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.

Presentation Objectives

• Introduction

• Background

• Methods

• Results

• Conclusion

Introduction Prominent Techniques For Asset Valuation

• Discounted Cash Flow Analysis (DCF) n

NPV = ∑CF/(1+ r´)n - Io

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.

DomainKnowledge

Base

DomainKnowledge

Base

ExpertExpert

UserUser

SpreadsheetSpreadsheet

Data Base Work Sheet

.WKS

Data Base Work Sheet

.WKSVP-Expert

.VPX

VP-Expert.VPX

Decision Rules.KBS

Decision Rules.KBS

The Architecture of the Expert System For The Project

SignificanceThe 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 1994.

• The simulation was based on Decision Rule and NPV.

Which Investment Model Maximizes Project’s Value?

Max. NPV = ∑ (1-δ)-t [(pt qt) – Cv,t qt] – Io1

n

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

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:

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 r), 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 ]

Process of project valuationAn Example

1

CFDcf, 1 to 10.

CFEs, 1 to 10.

2

34

56

CFDcf

CFEs’

NPV Dcf

NPV Es

For 10 Pcj with n price Iterations, n = 50

˝ ˝ ℓ = 10˝ ˝ ˝ ˝ ˝

78

910

for n = 50

Pc1

1) Using u & σ on historical gold price 2) Price forecast for n iterations3) Data period 1973 to 84, add a year for PCt +1

4) Ex post simulation 1985 - 94

μ NPVDcf

μ NPVEs

10 NPV =∑ [(CF1+ CF2 +…..+ CF10)/ (1+δ)t ]

1

Case I          

P_TODAY 317.32 Case 1  

Year_1 1985 1986 1987 1988 1989

  = = = = =

  Pf Pf Pf Pf Pf

  - - - - -

  5.00 4.00 3.00 2.00 1.00

CASE1_P 277.42 301.67 312.33 265.00 330.11

Total Revenue 2774.20 3016.70 3123.30 2650.00 3301.10

CASE1_AFC 0.00 0.00 0.00 0.00 0.00

CASE1_AVC 280.00 280.00 280.00 280.00 280.00

CASE1_TFC 0.00 0.00 0.00 0.00 0.00

CASE1_TotalVC 2800.00 2800.00 2800.00 2800.00 2800.00

  - - - - -

Total_Cost 2800.00 2800.00 2800.00 2800.00 2800.00

CASE1A_CF -25.80 216.70 323.30 -150.00 501.10

  - - - - -

CASE1A_NPV -566.23 -465.70 -593.60 -846.00 -660.44

CASE1A_ONPV 507.79 590.09 437.29 164.15 339.72

CASE1A_RNPV 487.23 573.75 426.43 157.77 335.55

RESULTS1B Wait Wait Wait Wait Wait

CASE1B_CF 0.00 0.00 0.00 0.00 0.00

NPV without expert system -566.23

NPV with expert system -1100.00  

 

- - - -

 

Example

Case VI                    

  317.20 Case 6  

Year_6 * * * * * 1990 1991 1992 1993 1994

  = = = = =

  5.00 4.00 3.00 2.00 1.00

  Pf Pf Pf Pf Pf

  - - - - -

CASE6_P * * * * * 272.23 350.99 340.37 295.87 350.19

Total Revenue 2722.30 3509.9

0 3403.7

0 2958.7

0 3501.9

0

CASE6_AFC * * * * * 0.00 0.00 0.00 0.00 0.00

CASE6_AVC * * * * * 280.00 280.00 280.00 280.00 280.00

CASE6_TFC * * * * * 0.00 0.00 0.00 0.00 0.00

CASE6_TotalVC * * * * * 2800.00

2800.00

2800.00

2800.00

2800.00

Total_Cost 2800.00 2800.0

0 2800.0

0 2800.0

0 2800.0

0

CASE6A_CF * * * * * -77.70 709.90 603.70 158.70 701.90

CASE6A_NPV * * * * * 244.08 509.95 25.44 -

420.70 -

484.30

CASE6A_ONPV * * * * * 1441.01 1659.2

0 1109.4

2 616.37 523.94

CASE6A_RNPV * * * * * 1393.85 1622.9

3 1087.3

2 604.36 518.09

RESULTS6B * * * * *Shutdown

ReStart

Operate

Operate

Operate

CASE6B_CF * * * * * -155.00 589.90 603.70 158.70 701.90

NPV without expert system

244.08

NPV with expert system 83.93  

 

Example

Year 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 NPV

= = = = = = = = = = = =

IT1  

CF I II III IV V VI VII VIII IX X  

   

C.CF52

-25.80

-71.40 267.40 385.00 351.40 -77.70

172.50 444.50 86.50

332.60 -280.95

   

VP.Inst. Wait Wait InvestOperat

eOperat

eShutdow

n

ReStart

Operate

Shutdown

ReStart  

   

ES.CF52 0.00 0.00

-832.60 385.00 351.40 -155.00 52.50 444.50 -155.00

212.60 -46.33

Cash Flows

Convergence test for the expected NPVs.

Methods Values % Change

μ NPVc, n = 30 7.70

μ Nave, n = 30 12.2

μ NPVc, n = 40 9.10 0.14

μ Nave, n = 40 13.5 0.10

μ NPVc, n =50 9.30 0.01

μ Nave, n = 50 13.9 0 02r =9% r’ = 14%

==========================

Value of Project with Alternative Valuation Methods

0

2

4

6

8

10

12

14

16

? NPVc, n =30

? NPVe, n =30

? NPVc, n =40

? NPVe, n =40

? NPVc, n=50

? NPVe, n =50

In m

illi

on

of

$

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 & σ Es = 6.00,

μ Dcf = 9.26 & σ Dcf = 5.53, n = 50

The ResultsItems μ Es μ Dcf

Minimum 3.60 -2.50

Maximum 26.41 21.95

Expected value 13.97 9.26

Standard Deviation 6.10 5.50

Coefficient of Variation (CVar)

0.43 0.60

P ( μ < 0 ) 0.00 5%

Risk of Project With Each Evaluation Method

The probability project will yield negative

return

( μ < 0 ) = 0.00

Where:

μ Es = 13.97 & σ E = 6.00, P (μ Es < 0) = 0

μ Dcf = 9.26 & σ Dcf = 5.53, P (μ Dcf < 0) = 5%

Sensitivity AnalysisItems 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)

18.80

7.908

0.41

0.00

13.90

6.00

0.41

0.00

10.50

4.35

0.41

0.00

1) 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 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

Identification Of Incremental Market Risk Captured By Expert System

1. Find μ Dcf @ r’ =14% (risk adjusted discount rate), which amounted to $9.30 million;

2) Find μ Es @ r = 9% (risk free rate of return), which amounted to $13.97 million;

3) 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

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:r = r + r m + r a

r m = market risk incrementr a = market risk increment due to other risk elementsr = risk free discount rater = risk adjusted discount rate

Estimation of Incremental Market Risk

0

5

10

15

20

25

0% 10% 20% 30%

Discount Rate

Va

lue

s o

f p

roje

ct

(M

$)

DCFEX

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

r = r + ßi (r m – r) = 9% + 1 (14% – 9%)

r = 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.