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?
% of variance
100
90
40
30
20
10
0
80
70
60
50
US UK JPN CAN GER FRA ITA
1st comp
2nd comp
3rd comp

What Do These Factors Look Like?
USA
1yr 2yr 3yr 4yr 5yr 7yr 10yr 15yr 20yr 30yr
1st Comp
2nd Comp
Maturity

What Do These Factors Look Like?
UK
1yr 2yr 3yr 4yr 5yr 7yr 10yr 15yr 20yr
Maturity
1st Comp
2nd Comp

What Do These Factors Look Like?
JPN
1yr 2yr 3yr 4yr 5yr 7yr 10yr 15yr 20yr
1st Comp
2nd Comp
Maturity

What Do These Factors Look Like?
CAN
1yr 2yr 3yr 4yr 5yr 7yr 10yr 15yr 20yr 30yr
Maturity
1st Comp
2nd Comp

What Do These Factors Look Like?
FRA
1yr 2yr 3yr 4yr 5yr 7yr 10yr 15yr 20yr 30yr
1st Comp
2nd Comp
Maturity

What Do These Factors Look Like?
GER
1yr 2yr 3yr 4yr 5yr 7yr 10yr 15yr 20yr 30yr
1st Comp
2nd Comp
Maturity

What Do These Factors Look Like?
ITA
1yr 2yr 3yr 4yr 5yr 7yr 10yr 15yr 20yr 30yr
1st Comp
2nd Comp
Maturity

Worldwide Principal Component
Analysis (US,UK,JPN,GER)
0.25
0.2
0.15
0.1
0.05
0
-0.05
1st Comp
2nd Comp.

% of Worldwide Movements in Term
Structure Explained by Factors
40
30
20
10
0
60
50
Components
1st comp.
2nd comp.
3rd comp.
4th comp.
5th comp.

Implications Continued...
APPROXIMATION of CHANGE IN BOND’S VALUE:

P
US
P

Dur
  r
US

P
Fn
P

Dur
  r
Fn
What’s the exposure of the foreign bond’s value to US rates?

P
Fn
P

Dur

 r
Fn
 r
US
  r
US
In other words, the % change in the foreign bond to a change in US rates is just the US bond change times 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., b )
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
UK JPN CAN FRA GER ITA
Beta

Sensitivities of Foreign Factor to
German Interest Rate Factor (i.e., b )
0.6
0.5
0.4
0.3
0.2
0.1
0
1
0.9
0.8
0.7
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
20
15
10
5
0
30
25
US UK JPN CAN FRA GER ITA
30-yr
1.5-yr

II. Currency Movements
• Introduction about bond price variation
• Facts about currency and interest rate comovements

Rates of Return on Zeroes
Consider a T-period zero in a foreign government bond.
What is it’s US $ rate of return?
R
$
Fn
( t , t

1 )
 d
T
Fn

1
( t

1 )
 d
T
Fn
( t )
S t
$

/
1
Fn
S t
$ / Fn
Taking logs of the above and rearranging gives us ln[ R
$
Fn
( t , t

1 )]
  ln[ d
T
Fn
( t , t

1 )]
  ln[ S
FN / $
( t , t

1 )]
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.

R
$
Fn

( Dur )
2  
2
 r
 
2

S

2
 dur
 
 r ,

S
Of course, if there is no exchange rate risk, we just get the usual result that the volatility of a bond is its duration 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
0.2
0.15
0.1
0.05
0
-0.05
-0.1
-0.15
-0.2
-0.25
-0.3
UK JPN CAN FRA GER ITA
Corr.

Volatility of Interest Rate Factor
Weekly in Basis Points
14
8
6
12
10
4
2
0
US UK JPN CAN FRA GER ITA
Vol. (bp)

Volatility of % Change in Fn./$ Exchange Rates
(Weekly % Terms)
0.025
0.02
0.015
0.01
0.005
0
UK JPN CAN FRA GER ITA
Vol.

Estimate of Volatility of US bond
& $-adjusted Foreign Bonds
0.03
0.025
0.02
0.015
0.01
0.005
0
US UK JPN CAN FRA GER ITA
Dur.=10
Dur.=5
Dur.=1

% of Volatility of $-adjusted Foreign
Bond Due to Currency Risk
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
UK JPN CAN FRA GER ITA
Dur.=10
Dur.=5
Dur.=1