discount rates in financial reporting: a practical guide · pdf filediscount rates in...

Discount Rates in Financial Reporting: A Practical Guide

Case Study: IAS 19R

Urs Barmettler

28 October 2014

Zurich, Switzerland

Definition of Discount Rate under IAS 19R

– 2 –

The rate used to discount post-employment benefit obligations (both funded and unfunded) shall be determined by reference to market yields at the end of the reporting period

• on high quality corporate bonds (hqcb), or

• on market yields on government bonds, in countries where there is no deep market in hqcb-bonds.

• The currency and term of the corporate bonds or government bonds shall be consistent with the currency and estimated term of the post-employment benefitobligations.

(IAS 19R Para 83)

First Conclusions

– 3 –

The discount rate

• does reflect the time value of money but not the actuarial or investment risk of the post-employment benefit obligations.

• does not reflect the entity-specific credit risk borne by the entity’s creditors, nor does it reflect the risk that future experience may differ from actuarial assumptions.

(IAS 19R Para 84)

Conditions to Determine the Discount Rate based on Corporate Bonds (1/4)

In the next slides we will focus on the following terms extracted from the definition:

• High-quality corporate bonds

• Deep market

• Currency equal to the currency of the pensions plans to be valued under IAS 19R

• Term equal to the estimated duration of the liabilities

– 4 –

High-quality corporate bonds

• Relative concept or absolute concept?

• Relative concept

– Could e.g. mean top-rated 100 bonds

– Reference point would change over time

• Absolute concept

– Should be consistent over time

– Linked to a credit rating (agency)

– IASB – Staff opinion: absolute concept

Currently common practice "high quality" is an absolute concept with a credit rating of AA and better.

– 5 –


Deep market

• No definition in IAS 19R

• Does it mean an active market ?

• Reference to IFRS 13 – definition of active market

"A market in which transactions for the asset or liability takes place with sufficient frequency and volume to provide pricing information on an ongoing basis."

No further guidance given by the IFRIC (Dec. 2013)

– 6 –


Currency

• IAS 19 Para 83 – Reference to "Country"

• Can the discount rate be determined by corporate bonds issued from a company in an other country but with the currency of the liabilities of the reporting company?

• IFRIC: "The reference to ‘in a country’ could reasonably be read as including high quality corporate bonds that are available in a regional market to which the entity has access, provided that the currency of the regional market and of the country were the same (e.g. the euro)."

• Interesting for EURO-Zone, but also for CHF since most CHF corporate bond issuer are foreign companies.

– 7 –


Discount Rate in CHF (1/2)

• Switzerland (CHF) is considered to have a deep market of AA corporate bonds in CHF

• Situation at September 30, 2014

– 418 bonds at Swiss Stock Market with a rating of AA

– Thereof 117 are Government Bonds (cantons, community, city of Paris, NRW, Hessen, etc.)

– Remaining 301 bonds can be considered as AA corporate bonds

– Significant number of non-Swiss companies (Total, Rabobank, Dexia, MetLife, etc.)

– Nominal amount CHF 84,2 billion

– 8 –

Discount Rate in CHF (2/2)

• September 30, 2014 – Switzerland

• Significant number of bonds with duration up to 10 years

– 9 –

Discount Rate in EURO

• Has the EURO-Zone a deep market of AA corporate bonds?

• Situation at October 24, 2014

– 152 AA corporate bonds within the iBoxx

– Split based on duration

– 10 –

IndexnameBase Market

Value

Weighting

%

# of

bonds

iBoxx € Corporates AA 1-3 58'562'569'006 30.04% 41




iBoxx € Corporates AA 10+ 20'605'506'479 10.57% 17

Total 194'960'472'720 100.00% 152

Discount Rate in USD

• There is a deep market for AA corporate bonds in USD

• Situation at October 24, 2014

– 478 AA corporate bonds with the iBoxx

– Split based on duration

– 11 –

Indexname Base Market ValueWeighting

%

# of

bonds

iBoxx $ Corporates AA 1-3Y 158'963'378'452 27.27% 148





iBoxx $ Corporates AA 15Y+ 120'109'761'680 20.61% 83

Total 582'746'447'744 100.00% 478

Summary of Discount Rate Approaches in Different Locations

Source: Internal Survey IAA October 2014

– 12 –

Discount Rate and Duration (1/2)

• In all three currencies CHF, EUR, USD

– Most AA corporate bonds have a duration (modified duration) below or equal to 10 years

• Pension Liabilities have typically a duration of 15 to 20 years

Still a deep market under IAS 19R requirements?

– 13 –

Discount Rate and Duration (2/2)

In some cases, there may be no deep market in bonds with a sufficiently long maturity to match the estimated maturity of all the benefit payments. In such cases, an entity uses current market rates of the appropriate term to discount shorter-term payments, and estimates the discount rate for longer maturities by extrapolating current market rates along the yield curve.

(IAS 19R Para 86)

– 14 –

Discount rate in CHF

Situation at September 30, 2014

– 15 –

-0.50%

0.00%

0.50%

1.00%

1.50%

2.00%

2.50%

3.00%

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Interest

Modified Duration

Interest yield

Government Bonds

Synthetische AA CHF Kurve

Methods for determining a IAS 19R Discount Rate

• Using an Index

– iBoxx

– Bloomberg, etc.

• Selecting a portfolio of corporate bonds from a data source and use process fitting techniques to generate yield curve

• Popular fitting technique: Nelson Svensson Siegel Model

– Exponential function with 6 variables to measure best fit depending on duration (D) and known interest yields

– b = (β1, β2, β3, β4, λ1, λ2)

– NSS(D,b) = β1+(β2*((1-EXP(-D/λ1))/(D/λ1)))+

(β3*((((1-EXP(-D/λ1))/(D/λ1)))-(EXP(-D/λ1))))+

(β4*((((1-EXP(-D/λ2))/(D/λ2)))-(EXP(-D/λ2))))

– 16 –

Case Study: Nelson Svensson Siegel (1/5)

• Excel with four columns

– Duration (D)

– Yield

– Nelson SvensonSiegel (NSS) function

– Residual = quadratic differential between Yield curve and NSS where interest is known

• Six variables: β1, β2, β3, β4, λ1; λ2

– 17 –

Year Yield NSS Residual β1

1 β2

2 β3

3 β4

4 λ1

5 λ2

8

10

15

20

25

30

Total Residuals 0.0000000000


• Known Bonds

– D=1: 0.2%

– D=2: 0.3%

– D=5: 0.8%

– D=10: 1.5%

– D=20: 1.95%

• Estimate D = 15, D=25, D = 30

– 18 –


• Choose starting variables b

• Calculate NSS

• Calculate Residuals

• Calculate Sum of Residuals

• Use Solver with Variables b and Sum of Residuals

– 19 –


Starting Point

– 20 –

Year Yield NSS Residual β1 0.1

1 0.20% 21.61% 0.0458218032 β2 0.1

2 0.30% 20.26% 0.0398531953 β3 0.1

3 18.51% β4 0.1

4 17.00% λ1 1.00

5 0.80% 15.82% 0.0225745017 λ2 1.00

8 13.74%

10 1.50% 13.00% 0.0132225985

15 12.00%

20 1.95% 11.50% 0.0091202499

25 11.20%

30 11.00%


0.00%

5.00%

10.00%

15.00%

20.00%

25.00%

0 5 10 15 20 25 30 35

Yield NSS


Use Solver

– 21 –

Year Yield NSS Residual β1 0.02389852

1 0.20% 0.21% 0.0000000045 β2 -0.1194721

2 0.30% 0.28% 0.0000000457 β3 -0.0307604

3 0.41% β4 -0.0565971

4 0.61% λ1 0.06

5 0.80% 0.82% 0.0000000314 λ2 1.41

8 1.30%

10 1.50% 1.50% 0.0000000013

15 1.80%

20 1.95% 1.94% 0.0000000036

25 2.03%

30 2.09%


0.00%

0.50%

1.00%

1.50%

2.00%

2.50%

0 5 10 15 20 25 30 35

Yield NSS

Results

– D=15: 1.80%

– D=25: 2.03%

– D=30: 2.09%

Discount rate to calculate the DBO under IAS 19R

• Method 1:

– Discounting using yield curve

• Method 2:

– Calculate duration of the future benefit payments (next 100 years) as included in DBO

– Calculate modified duration

– Use single discount rate corresponding to duration

– 22 –

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