Market risk management of public debt

First Annual Meeting of Latin American and Caribbean Public Debt Management Specialists Ove Sten Jensen & Morten Kjærgaard 18 March 2005

Observations from the OECD

    Risk management has been an important topic on the OECD agenda for years Still work-in-progress, but progress has been good Important similarities in approaches among countries - less important differences Work will continue   Inclusion of other balance sheet items Performance measurement DANMARKS NATIONALBANK

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Observations from the OECD

- common features Risk models have become important for supporting decision making Decisions on portfolio targets are based on analysis within risk models Simulation of future debt service costs is a widespread modelling methodology Issuance policy to some extent separated from interest-rate risk management by use of swaps Many leading risk managers operate in stable environments with few operational limitations DANMARKS NATIONALBANK

Interest-rate risk

- Trade-off and ”steady-state” strategies

Interest-rate exposure

100 90 80 70

High interest-rate risk Low debt service costs

60 50 40 30 20 10 0

Low interest-rate risk High debt service costs

1 2 3 4 5 6 7 8 9 10

Time

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Interest-rate risk

- Targets Exposure targets as reference for ongoing management Duration is the most commonly used target  Used as measure of average fixed-interest period  Summary measure of the cost-risk trade-off Supplementary target needed to control for absolute size of and year-to-year variation in interest-rate exposure   Redemption profile Interest-rate fixing (redemtions + floating rate debt + floating rate swap legs…) Often interest-rate swaps and buy-backs are used to manage exposure targets DANMARKS NATIONALBANK

Exchange-rate risk

   Foreign debt typically a relatively small share of total debt Denmark: Foreign borrowing only to refinance debt raised to maintain foreign exchange reserves in support of the fixed exchange-rate regime Exchange-rate risk management:   Hedging foreign liabilities and assets (ALM) Value-at-Risk (VaR)  Cost-at-Risk (CaR) DANMARKS NATIONALBANK

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Risk modelling

CaR simulations have become a widespread methodology CaR quantification: What is the maximum level of or increase in costs with a given probability Supplements ”what if”-analysis/stress-testing/scenario analysis (i.e. deterministic analysis) Simplicity vs. complexity   ”Costs will increase by R$ 1 billion if interest rates end up 1 per cent higher than expected” vs.

”With a probability of 95 per cent costs do not increase by more than 4 per cent of the budget surplus if the parameters of the term structure model are  =0.072,  =0.167,  =0.099 and  = 0.05” Risk models depend critically on underlying assumptions => no clear-cut solutions DANMARKS NATIONALBANK

Risk modelling

- simulated distribution of interest costs Frequency Only government debt or also other balance sheet items? 0,20 0,18 Median Expect ed cost s Absolut e CaR Tail CaR 0,16 0,14 0,12 0,10 Relat ive CaR Nominal costs?

Costs/GDP?

Costs/primary balance?

0,08 0,06 0,04 0,02 0,00 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 Int erest cost s, DKK billion DANMARKS NATIONALBANK

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Risk modelling

- scope of the analysis Balance sheet items:  Liabilities      Central-government debt Local government debt Contingent liabilities Financial assets     Foreign reserves Re-lending Government funds Equity Non-financial assets  The budget Nominal costs vs. ”real” costs DANMARKS NATIONALBANK

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Risk modelling

- budget smoothing Aims to ensure a debt structure that hedge budget balance variability  Example: Negative demand shock => short-term rates fall, inflation decreases and the budget deteriorates => short-term debt and inflation indexed debt reduce negative budget impact Short term borrowing increases variance of debt service cost => trade-off between debt service costs and debt service risk But effect from short-term borrowing on budget balance variance is ambiguous…depends on co-variance between debt service costs and the primary balance  Var(budget balance) = var(primary balance) + var(debt service costs) – 2cov(primary balance,debt service) Can we lower debt service costs balance variability?

and decrease budget DANMARKS NATIONALBANK

The Danish approach – in brief

- structure of the Danish Cost-at-Risk model

Simulated term structure of interest rates Borrowing requirement

Redemptions and interest payments on the existing portfolio Redemptions and interest payments on simulated portfolio Scenario for the government budget surplus (primary balance)

Calculation

Issue of new government securities Interest on new securities Interest on new swaps Capital losses on buy-back

Strategic assumptions

Distribution of new borrowing Interest-rate swaps Buy-backs

Key figures

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The Danish approach – in brief

elements in strategy analysis within the CaR model 1.

2.

3.

Analyse issuance strategy – issuance volume requirement to ensure liquidity Analyse buy-back strategies - smooth out yearly financing requirement Calculate trade-off under various swap volume assumptions (various duration and interest-rate fixing targets) DANMARKS NATIONALBANK

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The Danish approach – in brief

- Illustrations of output from the CaR model Future development in portfolio duration for various fixed ”interest-rate fixing/GDP”-ratios År 4,5 4,0 3,5 1,0 0,5 0,0 3,0 2,5 2,0 1,5 2005 2006 15 pct . Af BNP 20 pct . Af BNP 2007 2008 16 pct . Af BNP 25 pct . Af BNP 2009 2010 17 pct . Af BNP 2011 18 pct . Af BNP 2012 DANMARKS NATIONALBANK 2013 19 pct . Af BNP 2014

The Danish approach – in brief

- Illustrations of output from the CaR model  Relative Cost-at-Risk for various duration strategies  Relative CaR: Maximum amount, with a probability of 95 per cent, by which costs in a given year will exceed the expected costs 3 2 5 4 Mia.kr.

7 6 1 0 2005 2006 Varighed 2,0 2007 Varighed 2,5 2008 2009 2010 2011 2012 Varighed 2,75 Varighed 3,0 Varighed 3,25 DANMARKS NATIONALBANK Varighed 3,5 2013 Varighed 4,0 2014

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The Danish approach – in brief

- Illustrations of output from the CaR model Distribution for the accumulated gain of ”high” duration strategy compared to ”low” duration strategy 180 160 140 120 100 80 60 40 20 0 0M ia.kr

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The future of public debt risk management looks bright

Hits from a quick search on Google:  ”This paper derives the optimal composition of the Brazilian public debt…” NBER Working Paper 2004  ”Optimal maturity of government debt without state contingent bonds” Journal of Monetary Economics 2003 DANMARKS NATIONALBANK