International Financial Markets
Prices and Policies
Second Edition ©2001
Richard M. Levich
14B
&
International Asset Portfolios:
Bond Portfolios
Overview (B)
w Calculating Return and Risk in Foreign
Currency Bonds
è
Unhedged and Currency-Hedged Returns in US$
w Theory of Currency-Hedged Bonds
w Empirical Evidence on Return and Risk in
Global Bond Markets
è
Prof. Levich
The Efficient Frontier and Gains to International
Bond Portfolios
International Financial Markets
Chap 14 (A), p. 2
1
Return and Risk
in National Bond Markets
w In general, the return on a foreign bond, as
measured in US$ terms, has 3 components:
 Interest
income earned or accrued.
‚ The capital gain or loss on the bond, resulting from
the inverse relationship between interest rates and
bond prices.
ƒ The foreign exchange gain or loss, applied to the
above two items.
Prof. Levich
International Financial Markets
Chap 14 (A), p. 3
Calculating Unhedged Returns
in US$ Terms
Let Bt be the initial purchase price of the foreign
bond in foreign currency (FC) terms.
Let St be the spot exchange rate, in $/FC terms, on
the purchase date.
Then BtSt is the US$ purchase price of the bond.
Prof. Levich
International Financial Markets
Chap 14 (A), p. 4
2
Calculating Unhedged Returns
in US$ Terms
~
Let Bt+1 be the value of the bond after one month.
~
~
Bt +1 º Bt + D t +1 + Ct +1
where Bt = the initial bond price
~
D t +1 = the price change over the month
Ct +1 = accrued interest
~ ~
Then Bt +1St +1is the value of the bond after one
month in US$ terms.
Prof. Levich
International Financial Markets
Chap 14 (A), p. 5
Calculating Unhedged Returns
in US$ Terms
The continuous rate of return on the foreign bond
measured in US$ and on an unhedged basis is:
~
~ ~
~
Bt +1S t +1
Bt +1
St +1
~
~
~
) = ln(
) + ln(
) = BFC + SUS$,FC
R$,U = ln(
Bt S t
Bt
St
Note that the unhedged US$ return on the foreign
bond has two pieces:
~
return on the bond in FC terms (BFC), and
‚ the return on the foreign currency used to buy the
~
bond (SUS$,FC).
 the
Prof. Levich
International Financial Markets
Chap 14 (A), p. 6
3
Calculating Unhedged Returns
in US$ Terms
The variance of the returns on the foreign bond
reflects the variance of each term and the
covariance between the returns on the foreign
bond and the returns on spot foreign exchange:
~
~
~
~ ~
s 2 ( R$,U ) = s 2 ( BFC ) + s 2 ( S US$, FC ) + 2 Cov ( BFC ; S US$, FC )
Note that the covariance of bond returns and
currency returns can be either positive or
negative, and possibly changing over time.
Prof. Levich
International Financial Markets
Chap 14 (A), p. 7
Calculating Unhedged Returns
in US$ Terms
Combinations of Currency Market and Bond Market Returns
Currency Market Returns
Negative
Positive
Bond
Market
Returns
Prof. Levich
Negative
FC interest rates ­
Spot FX ¯
(A)
FC interest rates ­
Spot FX ­
(C)
Positive
FC interest rates ¯
Spot FX ¯
(D)
FC interest rates ¯
Spot FX ­
(B)
International Financial Markets
Chap 14 (A), p. 8
4
Theory of Currency Hedged Bonds
Attribute
Default risk
Interest rate
risk
FX risk
Exchange
control risk
Liquidity
10-Year
US Treasury
Bond
None
Yes, $-based
10-Year
German Bund
1-Month
Currency
Forward
Some
N/A
None
None
None
Yes, DMbased
Yes, DM/$
Very small
Yes, DM/$
N/A
German Bund
+ Forwards
(Synthetic $)
Some
Yes, DMbased
®® 0
Very small
Very high
Very high
Very high
Very high
• The interest rate risk of the U.S. Treasury security reflects those
determinants of interest rate risk in the U.S. Treasury market:
• The interest rate risk of the German government bond reflects
those determinants of interest rate risk in the German bond market:
• Claim: The interest rate risk of the synthetic dollar security
reflects those determinants of interest rate risk in the German
bond market.
Prof. Levich
International Financial Markets
Chap 14 (A), p. 9
The Expanded Opportunity Set of National Bond Markets
Currency Risk and Interest Rate Risk Dimensions
Currency Risk
United
States
Interest
EMU
Rate
Risk
Japan
US$
€
¥
U.S.
Treasury
Bond
U.S. T-Bond:
Currency
hedged to €
U.S. T-Bond:
Currency
hedged to ¥
German Bund:
Currency
hedged to $
German
Government
Bond (Bund)
German Bund:
Currency
hedged to ¥
JGB:
Currency
hedged to $
JGB:
Currency
hedged to €
Japanese
Government
Bond (JGB)
• Traditional portfolio leaves the investor exposed completely to US$ interest
rate risk as it reflects US monetary policy and macroeconomic performance.
• Expanded portfolio diversifies investor's exposure to interest rate risk as it
reflects monetary policy-making and macro performance in several countries.
Prof. Levich
International Financial Markets
Chap 14 (A), p. 10
5
Choosing a Currency-Hedging Strategy
w One possible hedging strategy is to sell all the
future coupon payments as well as the final
return of principal forward in exchange for
US$.
è
The return on this swapped-bond should be nearly
identical to a US$ bond of the same maturity.
w A less extreme strategy is to sell a one-month
forward currency contract for an amount equal
to next month’s estimated value of the bond
with accrued interest.
Prof. Levich
International Financial Markets
Chap 14 (A), p. 11
Calculating Hedged Returns
in US$ Terms
Let B^t+1 be the estimated value of the bond after
one month, with accrued interest.
Bˆ º B + Dˆ + C
t +1
t +1
t
where Bt
t +1
= the initial bond price
Dˆ t +1 = the estimated bond price change
Ct +1 = accrued interest
~
~
Then e~t +1 = Bt +1 - Bˆ t +1 = D t +1 - Dˆ t +1 is the price
prediction or hedging error.
Prof. Levich
International Financial Markets
Chap 14 (A), p. 12
6
Calculating Hedged Returns
in US$ Terms
The continuous rate of return on the currency
hedged foreign bond measured in US$ is:
Bˆ t +1 Ft + e~t +1St +1
Bˆ t +1
Ft
e~t +1St +1
~
R$, H = ln(
) = ln(
) + ln( ) + ln(1 +
)
Bt S t
Bt
St
Bˆ t +1 Ft
Then the return consists of:
 the
return from the predicted price change in the
bond in FC terms,
‚ the forward premium (or discount) on the foreign
currency used to buy the bond, and
ƒ the unpredicted price change in the bond that is
valued at a future uncertain spot exchange rate.
Prof. Levich
International Financial Markets
Chap 14 (A), p. 13
Risk of Currency-Hedged Returns
Re-stating the formula for currency-hedged returns:
Bˆt +1 Ft + eˆt +1St +1
Bˆ t +1
Ft
e~t +1St +1
~
R$, H = ln(
) = ln(
) + ln( ) + ln(1 +
)
Bt St
Bt
St
Bˆ t +1 Ft
w Under very general, plausible conditions
2 ~
2 ~
è Then s ( R
$, H ) < s ( R$,U )
w In the special case when the hedge is perfect:
~ = 0 and s 2 ( R~ ) = 0
è Then e
t +1
$, H
Prof. Levich
International Financial Markets
Chap 14 (A), p. 14
7
Performance of
Unhedged National Bond Markets & World Portfolios
January 1978 - September 1989
Portfolio
Return
U.S. dollar
10.1 %
Canadian dollar
10.4
German mark
8.9
Japanese yen
13.6
British pound
11.3
Swiss franc
6.4
Dutch guilder
9.4
French franc
9.5
Nondollar portfolio 11.3
(value weighted)
World portfolio
10.6
(value weighted)
World portfolio
10.0
(equal weighted)
Prof. Levich
Risk Return/Risk (Return-RF )/Risk
11.0 %
0.92
0.11
13.6
0.76
0.11
16.2
0.55
0.003
17.3
0.79
0.27
18.3
0.62
0.13
16.1
0.40
-0.15
15.3
0.61
0.04
14.2
0.67
0.05
13.8
0.82
0.18
10.2
1.04
0.16
12.0
0.83
0.10
International Financial Markets
Chap 14 (A), p. 15
Performance of
Currency-Hedged National Bond Markets & World Portfolios
January 1978 - September 1989
Portfolio
U.S. dollar
Canadian dollar
German mark
Japanese yen
British pound
Swiss franc
Dutch guilder
French franc
Global portfolio
(equal weighted)
Prof. Levich
Return
10.1 %
9.9
11.3
12.8
10.4
9.9
11.2
9.8
10.7
Risk Return/Risk (Return-RF )/Risk
11.0 %
0.92
0.11
11.5
0.86
0.09
5.8
1.95
0.42
6.4
2.00
0.62
10.4
1.00
0.15
4.1
2.41
0.26
5.7
1.96
0.41
5.9
1.66
0.16
5.5
1.95
International Financial Markets
0.34
Chap 14 (A), p. 16
8
Efficient Frontiers of
Unhedged and Currency-Hedged Global Bond Portfolios
Average Return (% per annum)
1977 - 1990
0.120
Global Portfolio
0.115
0.110
0.105
Global
Portfolio
Unhedged
Portfolios
0.100
0.095
0.090
Hedged
Portfolios
0.085
0.05
Dollar Portfolio
0.08
0.11
Risk: Standard Deviation of Returns
Prof. Levich
International Financial Markets
Chap 14 (A), p. 17
Summary
w International bonds exposure domestic investors to
è
è
Interest rate risk
Exchange rate risk
w Currency-hedged bonds create synthetic US$ bonds
è
è
è
Expand investor opportunity set
US$ securities with “foreign based” interest rate risk
Diversify investor’s exposure to “central banking” risk
w Empirical evidence shows gain in Return/Risk ratio in
currency hedged portfolios
è
è
è
Prof. Levich
What is the source of this gain? Is it costly to capture?
Will it exist in the future or decline? How to implement?
Active versus passive currency hedging strategies.
International Financial Markets
Chap 14 (A), p. 18
9