BANDWITH PORTFOLIO
RISK MANAGEMENT
ITU workshop
28-29 October 2004
Corrion Anne-Gaëlle
Anne-Gaëlle CORRION annegaelle.corrion @francetelecom .com - D1 -12/10/2004
Introduction and Context
è Telecommunications / long-distance operator
è Pre-defined need for Bandwidth
è Ressources needed (purchasing / lease from a third party operator)
4Different possible strategies
è Two types of risks taken into account:
4Market Risk
l Uncertainties on future returns resulting from changing market conditions
l Made of both a price effect and a quantity effect
l On a commodity market (physical substance, such as food, grains, and metals, which is
interchangeable with another product of the same type / more generally, a product which trades on a
commodity exchange; this would also include foreign currencies and financial instruments and
indexes):
–predominance of the price effect
l Illustration: contract with a duration longer than necessary
– Pros: to benefit from reduced monthly rates
– Risk: surplus sold off on the spot market at an unknown price
4Provider risk
l Appears when the provider fails to honour his agreements
l Is evaluated through the loss suffered when a replacement solution is to be set up
l Illustration: uncertainties on the provider capacity/incapacity to deliver the service
–Unknown time of failure
–Repurchase of bandwidth for replacement at an unknown price on the spot market
AG CORRION annegaelle.corrion@francetelecom .com - D2 - 12/10/2004
Definition of a need in Bandwidth
è Definition of a need in bandwidth
4Known demand:
è Example
4Known demand:
l Between a given couple of Origine-Destination PoPs
l for a given quantity
l From a specified date
l For a given period of time
l With a given quality-of-service
4Remarks:
l The Need is supposed to be deterministic
l The need is supposed to be unique (only one O-D couple)
l Between London and Brussels
l for 4 x 155Mbps
l From the 1st of Jan 2005
l during 11 months
l With a Qos of 99%
AG CORRION annegaelle.corrion@francetelecom .com - D3 - 12/10/2004
Products available on the market
è Bandwidth market
4forward/future contracts
l Forward: OTC, a cash market transaction in which a seller agrees to deliver a specific cash
commodity to a buyer at some point in the future, privately negotiated
l Future: standardized, occurs through a clearing firm
4Spot market contracts (a market in which commodities, such as grain/gold/crude oil are bought
and sold for cash and delivered immediately)
l Contracts: any couple of cities / 155Mbps / 1 month
è Hiring strategy
4The operator must satisfy a bandwidth demand for a given duration
l Long positions taken in forward contracts, the positions being longer than necessary to
answer to the initial need
l Bandwidth on the period of time remaining after the need has been answered is sold out on
the spot market
4Risks modelling
l Future spot prices are modelled by random variables (market risk)
l Operator’s failures and the financial compensation for them are modelled by random
variables (provider risk)
AG CORRION annegaelle.corrion@francetelecom .com - D4 - 12/10/2004
Problem Modelling
è Physical graph vs multi-graph of contracts
Porto
Paris
Porto
Paris
PoP D
Lisbon
Lisbon
PoP O
Madrid
Madrid
è Combinatorial problem
42 types of contracts/market ⇒ 24 contract-paths
44 types de contracts/market ⇒ 160 contract-paths
è Investment solution and path of contracts
4For each path of physical network links between an origin and a destination point for the demand
their can be one (or more than one) path of contracts that the operator can buy to satisfy his/her
need
4The purchase of a path of contracts is an investment decision which is more or less risky
l Uncertain evolution of the spot market for links making up a path until the bandwidth is to be
resold
l Risk of failure/deficiency in the service offered by the provider together with its financial
consequences
AG CORRION annegaelle.corrion@francetelecom .com - D5 - 12/10/2004
Financial Concepts
è Notions of Asset and Portfolio
è Value-at-Risk
è Asset:
ü Any item of economic value owned by an
è Principle:
ü To give a unique number characterizing a
individual or corporation, especially that
which could be converted to cash
ü Action, option, material property, etc.
è Financial portfolio:
ü A collection of financial assets all owned
by the same individual or organization
ü Interest = diversification or even hedging
• Diversification : a portfolio strategy
designed to reduce exposure to risk
by combining a variety of investments,
which are unlikely to all move in the
same direction. The goal of
diversification is to reduce the risk in a
portfolio.
(convexity of the variance function)
• Hedging : an investment is made in
order to reduce the risk of adverse
price movements in a security, by
taking an offsetting position in a
related security
position (portfolio) by also taking into
account the risk factors
è Definition:
ü Measure of the potential maximal loss in
value of a portfolio of (financial)
instruments with a given probability α and
time horizon t
AG CORRION annegaelle.corrion@francetelecom .com - D6 - 12/10/2004
Concepts transposed to telecoms
è Notions of Asset and Portfolio
è Value-at-Risk
è Telecom asset here considered:
ü Any path of bandwidth contracts
è Principle:
ü To give a unique number characterizing a
answering to the initial need
è Portfolio of paths
ü Set of contract path owned by a longdistance operator
portfolio of paths of bandwidth contracts
by also taking into account 2 risk factors,
namely
l Market risk
l Provider risk
è Definition:
ü Measure of the minimal return of a
portfolio of paths of bandwidth contracts
answering to a given need, with a given
probability α and on the time horizon of
the need
AG CORRION annegaelle.corrion@francetelecom .com - D7 - 12/10/2004
Investment Decision and Risk Management
(1)
è Investment decision in a « mono-asset » approach
4How to choose the « best possible path of contracts » ?
l A path of contracts = a random variable represented by its probability density function
l Question : is it better to invest in a path of contracts which will :
–Give the highest profit
–Give the less risky profit (minimal variance…)
–Give the highest minimal profit with a 80/90/95% confidence interval (Value-at-Risk concept)
l Answer : the adopted choice criterion reflects the investor’s degree of aversion to risk
Which is best between those two investment solutions (illustrated by their respective probability density
functions) ?
Representation of two investment solutions by their probability density function : which is the best ?
Distribution for Path1 / Random Total Cost/K10
Distribution for Path5 / Random Total Cost/K14
8
6
Mean=3535220
Mean=3383789
7
5
5
vs
4
3
Values in 10^ -6
Values in 10^ -6
6
4
3
2
2
1
1
0
3,3
3,6
3,9
4,2
0
2,8
3,4
4
4,6
Values in Millions
5%
90%
3,42
Values in Millions
5%
3,76
AG CORRION
90% annegaelle.corrion@francetelecom
5%.com - D8 - 12/10/2004
5%
3,2
3,68
Investment Decision and Risk Management(2)
è Investment Decision in a « multi-asset » approach: management of a portfolio of paths
4In which subset of contract-paths (rather than single contract-path) are we to invest in order
to drop the level of risk ?
4Risk management methodology
l Choice of a risk criterion : Value-at-Risk with a 95% confidence interval
l Decision-making issue : how to find a convex combination of potential paths of contracts
optimizing the risk criterion ?
⇒Stochastic optimization problem
⇒Heuristic solving method : Markowitz method
AG CORRION annegaelle.corrion@francetelecom .com - D9 - 12/10/2004
Process in progress… (1)
è Aim: to make a portfolio of bandwidth contracts allowing
4 to answer to our need… in an optimal way considering the criterion of Value-at-Risk on the
total cost
è The 3 Cost components taken into consideration for each path of contracts are
4 1 deterministic component: buying cost specified by the contracts
4 2 stochastic components:
l Surplus valuation for the contracts corresponding to positions longer than strictly necessary
l Backup cost in case of a failure of the provider
AG CORRION annegaelle.corrion@francetelecom .com - D10 - 12/10/2004
Process in progress… (2)
è Steps
1. Analyse of the need and all possible means to answer it
ü Characteristics of all the available forward contracts to be gathered
⇒ modeling of the stochastic variables linked to the failure of a provider
ü Spot prices history for all couples of involved O-D to be gathered / Forecasts to be made
⇒ modeling of the stochastic variables representing the spot prices in the future
2. Combination of available forward contracts to create all possible paths answering to the need
3. Estimation of the probability distributions of the costs associated with each path thanks to a Monte Carlo
simulation
ü Drawing of values for future spot prices stochastic variables (price of resale of the surplus bandwidth /
purchase price in case of failure/deficiency)
ü Drawing of values for provider failure stochastic variables
4. Determination of the efficient portfolios (portfolios contract-paths minimizing the risk for a given level of cost
= Markowitz frontier)
5. Selection, amongst the efficient portfolios, of the one optimizing the chosen criterion (95% VaR)
1. Contratcs and
spot market
2. Paths of
contracts
3. Simulation
of MC
4. Markowitz
Frontier
5. Optimal
portfolio
AG CORRION annegaelle.corrion@francetelecom .com - D11 - 12/10/2004
In brief on an example / Step 1
1. Contracts and
spot market
1. Analyse of the need and all possible means to answer it
4 Need: Known demand
l Between London and Brussels
l for 4 x 155Mbps
l From the 1st of Jan 2005
l during 11 months
l With a Qos of 99%
4 Available contracts and spot markets associated with them
l 2 types of contracts/market
C6
Brussels
C5
C3
London
C2
C4
C1
Paris
date\Link
j-04
f-04
m-04
a-04
m-04
j-04
j-04
a-04
s-04
o-04
n-04
d-04
j-05
f-05
m-05
a-05
m-05
j-05
j-05
a-05
s-05
o-05
n-05
d-05
j-06
Spot(London-Paris;1month;€)
523412
388255
343072
297890
254028
236527
212981
209232
189142
169052
165057
163443
150806
149938
149070
144304
108242
99617
98503
96349
94196
92212
83801
75390
75123
Spot(Paris-Brussels;1month;€)
650446
413899
368278
322658
275883
268621
244618
219878
195286
170694
163086
162100
146815
145707
144599
139200
91894
91652
89617
86479
83341
82767
62162
61408
55799
Spot(Londres-Brussels;1month;€)
1275892
809716
718308
626902
532868
519076
466830
417264
376174
335086
313172
310782
280694
280406
280116
270582
179088
178218
170950
163930
156910
154622
153964
153308
153334
AG CORRION annegaelle.corrion@francetelecom .com - D12 - 12/10/2004
In brief on an example / Step 2
2. Paths of
contracts
è Combination of available forward contracts to create all possible paths answering to the need
l Path1={C1, C3}, Path2={C2, C3}, Path3={C1, C4}, Path4={C2, C4}, Path5={C5}, Path6={C6}
In brief on an example / Step 3
3. MC
simulation
è Estimation of the probability distributions of the costs associated with each
path thanks to a Monte Carlo simulation
bandwith assets (paths)
3600000
mean cost (€)
3500000
path1
path5
path3
3400000
path2
3300000
path4
3200000
path6
3100000
3000000
50000
100000
150000
200000
250000
standard deviation (€)
AG CORRION annegaelle.corrion@francetelecom .com - D13 - 12/10/2004
In brief on an example / Step 4
4. Markowitz
frontier
è Determination of the efficient portfolios
C6
Brussels
C5
Markowitz frontier
3600000
mean cost (€)
3450000 portfolio9
3400000 portfolio8
3350000
3300000
3250000
3200000
3150000
3100000
C3
London
portfolio11 path1
3550000
3500000 portfolio10
C2
path3
C4
C1
Paris
path5
portfolio7
path2
portfolio6
portfolio5
path4
portfolio4
portfolio3
portfolio2
portrfolio1
path6
3050000
50000
100000
150000
200000
250000
standard deviation (€)
AG CORRION annegaelle.corrion@francetelecom .com - D14 - 12/10/2004
In brief on an example / Step 5
è Selection of the best efficient portfolio, in accordance with the VaR criterion
5. Optimal
portfolio
C6
Brussels
C5
C3
London
C2
C4
C1
Paris
Var of efficient bandwidth portfolios
3700000
Portfolio
2
Portfolio
8
Path 1
0%
0%
Path 2
0%
0%
Path 3
0%
0%
Path 4
13%
40%
Path 5
0%
25%
Path 6
87%
35%
risk indicators
3600000
portfolio8
3500000
3400000
3300000
portfolio2
3200000
3100000
3000000
50000
100000
150000
200000
250000
standard deviation (€)
mean cost
VaR_90%
VaR_95%
AG CORRION annegaelle.corrion@francetelecom .com - D15 - 12/10/2004
Conclusion
è Approach to be tested on real data
è Other domains in which the approach could be put into practice
4Management of a portfolio of projects
THANK YOU FOR YOUR ATTENTION…
AG CORRION annegaelle.corrion@francetelecom .com - D16 - 12/10/2004