international fixed income topic iiia: stylized facts and their implications

International Fixed Income

Topic IIIA:Stylized Facts and Their

Implications

Outline

• Explaining the Term Structure• The Effect of Currency

Movements

I. Explaining Term Structure Movements

• What factors explain movements in the term structure across countries?

• Case study:– G7 countries

(US,UK,JPN,CAN,GER,ITA,FR)– 1996-1999– Weekly movements in zeroes of 1yr-

30yr maturities

Principal Components Analysis

• Find the principal component that explains most of the variation in term structure movements across the maturities.– How much does it explain?– Are there additional components– How correlated are these components

across countries?– How much does the U.S. explain of

movements in foreign term structures?

How Many Factors?

0102030405060708090

100

% of variance

US UK JPN CANGER FRA ITA

1st comp2nd comp3rd comp

What Do These Factors Look Like?

USA

1yr 2yr 3yr 4yr 5yr 7yr 10yr 15yr 20yr 30yr

Maturity

Wei

ght

1st Comp2nd Comp


UK

1yr 2yr 3yr 4yr 5yr 7yr 10yr 15yr 20yr

Maturity

Wei

ght

1st Comp2nd Comp


JPN

1yr 2yr 3yr 4yr 5yr 7yr 10yr 15yr 20yr

Maturity

Wei

ght

1st Comp2nd Comp


CAN


Maturity

Wei

ght

1st Comp2nd Comp


FRA


Maturity

Wei

ght

1st Comp2nd Comp


GER


Maturity

Wei

ght

1st Comp2nd Comp


ITA


Maturity

Wei

ght

1st Comp2nd Comp

Worldwide Principal Component Analysis (US,UK,JPN,GER)

-0.05

0

0.05

0.1

0.15

0.2

0.25U

S

US

US

UK

UK

JPN

JPN

GE

R

GE

R

GE

R

Wei

ghts

1st Comp2nd Comp.

% of Worldwide Movements in Term

Structure Explained by Factors

0

10

20

30

40

50

60

Components

1st comp.2nd comp.3rd comp.4th comp.5th comp.

Implications Continued...APPROXIMATION of CHANGE IN BOND’S VALUE:

USUS rDurP

P

Fn

Fn rDurP

P

What’s the exposure of the foreignbond’s value to US rates?

USUS

FnFn rr

rDur

P

P

In other words, the % change in the foreign bondto a change in US rates is just the US bond changetimes the sensitivity of foreign rates to US rates.

Implications of Factor Analysis

• Most of the movements in the term structure, e.g., 90%, can be explained by one factor.– Caution: Ignoring short-term rates

here and focusing on 1-30 yr zeroes.

• This factor looks like a parallel shift in rates. (The second less important factor looks like a steepening/flattening.)

Sensitivities of Foreign Factor to US Interest Rate Factor (i.e., )

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

UK JPN CAN FRA GER ITA

Beta

Sensitivities of Foreign Factor to German

Interest Rate Factor (i.e., )

00.10.20.30.40.50.60.70.80.9

1

UK JPN CAN FRA US ITA

Beta

Example

• Consider from earlier in class, the 1.5-year and 30-year zeroes with durations of 1.46 and 29.26, respectively.

• If these were the durations of the foreign bonds, and you had them in your portfolio, what does that say about their durations in your $ portfolio? (That is, your exposure to US rates, not currencies).

Durations of Foreign Bonds

0

5

10

15

20

25

30

US UK JPN CAN FRA GER ITA

30-yr1.5-yr

II. Currency Movements

• Introduction about bond price variation

• Facts about currency and interest rate co-movements

Rates of Return on Zeroes

Fnt

Fnt

FnT

FnTFn

S

S

td

tdttR

/$

/$11

$ )(

)1()1,(

Consider a T-period zero in a foreign government bond.What is it’s US $ rate of return?

Taking logs of the above and rearranging gives us

)]1,(ln[)]1,(ln[)]1,(ln[ $/$ ttSttdttR FNFn

TFn

This is approximately equal to:

[zero rate] - [dur x (r)] - %S(Fn/$)

Rates of Return: Summary

• The $ return on a foreign bond has three components:– It’s yield (e.g., coupon, or imputed yield)

in the foreign currency.– It’s duration component in the foreign

currency.– It’s exchange rate exposure.

• The first two components are always true, while the second is unique to international fixed income.

Rates of Return: Summary Continued...

• The risk associated with this return can be broken up into two pieces:– interest rate risk (i.e., duration and

maybe convexity) as the first component (i.e., the coupon) is fixed.

– exchange rate risk.SrSrR

durDurFn ,222 2)(

$

Of course, if there is no exchange rate risk, we justget the usual result that the volatility of a bond is itsduration times the volatility of rates.

Interest Rate & Currency Factoids

• Correlation between interest factor in foreign country and the F/$ exchange rate.

• Volatility of interest rate factor.• Volatility of % change in

exchange rate.

Correlation Between Foreign Interest Rate Factor and Exchange Rate Changes

-0.3-0.25-0.2

-0.15-0.1

-0.050

0.050.1

0.150.2


Corr.

Volatility of Interest Rate Factor

Weekly in Basis Points

0

2

4

6

8

10

12

14


Vol. (bp)

Volatility of % Change in Fn./$ Exchange Rates

(Weekly % Terms)

0

0.005

0.01

0.015

0.02

0.025


Vol.

Estimate of Volatility of US bond & $-adjusted

Foreign Bonds

0

0.005

0.01

0.015

0.02

0.025

0.03


Dur.=10Dur.=5Dur.=1

% of Volatility of $-adjusted Foreign Bond Due to Currency Risk

00.10.20.30.40.50.60.70.80.9

1


Dur.=10Dur.=5Dur.=1

international fixed income topic iiia: stylized facts and their implications

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