Performance Analysis for Fixed Income Portfolios

8/9/2019 Performance Analysis for Fixed Income Portfolios

1/19

Performance Analysis for Fixed Income Portfolios

Paul Wild, 11.12.2002


2/19

· 2

Agenda

Fixed Income Investment Process

Key Rate Duration Concept

Option Adjusted Spreads

Performance Decomposition

Discussion


3/19

· 3

Starting Point


4/19

· 4

Investment Process

Allocation of Funds

Duration Credit

Risk TypesRisk Types

Curve Sector / Rating

Risk Composition


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· 5

Modelling of Term Structure

Modelling of interest rate curve by several key rates along time

Linear Interpolation Zero Coupon Spot Rates of Government Bonds


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· 6

Option Adjusted Spreads (OAS)

“By how many basis points may the yield of a bond increase such that its return

advantage as compared to a government bond will vanish?”

Mathematically: Given the discount factors Df i from the zero coupon government

bond curve and the bond’s observed market price, we need to solve the followingequation for OAS

∑= ++

=

n

it

i

i

iOAS DF

CF

1 )1(PriceBondMarket

Option Adjusted Spread

0

0.5

1

1.5

2

2.5

3

3.5

4

ON 3m 6m 1y 2y 3y 4y 5y 6y 7y 8y 9y 10y 15y 20y 25y 30y

Time to Maturity

D i s c o u n t R a t e

Government Rate


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OAS includes

credit spread for straight bonds

option price for callable/putable bonds

separation possible by considering probable redemption

suitable option pricing models required for more complex instruments (e.g.

convertibles)

Additional intermediate steps possible: Government --> Swap --> Credit

Analysis by further grouping: industry sectors, rating classes

Important: Development over time


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· 8

Interest Rate Risk

Key Rate Moves

4.8

4.9

5

5.1

5.25.3

5.4

5.5

5.6

1 2 3 4

Term (years)

S p o t R a t e

( % ) Key Rate 1

Key Rate 2Key Rate 3

Key Rate 4

Spot Rate

Calculation of portfolio (or single bond) sensitivity to change of each key rate leaving

all other things equal

Discounting of each bond’s future cash-flow (according to key rate curve) to get the

present value

Numerical approximation by calculating

i

i

i y P

P P

KRD ∆

−

−=


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Key Rate Duration Concept

Portfolio value change in response to key rate movements

As compared to the ‘Macauley Duration’ approach

the KRD concept is a ‘Multi-Factor’ model

KRD of Portfolio = Cap. Weighted sum of single bond’s KRDs

Shift of all key rates by same amount --> parallel shift of curve

Consequence: Sum of key rate durations equals Effective Duration

)(1

...)(1

)(1

2

2

21

1

1n

n

n y y

KRD y

y

KRD y

y

KRD

P

P ∆−

+++∆−

++∆−

+≈

∆

y D y P

P Mac ∆⋅⋅+

−≈∆

11


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· 10

Key Rate Duration Profile; Example


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· 11



12/19


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Summary

Portfolio Positions + Curve

Decision Support

Cashflows and Discount Factors

Scenario Simulation(Curve and/or Spreads)

Solve for OAS

Key Rate Shifts and KRD


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· 14

Performance Analysis

Portfolio Return

Change of

Term Structure

Change of

Credit Spread Accretion Rolldown Effect


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· 15


Return Factor Description

Accretion Return Accretion return is calculated by holding a cashflow’s yieldconstant while moving the settlement date forward. Thereturn is due to the convergence of the price to par as the

time approaches its maturity.Rolldown Effect(Time Passages)

Results from the predictable change in the cashflow’s yieldas time elapses; reflects the change in the placementalong the yield curve

Changes in theterm structure

In the present model, the term structure results from a setof key rates and intermediate linear interpolation. Changes

of the term structure are detailed on the changes of eachkey rate and their effect is contributed to each cashflowaffected.

Change in OAS The OAS (on total bond level) is the spread to be added tothe government spot rate curve in order to obtain the

bond’s actual market price. This spread may change over time and thus gives a contribution to the bond’s return.


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t1 + Dtt1 timeTa Tb

Discounting Factor

KRa

KRb

DKRb

DKRa

DFbegin

DFend

DFtermstr DFTime

Dt

Decomposition of Discounting Factors

OAS uretermstruct Timebeginend

DF DF DF DF DF ∆+∆+∆+=


17/19

· 17


OAS CF uretermstruct CF rolldownCF accretionCF

t t

begin

t

end

CF

returnreturnreturnreturn

DF CF

DF

CF

return

,,,,

1

)1(

)1(

1

1

+++=

−

+

+=

∆+

Algebraic manipulation results in additive decomposition of return

Calculation on level of each cashflow; capital weighted aggregation on bond position

and portfolio level

Correct overall return results on portfolio level

Re-calculation would be required at each time of transactions (purchases/sales)

since cashflow profile changes


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19/19

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Performance Analysis Cumulated

Return 2002

-1.00

-

1.00

2.00

3.00

4.00

5.00

6.00

7.00

8.00

9.00

10.00

T o t al

A c c r e t i on

R ol l d own

T er m T o t al

OA S C

h an g e

T er m ON

T er m 3 M

T er m 6 M

T er m 1 Y

T er m 2 Y

T er m 3 Y

T er m 4 Y

T er m 5 Y

T er m 6 Y

T er m 7 Y

T er m 8 Y

T er m 9 Y

T er m 1 0 Y

T er m 1 5 Y

T er m 2 0 Y

T er m 2 5 Y

T er m 3 0 Y

Portfolio Benchmark

Documents

Performance Analysis for Fixed Income Portfolios