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MANAGING RISK IN INTERNATIONAL BUSINESS Political Risk
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MODELLING STOCHASTIC
POLITICAL RISK FOR
CAPITAL BUDGETING
by
Ephraim Clark
&
Radu Tunaru
Ephraim CLARK, www.countrymetrics.com e.clark@countrymetrics.com
Outline
Overview of capital budgeting with political
risk
Modelling political risk
Bayesian updating process
Implementing the model
Ephraim CLARK, www.countrymetrics.com e.clark@countrymetrics.com
PAPER FOCUS
The amount at risk varies stochastically
– variation in asset value
– variation in severity of loss causing event
Differentarrival rates for different events
Parameters of arrival rate distribution can
change
Ephraim CLARK, www.countrymetrics.com e.clark@countrymetrics.com
The Three Steps to Effective
Political Risk Management
Identifythe individual risks
Assess risk magitudes and exposure
levels
Incorporate the risk assessment in the
decision making process
Ephraim CLARK, www.countrymetrics.com e.clark@countrymetrics.com
RISK IDENTIFICATION
What is political risk?
– Robock & Simmonds (73): discontinuities
– Root (73): transfer, operational, controls
– Brewer (81): miscellaneous
Global, macro, micro
– Hard and soft
Meldrum (2000):additional risks not present
in domestic transactions
Ephraim CLARK, www.countrymetrics.com e.clark@countrymetrics.com
RISK ASSESSMENT
Volatility of profitability: Robock(71),
Haendel et al. (75), Kobrin (79), Feils &
Sabac (2000)
Explicit loss causing event: Root (72),
Simon (82), Howell & Chaddick (94), Roy
& Roy (94), Meldrum (2000)
Ephraim CLARK, www.countrymetrics.com e.clark@countrymetrics.com
INCORPORATE
ASSESSMENT IN DCF
ANALYSIS
Adjust discount rate: Kobrin (71)
Adjust expected cash flow: Stonehill &
Nathanson (68), Shapiro (78)
Use option pricing techniques to price
political risk separately: Clark (97), Clark
and Tunaru (2003)
Ephraim CLARK, www.countrymetrics.com e.clark@countrymetrics.com
THE MODEL 1
s sol det cepxe eht si td) t(DY
dY (t ) Y (t )dt Y (t )ds(t )
dD(t ) D(t )dt D(t )dw(t )
Ephraim CLARK, www.countrymetrics.com e.clark@countrymetrics.com
THE MODEL 2
{N (t ), t 0} is the jump process (counting process)
The process {N (t ), t 0} is called a conditional Poisson
process if, given that , {N (t ), t 0} is a Poisson
process with rate .
Knowing that up to time t0 there were n losses, the
probability that a loss causing political event will
actually occur over the time interval dt is
E ( |{ N ( t 0 ) n}) .
Ephraim CLARK, www.countrymetrics.com e.clark@countrymetrics.com
THE MODEL 3
x(t ) Y (t ) D(t )
dx(t ) ( ) x(t )dt 2 2 2 x(t )dz(t )
dw ds
dz(t )
2 2 2
Ephraim CLARK, www.countrymetrics.com e.clark@countrymetrics.com
THE MODEL 4
V V ( x(t ))
E ( | N (t0 ) n) x(t )
V ( x(t )) A1 x(t ) 1
r
Ephraim CLARK, www.countrymetrics.com e.clark@countrymetrics.com
UPDATING THE POISSON
PROCESS
(m )
Let g be the probability density function of the probability distribution
n
G (m) , updated at the end of the time period (t m 1 , t m ] following a recording of m
events. From the Bayes' formula it follows that
n e(t t ) g(m1) ()
m m m1
g ()
(m)
n e(t t ) g(m1) ()d
m m m1
E ( | N (tm ) N (tm1 ) nm ) x(t ) ( m ) 1
0
V (m)
( x(t )) A1 x(t )
r
Ephraim CLARK, www.countrymetrics.com e.clark@countrymetrics.com
IMPLEMENTATION
Estimate parameters for Y(t) and D (t)
– For D growth rate and standard deviation are
standard inputs for capital budgeting
– For Y an existing index such as Heritage or Free
the World, etc. or use analysts to construct an
index
– For the Poisson process we need the pdf
Ephraim CLARK, www.countrymetrics.com e.clark@countrymetrics.com
EXAMPLE
x = $1 with a growth rate of 0 and a
standard deviation of 0.20; NPV without
political risk =$6; r = 8%
The Poisson parameter has a gamma
distribution
Ephraim CLARK, www.countrymetrics.com e.clark@countrymetrics.com
Based on an analysis of the China/Taiwan
situation over the last five years,
they estimate that loss causing events are very
likely to come at a rate of 0.6
and that it would be very uncommon (2.5%
probability) to have an arrival
rate higher than 1.5.
Ephraim CLARK, www.countrymetrics.com e.clark@countrymetrics.com
Simulation Results
Table 1. Evolution of insurance solution in time and
depending on the number of events occurred.
x(t) r Alpha w z tm nm V(x(t))
1 0.08 0 3 5 0 0 7.5
1 0.08 0 4 10 5 1 5
1 0.08 0 6 15 10 2 5
1 0.08 0 6 20 15 0 3.75
1 0.08 0 9 25 20 3 4.5
Ephraim CLARK, www.countrymetrics.com e.clark@countrymetrics.com
Figure 1. Bayesian evolution of quantified political
risk when the number of events are changing in
time.
Series 1 = the number of events (to be read on the
vertical axis) Series2 = the value of the insurance
policy
Evolution of cost of political risk
8
Number of events and cost of
7
6
political risk
5
Series1
4
Series2
3
2
1
0
1
4
7
10
13
16
19
Time in years since project started
Ephraim CLARK, www.countrymetrics.com e.clark@countrymetrics.com
Figure 2. Comparison between the solution
proposed in this paper and illustrated by Series 1 =
Doubly stochastic solution. Series 2 = Solution with
non stochastic Poisson process.
Political risk evaluation in time
14
12
Cost of political risk
10
8 Series1
6 Series2
4
2
0
1
3
5
7
9
11
13
15
17
19
Time in years since project started
Ephraim CLARK, www.countrymetrics.com e.clark@countrymetrics.com
CONCLUSIONS
Model accounts for three major sources of
uncertainty with respect to political risk
– stochastic asset value; stochastic political,
social, etc. conditions; stochastic arrival rate of
loss causing events (multivariate and
dependent).
Itincorporates new information through a
system of Bayesian updating
Easy to implement
Ephraim CLARK, www.countrymetrics.com e.clark@countrymetrics.com
