International Fixed Income Topic IIIA: Stylized Facts and Their Implications
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
What Do These Factors Look Like?
UK
1yr 2yr 3yr 4yr 5yr 7yr 10yr 15yr 20yr
Maturity
Wei
ght
1st Comp2nd Comp
What Do These Factors Look Like?
JPN
1yr 2yr 3yr 4yr 5yr 7yr 10yr 15yr 20yr
Maturity
Wei
ght
1st Comp2nd Comp
What Do These Factors Look Like?
CAN
1yr 2yr 3yr 4yr 5yr 7yr 10yr 15yr 20yr 30yr
Maturity
Wei
ght
1st Comp2nd Comp
What Do These Factors Look Like?
FRA
1yr 2yr 3yr 4yr 5yr 7yr 10yr 15yr 20yr 30yr
Maturity
Wei
ght
1st Comp2nd Comp
What Do These Factors Look Like?
GER
1yr 2yr 3yr 4yr 5yr 7yr 10yr 15yr 20yr 30yr
Maturity
Wei
ght
1st Comp2nd Comp
What Do These Factors Look Like?
ITA
1yr 2yr 3yr 4yr 5yr 7yr 10yr 15yr 20yr 30yr
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).
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
UK JPN CAN FRA GER ITA
Corr.
Volatility of Interest Rate Factor
Weekly in Basis Points
0
2
4
6
8
10
12
14
US UK JPN CAN FRA GER ITA
Vol. (bp)
Volatility of % Change in Fn./$ Exchange Rates
(Weekly % Terms)
0
0.005
0.01
0.015
0.02
0.025
UK JPN CAN FRA GER ITA
Vol.
Estimate of Volatility of US bond & $-adjusted
Foreign Bonds
0
0.005
0.01
0.015
0.02
0.025
0.03
US UK JPN CAN FRA GER ITA
Dur.=10Dur.=5Dur.=1