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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

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identification and quantification of incremental market risk

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
Presentation Objectives
  • Introduction
  • Background
  • Methods
  • Results
  • Conclusion
introduction prominent techniques for asset valuation
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

Comparison for Pricing ModelsStock Call Options and Undeveloped Reserves
problems
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
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
  • 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.
slide8

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

significance the result of this study will
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.
significance contd
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
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] – IoWhich 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

model specification
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
Model Specification…….Contd Net Present Value

  • 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 ]

process of project valuation an example
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

= 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

convergence test for the expected npvs

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%

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

hypothesis testing test of difference in means npv
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

risk of project with each evaluation method
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%

sensitivity analysis
Sensitivity Analysis
  • As r , μ Es
  • 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

Alternative Value OF The Project
identification of incremental market risk captured by expert system
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.
identification of incremental market risk captured by expert system1
(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
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 of Result
analysis contd
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 contd1
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.
risk adjusted discount rate
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.