DANMARKS NATIONALBANK Appr pproaches to to cost/ t/risk m model - - PowerPoint PPT Presentation

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DANMARKS NATIONALBANK Appr pproaches to to cost/ t/risk m model d developm pment World ld B Bank Sover ereign D Deb ebt M Managem emen ent F Forum - Octob ober 2 29-31, 31, 2 2012 12 Jacob W Wellend ndorph E Ejsi sing ng

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SLIDE 1

DANMARKS NATIONALBANK Appr pproaches to to cost/ t/risk m model d developm pment

World ld B Bank Sover ereign D Deb ebt M Managem emen ent F Forum - Octob

  • ber 2

29-31, 31, 2 2012 12

Jacob W Wellend ndorph E Ejsi sing ng

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SLIDE 2

October 2012 Jacob W

  • W. E

Ejsin ing - Cost/risk m model el d dev evel elopmen ent 2

Agenda da

  • What questions are we trying to answer?
  • Deterministic vs. stochastic models
  • Three approaches to implementing in-house cost/risk models
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SLIDE 3

October 2012 Jacob W

  • W. E

Ejsin ing - Cost/risk m model el d dev evel elopmen ent 3

What q questions a are w we tr trying to to answer w with th c cos

  • st/risk m

mod

  • dels?
  • Determinis

istic ic d debt p projectio ion

  • How will debt and interest costs develop
  • In a baseline scenario?
  • In a risk scenario?
  • For a given issuance strategy, how large will future redemptions be?
  • How do changes to the issuance strategy affect cost/risk outcomes?
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SLIDE 4

October 2012 Jacob W

  • W. E

Ejsin ing - Cost/risk m model el d dev evel elopmen ent 4

Determin inis istic ic m modelin ing: Defining a a medium-ter erm b baseline s e scenario

  • Existing debt portfolio
  • Projection of the primary budget balance
  • Issuance strategy
  • Projection of future yields

Maturities Shares of issuance 2-year 5-year 10-year LONG 2-year 5-year 10-year LONG 2013 2016 2018 2023 2034 20 20 60 2014 2016 2018 2025 2034 20 20 60 2015 2018 2020 2025 2034 20 20 60 2016 2018 2020 2027 2037 20 20 60 2017 2020 2022 2027 2037 20 20 60 2018 2020 2022 2029 2037 20 20 60 2019 2022 2024 2029 2040 20 20 60 2020 2022 2024 2031 2040 20 20 60 2021 2024 2026 2031 2040 20 20 60 2022 2024 2026 2033 2043 20 20 60

0,0 0,5 1,0 1,5 2,0 2,5 3,0 3,5 4,0 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 T-bills 2y 5y 10y 20y Per cent

Note: for illustration only, not a reflection of actual policy

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SLIDE 5

October 2012 Jacob W

  • W. E

Ejsin ing - Cost/risk m model el d dev evel elopmen ent 5

Projected bond issuance 2013 - 2022

S trategy: [40-20-40-0]

  • 50

50 100 150 200 250 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 Primary deficit Net interest cost (known) Net interest cost (variable) Redemptions (existing debt) Redemptions (new debt) Net new relending Total

Fina nanc ncing r ng requi quirem ent nt

DKK Billion

40 80 120 160 200 240 280 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 Financing requirement Accumulated prefunding Borrowing (after prefunding)

Issua uanc nce a and pr nd pref undi unding ng

DKK Billion

50 100 150 200 250 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 2 4 6 8 10 T-Bills Existing bonds New bonds Total (per cent of GDP, right axis) DKK Billion Per cent of GDP

1- 1-year ear r roll-over er

Projected bond issuance 2013 - 2022

S trategy: [20-20-60-0]

  • 50

50 100 150 200 250 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 Primary deficit Net interest cost (known) Net interest cost (variable) Redemptions (existing debt) Redemptions (new debt) Net new relending Total

Fina nanc ncing r ng requi quirem ent nt

DKK Billion

40 80 120 160 200 240 280 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 Financing requirement Accumulated prefunding Borrowing (after prefunding)

Issua uanc nce a and pr nd pref undi unding ng

DKK Billion

50 100 150 200 250 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 2 4 6 8 10 T-Bills Existing bonds New bonds Total (per cent of GDP, right axis) DKK Billion Per cent of GDP

1- 1-year ear r roll-over er

Note: for illustration only, not a reflection of actual policy

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SLIDE 6

October 2012 Jacob W

  • W. E

Ejsin ing - Cost/risk m model el d dev evel elopmen ent 6

What q questions a are w we tr trying to to answer w with th c cos

  • st/risk m

mod

  • dels?
  • Determinis

istic ic d debt p projectio ion

  • How will debt and interest costs develop?
  • For a given issuance strategy, how large will future redemptions be?
  • How do changes to the issuance strategy affect cost/risk outcomes (’scenario analysis’)
  • Stoc
  • chastic m

mod

  • delling
  • Given the dynamics of the yield curve, what distribution of outcomes for interest cost can we expect? (example of

”Cost-at-Risk”)

  • Given joint dynamics of the macroeconomy and key risk factors, what distribution of budgetary outcomes can we

expect? (”Budget-at-Risk”)

  • Example of a stochastic model of the term structure …
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SLIDE 7

October 2012 Jacob W

  • W. E

Ejsin ing - Cost/risk m model el d dev evel elopmen ent 7 1997 2000 2002 2005 2007 2010 2012 2015 2017 2020 2022

  • 0.02

0.02 0.04 0.06 0.08

Observed 1-year yield

Observed 1997 2000 2002 2005 2007 2010 2012 2015 2017 2020 2022

  • 0.02

0.02 0.04 0.06 0.08

Observed 10-year yield

Observed

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SLIDE 8

October 2012 Jacob W

  • W. E

Ejsin ing - Cost/risk m model el d dev evel elopmen ent 8 1997 2000 2002 2005 2007 2010 2012 2015 2017 2020 2022

  • 0.02

0.02 0.04 0.06 0.08

Observed 1-year yield

Observed 1997 2000 2002 2005 2007 2010 2012 2015 2017 2020 2022

  • 0.02

0.02 0.04 0.06 0.08

Observed 10-year yield

Observed

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SLIDE 9

October 2012 Jacob W

  • W. E

Ejsin ing - Cost/risk m model el d dev evel elopmen ent 9 1997 2000 2002 2005 2007 2010 2012 2015 2017 2020 2022

  • 0.02

0.02 0.04 0.06 0.08

Observed and simulated 1-year yield

Observed Mean 90% confidence bands 1997 2000 2002 2005 2007 2010 2012 2015 2017 2020 2022

  • 0.02

0.02 0.04 0.06 0.08

Observed and simulated 10-year yield

Observed Mean 90% confidence bands

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SLIDE 10

October 2012 Jacob W

  • W. E

Ejsin ing - Cost/risk m model el d dev evel elopmen ent 10

1997 2000 2002 2005 2007 2010 2012 2015 2017 2020 2022

  • 0.02

0.02 0.04 0.06 0.08

Observed and simulated 1-year yield

Observed Mean 90% confidence bands 1997 2000 2002 2005 2007 2010 2012 2015 2017 2020 2022

  • 0.02

0.02 0.04 0.06 0.08

Observed and simulated 10-year yield

Observed Mean 90% confidence bands

P Projec ect ed ed b bond i issuan ance 2013 - e 2013 - 2022 2022

S trategy: [20-20-60-0]

  • 50

50 100 150 200 250 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 Primary deficit Net interest cost (known) Net interest cost (variable) Redemptions (existing debt) Redemptions (new debt) Net new relending Total

Fina nanc ncing r ng requi quirem ent nt

DKK Billion

40 80 120 160 200 240 280 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 Financing requirement Accumulated prefunding Borrowing (after prefunding)

Issua uanc nce a and pr nd pref undi unding ng

DKK Billion

20 40 60 80 100 120 140 160 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 1 2 3 4 5 6 7 T-Bills Existing bonds New bonds Total (per cent of GDP, right axis) DKK Billion Per cent of GDP

1- 1-year ear r roll-over er

Note: for illustration only, not a reflection of actual policy

2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 5 10 15 20 25 30 35 40

Simulated interest cost distribution

DKK billions

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SLIDE 11

October 2012 Jacob W

  • W. E

Ejsin ing - Cost/risk m model el d dev evel elopmen ent 11

Nuts ts a and b bol

  • lts

ts: How

  • w to

to build a a mod

  • del i

in practise?

Three a ee approaches es

  • Spreadsheet
  • Programming
  • Hybrid approach
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SLIDE 12

October 2012 Jacob W

  • W. E

Ejsin ing - Cost/risk m model el d dev evel elopmen ent 12

The s spr preadsheet a appr pproach

  • Pr

Pros

  • Excel is a standard tool already used intensively by staff
  • Good for prototyping and organizing initial ideas
  • Convenient graphical user interface ”out-of-the-box”
  • Good choice for setting up a basic, deterministic model
  • Cons
  • As complexity increases, spreadsheet solutions tend to become messy
  • Overview is rapidly lost
  • Difficult to document, validate and maintain
  • Can be more cumbersome to update
  • Can be too slow for stochastic models (less critical today)
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SLIDE 13

October 2012 Jacob W

  • W. E

Ejsin ing - Cost/risk m model el d dev evel elopmen ent 13

The pr programming a appr pproach (e.g. M . Matlab, P , Python, e etc.) .)

  • Pr

Pros

  • Allows for tailor-made data structures
  • Easier to expand and generalize models
  • Computational logic can be encapsulated and more easily be reused
  • More easy to test and maintain over time
  • Skills acquired can be extremely useful for other DMO tasks
  • Cons
  • Does require staff with some knowledge of sound software development practices, including:
  • How to develop clear, modular code?
  • How to best testing and document code?
  • Can be more costly (licenses, training)
  • But: good open-source alternatives exist
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SLIDE 14

October 2012 Jacob W

  • W. E

Ejsin ing - Cost/risk m model el d dev evel elopmen ent 14

Hybri rid a d approach

  • In practice, a ”hydrid” approach can work very well
  • The role of Excel:
  • Use spreadsheet as the main user interface
  • Easy to enter input, e.g. fiscal and macro assumptions/scenarios
  • Reporting results: charts, tables, etc.
  • The role of the programming environment (Matlab, Python, etc.):
  • Complex numerical computations can be done efficiently using suitable data structures
  • Interfacing efficiently with the spreadsheet model
  • A hybrid approach has important advantages:
  • Users can continue to interact with the well-known Excel user interface
  • Complex computations can be moved outside of Excel
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SLIDE 15

October 2012 Jacob W

  • W. E

Ejsin ing - Cost/risk m model el d dev evel elopmen ent 15

Moving b bey eyond t the d e det eter erministic m model

  • Once a well-designed deterministic model has been built, adding stochasticity model can be relatively

simple

  • The determistic model can be seen as a function f(x)
  • f(x) returns measures of future costs, given input x
  • ’x’ can be future path of yields (for given strategy), for example
  • Evaluate f(x) for a number of well-chosen x’s (scenarios)
  • Keep complexity of stochastic model low
  • Recent developments can help. For example, consider the new ”Arbitrage-Free Nelson-Siegel” (AFNS) class of term structure

models

  • See Christensen, Diebold, Rudebusch, Journal of Econometrics 164 (2011)
  • Simplest AFNS-model with three independent factors appears to work well
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SLIDE 16

October 2012 Jacob W

  • W. E

Ejsin ing - Cost/risk m model el d dev evel elopmen ent 16

A few i implementa tati tion

  • n t

tips

  • Speeding up the hybrid approach
  • Build basic projection in Excel
  • But try to avoid too much VBA and links between workbooks
  • Use a proper programming language to
  • estimate/calibrate stochastic models (e.g. a dynamic term-structure model)
  • simulate a large number of scenarios and compute distributions of interest
  • Connect to the deterministic Excel-model via ’COM Automation Server’
  • In Matlab, have a look at the command ”actxserver”
  • Feasible to do 5000 cost simulations in about 2 minutes
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SLIDE 17

October 2012 Jacob W

  • W. E

Ejsin ing - Cost/risk m model el d dev evel elopmen ent 17

Final t l thoughts

  • Spend your time wisely!
  • If you want a stochastic model, consider a hybrid approach

Deterministic model S tochastic model Deterministic model S tochastic model

Time spent modeling? Insights gained?