International Fixed Income Topic VA: Emerging Markets-Brady Bonds.
International Fixed Income
description
Transcript of International Fixed Income
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International Fixed Income
Topic IIIA:Stylized Facts and Their
Implications
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Outline• Explaining the Term Structure• The Effect of Currency
Movements
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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
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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?
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How Many Factors?
0102030405060708090
100
% of variance
US UK JPN CANGER FRA ITA
1st comp2nd comp3rd comp
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What Do These Factors Look Like?
USA
1yr 2yr 3yr 4yr 5yr 7yr 10yr 15yr 20yr 30yr
Maturity
Weig
ht 1st Comp2nd Comp
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What Do These Factors Look Like?
UK
1yr 2yr 3yr 4yr 5yr 7yr 10yr 15yr 20yr
Maturity
Weig
ht 1st Comp2nd Comp
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What Do These Factors Look Like?
JPN
1yr 2yr 3yr 4yr 5yr 7yr 10yr 15yr 20yr
Maturity
Weig
ht 1st Comp2nd Comp
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What Do These Factors Look Like?
CAN
1yr 2yr 3yr 4yr 5yr 7yr 10yr 15yr 20yr 30yr
Maturity
Weig
ht 1st Comp2nd Comp
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What Do These Factors Look Like?
FRA
1yr 2yr 3yr 4yr 5yr 7yr 10yr 15yr 20yr 30yr
Maturity
Weig
ht 1st Comp2nd Comp
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What Do These Factors Look Like?
GER
1yr 2yr 3yr 4yr 5yr 7yr 10yr 15yr 20yr 30yr
Maturity
Weig
ht 1st Comp2nd Comp
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What Do These Factors Look Like?
ITA
1yr 2yr 3yr 4yr 5yr 7yr 10yr 15yr 20yr 30yr
Maturity
Weig
ht 1st Comp2nd Comp
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Worldwide Principal Component Analysis (US,UK,JPN,GER)
-0.05
0
0.05
0.1
0.15
0.2
0.25US US US UK UK JPN
JPN
GER
GER
GER
Weig
hts
1st Comp2nd Comp.
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% 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.
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Implications Continued...APPROXIMATION of CHANGE IN BOND’S VALUE:
USUS rDurPP
FnFn rDurPP
What’s the exposure of the foreignbond’s value to US rates?
USUS
FnFn rrrDur
PP
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.
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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.)
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Sensitivities of Foreign Factor to US Interest Rate Factor (i.e., )
00.10.20.30.40.50.60.70.80.9
UK JPN CAN FRA GER ITA
Beta
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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
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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).
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Durations of Foreign Bonds
0
5
10
15
20
25
30
US UK JPN CAN FRA GER ITA
30-yr1.5-yr
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II. Currency Movements• Introduction about bond price
variation• Facts about currency and
interest rate co-movements
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Rates of Return on Zeroes
Fnt
Fnt
FnT
FnTFn
SS
tdtdttR /$
/$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/$)
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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.
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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.
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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.
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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.
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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)
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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.
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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
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% of Volatility of $-adjusted Foreign Bond Due to Currency Risk
00.10.20.30.40.50.60.70.80.9
1
UK JPN CAN FRA GER ITA
Dur.=10Dur.=5Dur.=1