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
2 Agenda da • What questions are we trying to answer? • Deterministic vs. stochastic models • Three approaches to implementing in-house cost/risk models 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 ost/risk m mod odels? • 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? 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 Per cent Maturities Shares of issuance 4,0 2-year 5-year 10-year LONG 2-year 5-year 10-year LONG 3,5 2013 2016 2018 2023 2034 20 20 60 0 3,0 2014 2016 2018 2025 2034 20 20 60 0 2015 2018 2020 2025 2034 20 20 60 0 2,5 2016 2018 2020 2027 2037 20 20 60 0 2,0 2017 2020 2022 2027 2037 20 20 60 0 2018 2020 2022 2029 1,5 2037 20 20 60 0 2019 2022 2024 2029 2040 20 20 60 0 1,0 2020 2022 2024 2031 2040 20 20 60 0 0,5 2021 2024 2026 2031 2040 20 20 60 0 2022 2024 2026 2033 2043 20 20 60 0 0,0 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 T-bills 2y 5y 10y 20y Note: for illustration only, not a reflection of actual October 2012 policy Jacob W W. E Ejsin ing - Cost/risk m model el d dev evel elopmen ent
S trategy: S trategy: Projected bond issuance 2013 - 2022 Projected bond issuance 2013 - 2022 5 [20-20-60-0] [40-20-40-0] DKK Billion DKK Billion Fina nanc ncing r ng requi quirem ent nt Fina nanc ncing r ng requi quirem ent nt 250 250 200 200 150 150 100 100 50 50 0 0 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 -50 -50 Primary deficit Net interest cost (known) Net interest cost (variable) Primary deficit Net interest cost (known) Net interest cost (variable) Redemptions (existing debt) Redemptions (new debt) Net new relending Redemptions (existing debt) Redemptions (new debt) Net new relending Total Total DKK Billion Issua uanc nce a and pr nd pref undi unding ng DKK Billion Issua uanc nce a and pr nd pref undi unding ng 280 280 240 240 200 200 160 160 120 120 80 80 40 40 0 0 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 Financing requirement Accumulated prefunding Borrowing (after prefunding) Financing requirement Accumulated prefunding Borrowing (after prefunding) DKK Billion 1- 1-year ear r roll-over er Per cent of GDP DKK Billion 1-year 1- ear r roll-over er Per cent of GDP 250 10 250 10 200 8 200 8 150 6 150 6 100 4 100 4 50 2 50 2 0 0 0 0 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 T-Bills Existing bonds New bonds Total (per cent of GDP, right axis) T-Bills Existing bonds New bonds Total (per cent of GDP, right axis) October 2012 Note: for illustration only, not a reflection of actual policy 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 ost/risk m mod odels? • 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 ochastic m mod odelling • 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 … October 2012 Jacob W W. E Ejsin ing - Cost/risk m model el d dev evel elopmen ent
7 Observed 1-year yield 0.08 0.06 0.04 0.02 0 Observed -0.02 1997 2000 2002 2005 2007 2010 2012 2015 2017 2020 2022 Observed 10-year yield 0.08 0.06 0.04 0.02 0 Observed -0.02 1997 2000 2002 2005 2007 2010 2012 2015 2017 2020 2022 October 2012 Jacob W W. E Ejsin ing - Cost/risk m model el d dev evel elopmen ent
8 Observed 1-year yield 0.08 0.06 0.04 0.02 0 Observed -0.02 1997 2000 2002 2005 2007 2010 2012 2015 2017 2020 2022 Observed 10-year yield 0.08 0.06 0.04 0.02 0 Observed -0.02 1997 2000 2002 2005 2007 2010 2012 2015 2017 2020 2022 October 2012 Jacob W W. E Ejsin ing - Cost/risk m model el d dev evel elopmen ent
9 Observed and simulated 1-year yield 0.08 0.06 0.04 0.02 Observed 0 Mean 90% confidence bands -0.02 1997 2000 2002 2005 2007 2010 2012 2015 2017 2020 2022 Observed and simulated 10-year yield 0.08 0.06 0.04 0.02 Observed 0 Mean 90% confidence bands -0.02 1997 2000 2002 2005 2007 2010 2012 2015 2017 2020 2022 October 2012 Jacob W W. E Ejsin ing - Cost/risk m model el d dev evel elopmen ent
10 Observed and simulated 1-year yield 0.08 0.06 S trategy: P Projec ect ed ed b bond i issuan ance 2013 - e 2013 - 2022 2022 0.04 [20-20-60-0] DKK Billion 0.02 Fina nanc ncing r ng requi quirem ent nt Observed 250 0 Mean 90% confidence bands 200 -0.02 1997 2000 2002 2005 2007 2010 2012 2015 2017 2020 2022 150 Observed and simulated 10-year yield 100 0.08 50 0.06 0 0.04 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 -50 0.02 Primary deficit Net interest cost (known) Net interest cost (variable) Redemptions (existing debt) Redemptions (new debt) Net new relending Observed 0 Total Mean 90% confidence bands DKK Billion Issua uanc nce a and pr nd pref undi unding ng -0.02 1997 2000 2002 2005 2007 2010 2012 2015 2017 2020 2022 280 240 200 160 120 Simulated interest cost distribution 80 40 40 0 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 35 Financing requirement Accumulated prefunding Borrowing (after prefunding) DKK Billion 1- 1-year ear r roll-over er Per cent of GDP 30 160 7 140 6 120 5 DKK billions 25 100 4 80 3 60 20 2 40 1 20 0 0 15 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 T-Bills Existing bonds New bonds Total (per cent of GDP, right axis) 10 Note: for illustration only, not a reflection of actual 5 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 policy 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 olts ts: How ow to to build a a mod odel i in practise? Three a ee approaches es • Spreadsheet • Programming • Hybrid approach 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) 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 October 2012 Jacob W W. E Ejsin ing - Cost/risk m model el d dev evel elopmen ent
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