# Presentation: 237435

## 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 - 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:
**explore the alternatives; **
**recommend strategies; **
**determine the value of a project for given strategy; and **
**explain the expert system’s reasoning process**.

## The Architecture of the Expert System For The Project

- Knowledge
- Base

- Expert

- User

- Spreadsheet

- Data Base
- Work Sheet
- .WKS

- VP-Expert
- .VPX

- Decision Rules
- .KBS

**The Architecture of the Expert System For The Project**

## SignificanceThe 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.

- 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] – Io

- 1

- 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 *Pc**j**,* j = 1 to 10.  Net present
- value of each project cycle is determine as:

## Model Specification.......Contd Net Present Value

-                      l
- Pcj = *I**o **-* *∑* [(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 valuationAn Example

- 1

- CFDcf, 1 to 10.

- CFEs, 1 to 10.

- 2

- 3

- 4

- 5

- 6

- CFDcf

- CFEs

- ’

- NPV Dcf

- NPV Es

*For 10 Pcj with n price *
*Iterations, n = 50*

-  ̋

-  ̋

- l

-  = 10

-  ̋

-  ̋

-  ̋

-  ̋

-  ̋

- 7

- 8

- 9

- 10

*for n = 50*

- Pc1

- 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

*μ **NPVDcf*

*μ **NPVEs*

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

- 1

## Example

| 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  |  |   |
|  |  |  |  |  |   |
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|  | - | - | - | - |  |
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_**Example**_

## 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  |  | 3509.90  | 3403.70  | 2958.70  | 3501.90  |
| 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  |  | 2800.00  | 2800.00  | 2800.00  | 2800.00  |
| 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  |  | 1659.20  | 1109.42  | 616.37  | 523.94  |
| CASE6A_RNPV | * | * | * | * | * | 1393.85  |  | 1622.93  | 1087.32  | 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  |  |  |   |
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_**Example**_

## Cash Flows

| 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 | Invest | Operate | Operate | Shutdown | 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  |

## 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 02**
- r =9%   r’ = 14%
**==========================**

## 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 Results

| Items | 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 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) | 
 18.80
    7.908
    0.41 
    0.00

 13.90
   6.00
   0.41
   0.00

10.50  
  4.35
  0.41
  0.00
 |

- 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

## 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 *μ**Dcf* 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 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%

***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, 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. *