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

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

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.

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: 1.explore the alternatives; 2.recommend strategies; 3.determine the value of a project for given strategy; and 4.explain the expert system’s reasoning process.

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

Significance The result of this study will: 1)Establish an empirical decision support system that mimics the actual decision process for investment and operation strategies; and 2)Provide an alternative valuation method for investment and operation decision making.

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.

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 The simulation was based on Decision Rule and NPV.

Which Investment Model Maximizes Project’s Value? Max. NPV = ∑ (1-δ) -t [(p t q t ) – C v, t q t ] – I o 1 n Subject to R t = q t, Investment method Given R o, q t ≥ 0 Where: NPV = expected net present value, P t = exogenous gold price q t = gold output per year, C v = extraction cost I o = initial capital expenditure, R o = original stock of ore δ = discount rate

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

Model Specification…….Contd Net Present Value ℓ Pc j = I o - ∑ [(P i – V i ) Q i / (1+δ) t ], j = 1 to where 1(1+δ) t discount factor (r and r), t = 1, 2,….T ℓ = the life of gold mine project, (ℓ = 10). Pc j, j = 1 to10 (number of individual project cycles, i.e. jth project cycle). n = life of each individual project cycle (PC j ), and for j = 1 to 6, n is 5, and for j = 7 to 10, n is 11 - j, (ℓ = 10). I o Capital outlay 10 NPV =∑ [(CF 1 + CF 2 +…..+ CF 0 )/ (1+δ) t ]

Process of project valuation An Example 1 CF Dcf, 1 to 10. CF Es, 1 to CF Dcf CF Es ’ NPV Dcf NPV Es For 10 Pcj with n price Iterations, n = 50 ˝˝ ℓ = 10 ˝˝˝˝˝ for n = 50 Pc 1 1)Using u & σ on historical gold price 2)Price forecast for n iterations 3)Data period 1973 to 84, add a year for PC t +1 4)Ex post simulation μ NPVDcf μ NPVEs 10 NPV =∑ [(CF1+ CF2 +…..+ CF10)/ (1+δ)t ] 1

Case I P_TODAY317.32Case 1 Year_ ===== Pf CASE1_P Total Revenue CASE1_AFC0.00 CASE1_AVC CASE1_TFC0.00 CASE1_TotalVC Total_Cost CASE1A_CF CASE1A_NPV CASE1A_ONPV CASE1A_RNPV RESULTS1BWait CASE1B_CF0.00 NPV without expert system NPV with expert system Example

Case VI Case 6 Year_6***** ===== Pf CASE6_P***** Total Revenue CASE6_AFC*****0.00 CASE6_AVC***** CASE6_TFC*****0.00 CASE6_TotalVC***** Total_Cost CASE6A_CF***** CASE6A_NPV***** CASE6A_ONPV***** CASE6A_RNPV***** RESULTS6B*****ShutdownReStartOperate CASE6B_CF***** NPV without expert system244.08NPV with expert system83.93 Example

Year NPV ============ IT1 CFIIIIIIIVVVIVIIVIIIIXX C.CF VP.Inst.Wait InvestOperate ShutdownReStartOperateShutdownReStart ES.CF Cash Flows

Convergence test for the expected NPVs. MethodsValues% Change μ NPVc, n = μ Nave, n = μ NPVc, n = μ Nave, n = μ NPVc, n = μ Nave, n = r =9% r’ = 14% ========================== Value of Project with Alternative Valuation Methods ? NPVc, n = 30 ? NPVe, n = 30 ? NPVc, n = 40 ? NPVe, n = 40 ? NPVc, n =50 ? NPVe, n = 50 In million of $

Hypothesis Testing: Test of Difference in means μ NPV State hypothesis H o μ NPVEs - μ NPV Dcf = 0 H 1 μ NPVEs - μ NPV Dcf # α =0.05 (+ & ) The test of significant rejects the null hypothesis and accepts the alternative hypothesis μ Es = & σ Es = 6.00, μ Dcf = 9.26 & σ Dcf = 5.53, n = 50

The Results Items μ Es μ Dcf Minimum Maximum Expected value Standard Deviation Coefficient of Variation (CVar) P ( μ < 0 )0.005%

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

Sensitivity Analysis Items μ Es (M $) Discount rate 5% Mean Std CVar ρ (u < 0) Discount rate 9% Mean Std CVar ρ (u < 0) Discount rate 13% Mean Std CVar ρ (u < 0) )As r, μ Es 2)ρ (u < 0) = 0.00, invest. & operations are postponed.

Alternative Value OF The Project n = 30 μ Dcf 7.96 μ Es OPM n = 40 μ Dcf 9.10 μ Es OPM n = 50 μ Dcf 9.30 μ Es OPM 22.30

Identification Of Incremental Market Risk Captured By Expert System 1.Find μ r’ = 14% (risk adjusted discount rate), which amounted to $9.30 million; 2)Find μ r = 9% (risk free rate of return), which amounted to $13.97 million; 3)Find that discount rate (r*) which equates μ Dcf to μ Es at r = 9% (risk free rate of return), which is 10.6%; and 4)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.

Identification Of Incremental Market Risk Captured By Expert System (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

9%14% 10.60% - 9% = 1.60%

Analysis of Result 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 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.

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.

Thank you

Questions

Risk Adjusted Discount Rate ŕ = r + ß i (r m – r) = 9% + 1 (14% – 9%) ŕ= 14% (rate of return on gold investment, ), 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.