Market risk management of public

debt

First Annual Meeting of Latin American and Caribbean Public

Debt Management SpecialistsOve Sten Jensen & Morten Kjærgaard

18 March 2005

DANMARKS NATIONALBANK

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

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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

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Interest-rate risk- Trade-off and ”steady-state” strategies

12 3

45

67

89

10

0

10

20

30

40

50

60

70

80

90

100

Interest-rate exposure

Time

High interest-rate risk

Low debt service costs

Low interest-rate risk

High debt service costs

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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

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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)

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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

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Risk modelling- simulated distribution of interest costs

0,00

0,02

0,04

0,06

0,08

0,10

0,12

0,14

0,16

0,18

0,20

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

Frequency

Interest costs, DKK billion

Relative CaR

Median Expected costs Absolute CaR Tail CaR

Nominal costs?

Costs/GDP?

Costs/primary balance?

Only government debt or also other balance sheet items?

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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

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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 and decrease budget

balance variability?

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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)

Strategic assumptions

Distribution of new borrowing

Interest-rate swaps

Buy-backs

Calculation

Issue of new government securities

Interest on new securities

Interest on new swaps

Capital losses on buy-back

Key figures

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The Danish approach – in brief- elements in strategy analysis within the CaR model1. Analyse issuance strategy –

issuance volume requirement to ensure liquidity

2. Analyse buy-back strategies - smooth out yearly financing requirement

3. Calculate trade-off under various swap volume assumptions (various duration and interest-rate fixing targets)

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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

0,0

0,5

1,0

1,5

2,0

2,5

3,0

3,5

4,0

4,5

2005 2006 2007 2008 2009 2010 2011 2012 2013 2014

15 pct. Af BNP 16 pct. Af BNP 17 pct. Af BNP 18 pct. Af BNP 19 pct. Af BNP

20 pct. Af BNP 25 pct. Af BNP

År

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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

0

1

2

3

4

5

6

7

2005 2006 2007 2008 2009 2010 2011 2012 2013 2014

Varighed 2,0 Varighed 2,5 Varighed 2,75 Varighed 3,0 Varighed 3,25 Varighed 3,5 Varighed 4,0

Mia.kr.

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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

0

20

40

60

80

100

120

140

160

180

-16.500

-15.500

-14.000

-13.000

-12.000

-11.000

-10.000

-9.000

-8.000

-7.000

-6.000

-5.000

-4.000

-3.000

-2.000

-1.000 0

1.000

2.000

3.000

4.000

5.500

6.500

7.500

15.500

18.000

19.500

22.500

25.000Mia.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