Identification and Quantification of Incremental Market Risk By Sy Sarkarat Ph. D.* * Dr. Sarkarat...
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Transcript of Identification and Quantification of Incremental Market Risk By Sy Sarkarat Ph. D.* * Dr. Sarkarat...
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.